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Penn State University
1.
Todt, Heiko.
Asymptotics of partition functions
.
Degree: 2011, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/12413 
► First an overview of important results and techniques for asymptotics of partition functions will be given. Two important theorems, one by Meinardus, the other one…
(more)
▼ First an overview of important results and techniques for
asymptotics of partition functions will be given. Two important theorems, one by Meinardus, the other one by Ingham, will be discussed in more detail, since the main theorem of this thesis is closely related to them. After the proof of the main theorem, we will then apply it to certain partition ideals of order 1. The final chapter gives a new proof for an asymptotic formula for partitions into distinct parts.
Advisors/Committee Members: George E Andrews, Dissertation Advisor/Co-Advisor, George E Andrews, Committee Chair/Co-Chair, Ae Ja Yee, Committee Member, James Allen Sellers, Committee Member, Robert Charles Vaughan, Committee Member, Donald Richards, Committee Member.
Subjects/Keywords: asymptotics; partitions
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APA (6th Edition):
Todt, H. (2011). Asymptotics of partition functions
. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/12413
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Todt, Heiko. “Asymptotics of partition functions
.” 2011. Thesis, Penn State University. Accessed March 07, 2021.
https://submit-etda.libraries.psu.edu/catalog/12413.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Todt, Heiko. “Asymptotics of partition functions
.” 2011. Web. 07 Mar 2021.
Vancouver:
Todt H. Asymptotics of partition functions
. [Internet] [Thesis]. Penn State University; 2011. [cited 2021 Mar 07].
Available from: https://submit-etda.libraries.psu.edu/catalog/12413.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Todt H. Asymptotics of partition functions
. [Thesis]. Penn State University; 2011. Available from: https://submit-etda.libraries.psu.edu/catalog/12413
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Edinburgh
2.
Ogilvie, Karen Anna.
Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter.
Degree: PhD, 2016, University of Edinburgh
URL: http://hdl.handle.net/1842/25390
► We are interested in rigorous asymptotic results pertaining to three different differential equations which lie in the Heun class (see [1] §31). The Heun class…
(more)
▼ We are interested in rigorous asymptotic results pertaining to three different differential equations which lie in the Heun class (see [1] §31). The Heun class contains those ordinary linear second-order differential equations with four regular singularities. We first investigate the Lamé equation d²w/dz² +(h − v(v + 1)k² sn²(z, k)) w = 0, z ∈ [−K,K], where 0 < k < 1, sn(z, k) is a Jacobi elliptic function, and K = ∫ 1 0 dz/√(1 − z²)(1 − k²z²) is the complete elliptic integral of the first kind. We obtain rigorous uniform asymptotic approximations complete with error bounds for the Lamé functions Ecm/v (z, k²) and Esm/v+¹ (z, k²) for z ∈ [0,K] and m ∈ N0, and rigorous approximations for their respective eigenvalues am/v and bm/v+¹, as v →∞. Then we obtain asymptotic expansions for the Lamé functions complete with error bounds, which hold only in a shrinking neighbourhood of the origin as v →∞. We also find corresponding expansions for the eigenvalues complete with order estimates for the errors. Then finally we give rigorous result for the exponentially small difference between the eigenvalues bm/v+¹ and am/v as v →∞. Second we investigate Mathieu’s equation d²w/dz² + (λ − 2h² cos 2z) w = 0, z ∈ [0, π], and obtain analogous results for the Mathieu functions cem(h, z) and sem+1(h, z) and their corresponding eigenvalues am and bm+1 for m ∈ N0 as h→∞, which are derived from those of Lamé ’s equation by considering a limiting case. Lastly we investigate the spheroidal wave equation d /dz ((1 − z²) dw/dz) + ( λ+ γ²(1 − z²) − μ²/1 − z²) w = 0, z ∈ [−1, 1], and consider separately the cases where γ² > 0 and γ² < 0. In the first case we give similar results to those previously for the prolate spheroidal wave functions Ps(z, γ²) and their corresponding eigenvalues λm/n for m, n ∈ N0 and n ≥ m as γ² →∞, and in the second we discuss the gap in theory which makes it difficult to obtain rigorous results as γ² → -∞, and how one would bridge this gap to obtain these.
Subjects/Keywords: 515; asymptotics
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APA (6th Edition):
Ogilvie, K. A. (2016). Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/25390
Chicago Manual of Style (16th Edition):
Ogilvie, Karen Anna. “Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter.” 2016. Doctoral Dissertation, University of Edinburgh. Accessed March 07, 2021.
http://hdl.handle.net/1842/25390.
MLA Handbook (7th Edition):
Ogilvie, Karen Anna. “Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter.” 2016. Web. 07 Mar 2021.
Vancouver:
Ogilvie KA. Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter. [Internet] [Doctoral dissertation]. University of Edinburgh; 2016. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1842/25390.
Council of Science Editors:
Ogilvie KA. Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter. [Doctoral Dissertation]. University of Edinburgh; 2016. Available from: http://hdl.handle.net/1842/25390
University of Edinburgh
3.
Foley, Christopher Neal.
Exponential asymptotics in wave propagation problems.
Degree: PhD, 2013, University of Edinburgh
URL: http://hdl.handle.net/1842/8838
► We use the methods of exponential asymptotics to study the solutions of a one dimensional wave equation with a non-constant wave speed c(x,t) modelling, for…
(more)
▼ We use the methods of exponential asymptotics to study the solutions of a one dimensional wave equation with a non-constant wave speed c(x,t) modelling, for example, a slowly varying spatio-temporal topography. The equation reads htt(x,t) = (c2(x,t)hx(x,t))x' (1) where the subscripts denote differentiation w.r.t. the parameters x and t respectively. We focus on the exponentially small reflected wave that appears as a result of a Stokes phenomenon associated with the complex singularities of the speed. This part of the solution is not captured by the standard WKBJ (geometric optics) approach. We first revisit the time-independent propagation problem using resurgent analysis. Our results recover those obtained using Meyers integral-equation approach or the Kruskal-Segur (K-S) method. We then consider the time-dependent propagation of a wavepacket, assuming increasingly general models for the wave speed: time independent, c(x), and separable, c1(x)c2(t). We also discuss the situation when the wave speed is an arbitrary function, c(x,t), with the caveat that the analysis of this setup has yet to be completed. We propose several methods for the computation of the reflected wavepacket. An integral transform method, using the Dunford integral, provides the solution in the time independent case. A second method exploits resurgence: we calculate the Stokes multiplier by inspecting the late terms of the dominant asymptotic expansion. In addition, we explore the benefits of an integral transform that relates the coefficients of the dominant solution in the time-dependent problem to the coefficients of the dominant solution in the time-independent problem. A third method is a partial differential equation extension of the K-S complex matching approach, containing details of resurgent analysis. We confirm our asymptotic predictions against results obtained from numerical integration.
Subjects/Keywords: 515; exponential asymptotics
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APA (6th Edition):
Foley, C. N. (2013). Exponential asymptotics in wave propagation problems. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/8838
Chicago Manual of Style (16th Edition):
Foley, Christopher Neal. “Exponential asymptotics in wave propagation problems.” 2013. Doctoral Dissertation, University of Edinburgh. Accessed March 07, 2021.
http://hdl.handle.net/1842/8838.
MLA Handbook (7th Edition):
Foley, Christopher Neal. “Exponential asymptotics in wave propagation problems.” 2013. Web. 07 Mar 2021.
Vancouver:
Foley CN. Exponential asymptotics in wave propagation problems. [Internet] [Doctoral dissertation]. University of Edinburgh; 2013. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1842/8838.
Council of Science Editors:
Foley CN. Exponential asymptotics in wave propagation problems. [Doctoral Dissertation]. University of Edinburgh; 2013. Available from: http://hdl.handle.net/1842/8838
Cornell University
4.
Li, Yingxing.
Aspects Of Penalized Splines.
Degree: PhD, Statistics, 2011, Cornell University
URL: http://hdl.handle.net/1813/33653
► Penalized splines approach has very important applications in statistics. The idea is to fit the unknown regression mean using a high-dimensional spline basis, subject to…
(more)
▼ Penalized splines approach has very important applications in statistics. The idea is to fit the unknown regression mean using a high-dimensional spline basis,
subject to penalization on the roughness. Such an approach avoids the stringency of a parametric model and enables a considerable reduction in computational cost without a loss of statistical precision. Moreover, the idea can also be connected with ridge regression and mixed models, thus allowing more flexible handling of longitudinal and spatial correlation. This thesis focuses on nonparametric and semiparametric estimation and inference using penalized splines. First, we consider the penalized splines approach proposed by Eilers and Marx (1996), which is also called P-splines approach. We derive its asymptotic property when the number of spline basis increases as the sample size does. For both the univariate model and the additive models, we establish the asymptotic distribution of the estimators and give simple expressions for the asymptotic mean and variance. Such an asymptotic theory allows P-splines estimators to be compared theoretically with other nonparametric estimators and offers guidance for practitioners when considering the choice of the penalty and basis functions. Next, we turn to the global inferential problems for functional data. We model the population mean function using polynomial splines. By utilizing the mixed model based penalized splines approach, we treat some of the spline coefficients as random effects with a single variance component and relate hy- potheses of interest to tests with this variance component being zero. To take into account the dependent structure or within
subject correlation, we propose a pseudo likelihood test statistic and derive its null distribution. This work extends existing results on pseudo likelihood by allowing the use of nonparametric smoothing (usually with a slower convergence rate). Its effectiveness is demonstrated via simulations and the empirical application from the Sleep Health Heart Study.
Advisors/Committee Members: Ruppert, David (chair), Booth, James (committee member), Hooker, Giles J. (committee member).
Subjects/Keywords: P-splines; asymptotics; global inference
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APA (6th Edition):
Li, Y. (2011). Aspects Of Penalized Splines. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/33653
Chicago Manual of Style (16th Edition):
Li, Yingxing. “Aspects Of Penalized Splines.” 2011. Doctoral Dissertation, Cornell University. Accessed March 07, 2021.
http://hdl.handle.net/1813/33653.
MLA Handbook (7th Edition):
Li, Yingxing. “Aspects Of Penalized Splines.” 2011. Web. 07 Mar 2021.
Vancouver:
Li Y. Aspects Of Penalized Splines. [Internet] [Doctoral dissertation]. Cornell University; 2011. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1813/33653.
Council of Science Editors:
Li Y. Aspects Of Penalized Splines. [Doctoral Dissertation]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/33653
Duke University
5.
Teguia, Alberto Mokak.
Stochastic Microlensing: Mathematical Theory and Applications
.
Degree: 2011, Duke University
URL: http://hdl.handle.net/10161/3875
► Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory…
(more)
▼ Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time delay functions' random critical sets. Next we study stochastic microlensing in two distinct random microlensing scenarios: The uniform stars' distribution with constant mass spectrum and the spatial stars' distribution with general mass spectrum. For each scenario, we determine exact and asymptotic (in the large number of point masses limit) stochastic properties of the random time delay functions and associated random lensing maps and random shear tensors, including their moments and asymptotic density functions. We use these results to study certain random observables, such as random fixed lensed images, random bending angles, and random magnifications. These results are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing. Continuing our development of a mathematical theory of stochastic microlensing, we study the stochastic version of the Image Counting Problem, first considered in the non-random setting by Einstein and generalized by Petters. In particular, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images for a general random lensing scenario. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to the uniform stars' distribution random microlensing scenario, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. Finally, we outline a framework for the study of stochastic microlensing in the neighbourhood of lensed images. This framework is related to the study of the local geometry of a random surface. In our case, the surface is non-Gaussian, and therefore standard literature on the
subject does not apply. We explore the case of a random gravitational field caused by a random star.
Advisors/Committee Members: Petters, Arlie O (advisor).
Subjects/Keywords: Mathematics;
Physics;
Asymptotics;
Microlensing;
Probability
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APA ·
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APA (6th Edition):
Teguia, A. M. (2011). Stochastic Microlensing: Mathematical Theory and Applications
. (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/3875
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Teguia, Alberto Mokak. “Stochastic Microlensing: Mathematical Theory and Applications
.” 2011. Thesis, Duke University. Accessed March 07, 2021.
http://hdl.handle.net/10161/3875.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Teguia, Alberto Mokak. “Stochastic Microlensing: Mathematical Theory and Applications
.” 2011. Web. 07 Mar 2021.
Vancouver:
Teguia AM. Stochastic Microlensing: Mathematical Theory and Applications
. [Internet] [Thesis]. Duke University; 2011. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/10161/3875.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Teguia AM. Stochastic Microlensing: Mathematical Theory and Applications
. [Thesis]. Duke University; 2011. Available from: http://hdl.handle.net/10161/3875
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Sydney
6.
Twiton, Michael.
Analysis of Singular Solutions of Certain Painlevé Equations
.
Degree: 2018, University of Sydney
URL: http://hdl.handle.net/2123/18206
► The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found…
(more)
▼ The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found numerous applications in mathematics and physics. The solutions of the Painlevé equations are, in most cases, highly transcendental and hence cannot be expressed in closed form. Asymptotic methods do better, and can establish the behaviour of some of the solutions of the Painlevé equations in the neighbourhood of a singularity, such as the point at infinity. Although the quantitative nature of these neighbourhoods is not initially implied from the asymptotic analysis, some regularity results exist for some of the Painlevé equations. In this research, we will present such results for some of the remaining Painlevé equations. In particular, we will provide concrete estimates of the intervals of analyticity of a one-parameter family of solutions of the second Painlevé equation, and estimate the domain of analyticity of a “triply-truncated” solution of the fourth Painlevé equation. In addition we will also deduce the existence of solutions with particular asymptotic behaviour for the discrete Painlevé equations, which are discrete integrable nonlinear systems.
Subjects/Keywords: nonlinear;
systems;
painlevé;
asymptotics
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APA ·
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APA (6th Edition):
Twiton, M. (2018). Analysis of Singular Solutions of Certain Painlevé Equations
. (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/18206
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Twiton, Michael. “Analysis of Singular Solutions of Certain Painlevé Equations
.” 2018. Thesis, University of Sydney. Accessed March 07, 2021.
http://hdl.handle.net/2123/18206.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Twiton, Michael. “Analysis of Singular Solutions of Certain Painlevé Equations
.” 2018. Web. 07 Mar 2021.
Vancouver:
Twiton M. Analysis of Singular Solutions of Certain Painlevé Equations
. [Internet] [Thesis]. University of Sydney; 2018. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/2123/18206.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Twiton M. Analysis of Singular Solutions of Certain Painlevé Equations
. [Thesis]. University of Sydney; 2018. Available from: http://hdl.handle.net/2123/18206
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
7.
Kesavan, Aruna.
Asymptotic structure of space-time with a positive cosmological constant.
Degree: 2016, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/f4752g72m
► In general relativity a satisfactory framework for describing isolated systems exists when the cosmological constant Λ is zero. The detailed analysis of the asymptotic structure…
(more)
▼ In general relativity a satisfactory framework for describing isolated systems exists when the cosmological constant Λ is zero. The detailed analysis of the asymptotic structure of the gravitational field,
which constitutes the framework of asymptotic flatness, lays the foundation for research in diverse areas in gravitational science. However, the framework is incomplete in two respects. First, asymptotic flatness provides well-defined expressions for physical observables such as energy and momentum as `charges' of asymptotic symmetries at null infinity, \scri
+. But the asymptotic symmetry group, called the Bondi-Metzner-Sachs group is infinite-dimensional and a tensorial expression for the `charge' integral of an arbitrary BMS element is missing. We address this issue by providing a charge formula which
is a 2-sphere integral over fields local to the 2-sphere and refers to no extraneous structure.
The second, and more significant shortcoming is that observations have established that Λ is not zero but positive in our universe. Can the framework describing isolated systems and their gravitational radiation be extended to incorporate this fact? In this dissertation we show that, unfortunately,
the standard framework does not extend from the Λ =0 case to the Λ >0 case in a physically useful manner. In particular, we do not have an invariant notion of gravitational waves in the non-linear regime, nor an analog of the Bondi `news tensor', nor positive energy theorems. In addition, we argue that the stronger boundary condition of conformal flatness of intrinsic metric on \scri
+, which reduces the asymptotic symmetry group from \Diff to the de Sitter group, is insufficient to characterize gravitational fluxes and is physically unreasonable.
To obtain guidance for the full non-linear theory with Λ > 0, linearized gravitational waves in de Sitter space-time are analyzed in detail. i) We show explicitly that conformal flatness of the boundary removes half the degrees of freedom of the gravitational field by hand and is not justified by physical considerations; ii) We obtain gauge invariant expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at \scrip; iii) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit Λ → 0 is discontinuous (since, in particular, \scrip changes its space-like character to null in the limit); iv) We obtain a generalization of Einstein's 1918 quadrupole formula for power emission by a linearized source to include a positive Λ; and, finally v) We show that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy.
Advisors/Committee Members: Abhay Vasant Ashtekar, Dissertation Advisor/Co-Advisor, Abhay Vasant Ashtekar, Committee Chair/Co-Chair, Sarah Elizabeth Shandera, Committee Member, Eugenio Bianchi, Committee Member, Steinn Sigurdsson, Outside Member.
Subjects/Keywords: Asymptotics; Dark Energy; Gravitational Radiation; Cosmological Constant
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APA (6th Edition):
Kesavan, A. (2016). Asymptotic structure of space-time with a positive cosmological constant. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/f4752g72m
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Kesavan, Aruna. “Asymptotic structure of space-time with a positive cosmological constant.” 2016. Thesis, Penn State University. Accessed March 07, 2021.
https://submit-etda.libraries.psu.edu/catalog/f4752g72m.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kesavan, Aruna. “Asymptotic structure of space-time with a positive cosmological constant.” 2016. Web. 07 Mar 2021.
Vancouver:
Kesavan A. Asymptotic structure of space-time with a positive cosmological constant. [Internet] [Thesis]. Penn State University; 2016. [cited 2021 Mar 07].
Available from: https://submit-etda.libraries.psu.edu/catalog/f4752g72m.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kesavan A. Asymptotic structure of space-time with a positive cosmological constant. [Thesis]. Penn State University; 2016. Available from: https://submit-etda.libraries.psu.edu/catalog/f4752g72m
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Queensland University of Technology
8.
Lustri, Christopher Jessy.
Exponential asymptotics with multiple stokes lines.
Degree: 2009, Queensland University of Technology
URL: https://eprints.qut.edu.au/33237/
► When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they…
(more)
▼ When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.
Subjects/Keywords: exponential asymptotics; multiple stokes lines; applied mathematics
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Manager
APA (6th Edition):
Lustri, C. J. (2009). Exponential asymptotics with multiple stokes lines. (Thesis). Queensland University of Technology. Retrieved from https://eprints.qut.edu.au/33237/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Lustri, Christopher Jessy. “Exponential asymptotics with multiple stokes lines.” 2009. Thesis, Queensland University of Technology. Accessed March 07, 2021.
https://eprints.qut.edu.au/33237/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lustri, Christopher Jessy. “Exponential asymptotics with multiple stokes lines.” 2009. Web. 07 Mar 2021.
Vancouver:
Lustri CJ. Exponential asymptotics with multiple stokes lines. [Internet] [Thesis]. Queensland University of Technology; 2009. [cited 2021 Mar 07].
Available from: https://eprints.qut.edu.au/33237/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lustri CJ. Exponential asymptotics with multiple stokes lines. [Thesis]. Queensland University of Technology; 2009. Available from: https://eprints.qut.edu.au/33237/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
New Jersey Institute of Technology
9.
Fong, Daniel.
Mathematical models of combustion at high pressure.
Degree: PhD, Mathematical Sciences, 2012, New Jersey Institute of Technology
URL: https://digitalcommons.njit.edu/dissertations/320
► In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the…
(more)
▼ In this dissertation, we develop new mathematical theories of flame propagation that are valid at elevated, or extreme, pressures. Of particular interest is the regime of burning in which the pressure exceeds the critical pressure of the species undergoing chemical reaction. Fluids and flames are known to behave differently under these extreme conditions as opposed to atmospheric pressure. The focus of this dissertation is to investigate these differences by deriving reduced models that contain the unique features.
In the first part of this dissertation, we analyze the structure of laminar diffusion flames at high pressure in the limit of large activation energy for the particular configuration of a steady flame in counterflow. We consider a dense fluid in which normal Fickian diffusion of the fuel is limited, and thermal diffusion, i.e., the Soret effect, is the dominant mechanism for fuel mass transport. Temperature and species profiles, as well as flame temperature and location, are determined as a function of Damköhler number and Soret diffusion coefficient. In particular, we find that oxidant is entirely consumed by the flame, while some fuel leaks through. For light fuels, the fuel profile is found to have a local peak on the oxidant side as a result of thermal diffusion. Our analysis includes a description of extinction phenomenon, including explicit criteria in terms of the Soret diffusion coefficient, ratio of temperature of the two streams, and the Damköhler number at extinction.
In the second part of this dissertation, we derive an asymptotic theory of laminar premixed flames in high density fluids in the limit of large activation energy. The model is intended to provide insights into the structure and dynamics of deflagration waves in high pressure, dense fluids where normal Fickian diffusion is limited. In such cases, particularly under conditions exceeding the thermodynamic critical point of the fluid, the primary mode of species transport is through thermal diffusion, i.e., the Soret effect. Such a model for diffusive transport is considered, and we derive a model with an explicit dependence on the Soret effect for a one-step overall reaction. The density is assumed sufficiently high to adopt a constant density formulation. The local reaction-diffusion structure is found to be fundamentally different from that of an ideal gas with Fickian diffusion, which results in new conditions relating the equations for thermal and mass transport in the bulk flow. The model is used to investigate the basic structure of planar flames, as well as their stability. Stability boundaries are identified that mark the transition from planar to either steady, spatially periodic structures, or time-dependent modes of propagation. The combined effects of the Soret diffusion coefficient and Lewis number are discussed. Furthermore, a weakly nonlinear analysis of the derived model is carried out, resulting in a modified Kuramoto-Sivashinsky (K-S) equation, accounting for effects of Soret Diffusion. Linear…
Advisors/Committee Members: John Kenneth Bechtold, Shahriar Afkhami, Michael R. Booty.
Subjects/Keywords: Combustion; Mathematical modeling; Reacting flows; Asymptotics; Mathematics
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APA (6th Edition):
Fong, D. (2012). Mathematical models of combustion at high pressure. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/320
Chicago Manual of Style (16th Edition):
Fong, Daniel. “Mathematical models of combustion at high pressure.” 2012. Doctoral Dissertation, New Jersey Institute of Technology. Accessed March 07, 2021.
https://digitalcommons.njit.edu/dissertations/320.
MLA Handbook (7th Edition):
Fong, Daniel. “Mathematical models of combustion at high pressure.” 2012. Web. 07 Mar 2021.
Vancouver:
Fong D. Mathematical models of combustion at high pressure. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2012. [cited 2021 Mar 07].
Available from: https://digitalcommons.njit.edu/dissertations/320.
Council of Science Editors:
Fong D. Mathematical models of combustion at high pressure. [Doctoral Dissertation]. New Jersey Institute of Technology; 2012. Available from: https://digitalcommons.njit.edu/dissertations/320
Louisiana State University
10.
Mihai, Claudiu.
Asymptotic Laplace transforms.
Degree: PhD, Applied Mathematics, 2004, Louisiana State University
URL: etd-11052004-083332
;
https://digitalcommons.lsu.edu/gradschool_dissertations/3941
► In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus…
(more)
▼ In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus methods. The approach explored here suggests an interpretation of the Heaviside operator {cdot} based on the "Asymptotic Laplace Transform." The asymptotic approach presented here is based on recent work by G. Lumer and F. Neubrander on the subject. In particular, we investigate the two competing definitions of the asymptotic Laplace transform used in their works, and add a third one which we suggest is more natural and convenient than the earlier ones given. We compute the asymptotic Laplace transforms of the functions tmapsto etn for nin N and we show that elements in the same asymptotic class have the same asymptotic expansion at infty. In particular, we present a version of Watson's Lemma for the asymptotic Laplace transforms.
Subjects/Keywords: Laplace transforms; asymptotics
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APA (6th Edition):
Mihai, C. (2004). Asymptotic Laplace transforms. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-11052004-083332 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3941
Chicago Manual of Style (16th Edition):
Mihai, Claudiu. “Asymptotic Laplace transforms.” 2004. Doctoral Dissertation, Louisiana State University. Accessed March 07, 2021.
etd-11052004-083332 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3941.
MLA Handbook (7th Edition):
Mihai, Claudiu. “Asymptotic Laplace transforms.” 2004. Web. 07 Mar 2021.
Vancouver:
Mihai C. Asymptotic Laplace transforms. [Internet] [Doctoral dissertation]. Louisiana State University; 2004. [cited 2021 Mar 07].
Available from: etd-11052004-083332 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3941.
Council of Science Editors:
Mihai C. Asymptotic Laplace transforms. [Doctoral Dissertation]. Louisiana State University; 2004. Available from: etd-11052004-083332 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3941
Virginia Tech
11.
Toloza, Julio Hugo.
Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues.
Degree: PhD, Physics, 2002, Virginia Tech
URL: http://hdl.handle.net/10919/30072
► We study the behavior of truncated Rayleigh-Schröodinger series for the low-lying eigenvalues of the time-independent Schröodinger equation, when the Planck's constant is considered in the…
(more)
▼ We study the behavior of truncated Rayleigh-Schröodinger series for the low-lying eigenvalues of the time-independent Schröodinger equation, when the Planck's constant is considered in the semiclassical limit.
Under certain hypotheses on the potential energy, we prove that, for any given small value of the Planck's constant, there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and actual eigenvalue is smaller than an exponentially small function of the Planck's constant. We also prove the analogous results concerning the eigenfunctions.
Advisors/Committee Members: Hagedorn, George A. (committeechair), Kohler, Werner E. (committee member), Schmittmann, Beate (committee member), Klaus, Martin (committee member), Chang, Lay Nam (committeecochair).
Subjects/Keywords: exponentially accurate asymptotics
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APA (6th Edition):
Toloza, J. H. (2002). Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/30072
Chicago Manual of Style (16th Edition):
Toloza, Julio Hugo. “Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues.” 2002. Doctoral Dissertation, Virginia Tech. Accessed March 07, 2021.
http://hdl.handle.net/10919/30072.
MLA Handbook (7th Edition):
Toloza, Julio Hugo. “Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues.” 2002. Web. 07 Mar 2021.
Vancouver:
Toloza JH. Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues. [Internet] [Doctoral dissertation]. Virginia Tech; 2002. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/10919/30072.
Council of Science Editors:
Toloza JH. Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues. [Doctoral Dissertation]. Virginia Tech; 2002. Available from: http://hdl.handle.net/10919/30072
University of Sydney
12.
Luu, Steven.
Exponential asymptotics for discrete Painlevé equations
.
Degree: 2018, University of Sydney
URL: http://hdl.handle.net/2123/18284
► In this thesis we study Stokes phenomena behaviour present in the solutions of both additive and multiplicative difference equations. Specifically, we undertake an asymptotic study…
(more)
▼ In this thesis we study Stokes phenomena behaviour present in the solutions of both additive and multiplicative difference equations. Specifically, we undertake an asymptotic study of the second discrete Painlevé equation (dPII) as the independent variable approaches infinity, and consider the asymptotic behaviour of solutions of the q-Airy equation and the first q-Painlevé equation in the limits q□(→┴ ) 1 and n□(→┴ ) ∞. Exponential asymptotic methods are used to investigate Stokes phenomena and obtain uniform asymptotic expansions of solutions of these equations. In the first part of this thesis, we obtain two types of asymptotic expansions which describe vanishing and non-vanishing type solution behaviour of dPII. In particular, we show that both types of solution behaviour can be expressed as the sum of an optimally-truncated asymptotic series and an exponentially subdominant correction term. We then determine the Stokes structure and investigate Stokes behaviour present in these solutions. From this information we show that the asymptotic expansions contain one free parameter hidden beyond-all-orders and determine regions of the complex plane in which these asymptotic descriptions are valid. Furthermore, we deduce special asymptotic solutions which are valid in extended regions and draw parallels between these asymptotic solutions to the tronquée and tri-tronquée solutions of the second Painlevé equation. In the second part of this thesis, we then extend the exponential asymptotic method to q-difference equations. In our analysis of both the q-Airy and first q-Painlevé equations, we find that the Stokes structure is described by curves referred to as q-spirals. As a consequence, we discover that the Stokes structure for solutions of q-difference equations separate the complex plane into sectorial regions bounded by arcs of spirals rather than traditional rays.
Subjects/Keywords: Painlevé;
nonlinear;
asymptotics;
exponential;
Stokes Phenomena;
difference
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APA ·
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Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Luu, S. (2018). Exponential asymptotics for discrete Painlevé equations
. (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/18284
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Luu, Steven. “Exponential asymptotics for discrete Painlevé equations
.” 2018. Thesis, University of Sydney. Accessed March 07, 2021.
http://hdl.handle.net/2123/18284.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Luu, Steven. “Exponential asymptotics for discrete Painlevé equations
.” 2018. Web. 07 Mar 2021.
Vancouver:
Luu S. Exponential asymptotics for discrete Painlevé equations
. [Internet] [Thesis]. University of Sydney; 2018. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/2123/18284.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Luu S. Exponential asymptotics for discrete Painlevé equations
. [Thesis]. University of Sydney; 2018. Available from: http://hdl.handle.net/2123/18284
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Arizona State University
13.
Shapiro, Bruce G.
Computational Methods for Kinetic Reaction Systems.
Degree: Applied Mathematics, 2020, Arizona State University
URL: http://repository.asu.edu/items/57206
► This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar…
(more)
▼ This work is concerned with the study and numerical
solution of large reaction diffusion systems with applications to
the simulation of degradation effects in solar cells. A discussion
of the basics of solar cells including the function of solar cells,
the degradation of energy efficiency that happens over time,
defects that affect solar cell efficiency and specific defects that
can be modeled with a reaction diffusion system are included. Also
included is a simple model equation of a solar cell. The basics of
stoichiometry theory, how it applies to kinetic reaction systems,
and some conservation properties are introduced. A model that
considers the migration of defects in addition to the reaction
processes is considered. A discussion of asymptotics and how it
relates to the numerical simulation of the lifetime of solar cells
is included. A reduced solution is considered and a presentation of
a numerical comparison of the reduced solution with the full
solution on a simple test problem is included. Operator splitting
techniques are introduced and discussed. Asymptotically preserving
schemes combine asymptotics and operator splitting to use
reasonable time steps. A presentation of a realistic example of
this study applied to solar cells follows.
Subjects/Keywords: Applied mathematics; Asymptotics; Computational; Solar; Stoichiometry
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APA ·
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Export
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Manager
APA (6th Edition):
Shapiro, B. G. (2020). Computational Methods for Kinetic Reaction Systems. (Doctoral Dissertation). Arizona State University. Retrieved from http://repository.asu.edu/items/57206
Chicago Manual of Style (16th Edition):
Shapiro, Bruce G. “Computational Methods for Kinetic Reaction Systems.” 2020. Doctoral Dissertation, Arizona State University. Accessed March 07, 2021.
http://repository.asu.edu/items/57206.
MLA Handbook (7th Edition):
Shapiro, Bruce G. “Computational Methods for Kinetic Reaction Systems.” 2020. Web. 07 Mar 2021.
Vancouver:
Shapiro BG. Computational Methods for Kinetic Reaction Systems. [Internet] [Doctoral dissertation]. Arizona State University; 2020. [cited 2021 Mar 07].
Available from: http://repository.asu.edu/items/57206.
Council of Science Editors:
Shapiro BG. Computational Methods for Kinetic Reaction Systems. [Doctoral Dissertation]. Arizona State University; 2020. Available from: http://repository.asu.edu/items/57206
King Abdullah University of Science and Technology
14.
Faria, Luiz.
Qualitative and Asymptotic Theory of Detonations.
Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2014, King Abdullah University of Science and Technology
URL: http://hdl.handle.net/10754/335798
► Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the…
(more)
▼ Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves.
The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Advisors/Committee Members: Kasimov, Aslan R. (advisor), Samtaney, Ravi (committee member), Ketcheson, David I. (committee member), Keyes, David E. (committee member).
Subjects/Keywords: detonation; Stability; chaos; shock waves; asymptotics
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APA (6th Edition):
Faria, L. (2014). Qualitative and Asymptotic Theory of Detonations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/335798
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Faria, Luiz. “Qualitative and Asymptotic Theory of Detonations.” 2014. Thesis, King Abdullah University of Science and Technology. Accessed March 07, 2021.
http://hdl.handle.net/10754/335798.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Faria, Luiz. “Qualitative and Asymptotic Theory of Detonations.” 2014. Web. 07 Mar 2021.
Vancouver:
Faria L. Qualitative and Asymptotic Theory of Detonations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2014. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/10754/335798.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Faria L. Qualitative and Asymptotic Theory of Detonations. [Thesis]. King Abdullah University of Science and Technology; 2014. Available from: http://hdl.handle.net/10754/335798
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Purdue University
15.
Zhang, Xin.
Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models.
Degree: PhD, Mathematics, 2016, Purdue University
URL: https://docs.lib.purdue.edu/open_access_dissertations/894
► Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in…
(more)
▼ Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive
asymptotics for the asset price density for large or small values of the variable, and study the wing behavior of the implied volatility in these models. Our main result provides explicit expressions for the first five terms in the expansion of the implied volatility, based on three basic spectral-type statistics of the Gaussian process: the top eigenvalue of its covariance operator, the multiplicity of this eigenvalue, and the
L2 norm of the projection of the mean function on the top eigenspace. Strategies for using this expansion for calibration purposes are discussed.
For small time, we consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity)
asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike
asymptotics, small-time behaviors of the above depend heavily on the model, and require a control of the asset price density which is uniform with respect to the asset price variable, in order to translate into results for call prices and implied volatilities. Away from the money, we express the
asymptotics explicitly using the volatility process' self-similarity parameter
H, its first Karhunen-Loève eigenvalue at time 1, and the latter's multiplicity. Several model-free estimators for
H result is discussed. At the money, a separate study is required: the
asymptotics for small time depend instead on the integrated variance's moments of orders 1/2 and 3/2, and the estimator for
H sees an affine adjustment.
Advisors/Committee Members: Frederi Viens, Frederi Viens, Kiseop Lee, Raghu Pasupathy, Jonathon Peterson.
Subjects/Keywords: Pure sciences; Implied volatility; Karhunen-loeve expansion; Large strike asymptotics; Small time asymptotics; Stochastic volatility model; Mathematics; Statistics and Probability
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APA (6th Edition):
Zhang, X. (2016). Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/894
Chicago Manual of Style (16th Edition):
Zhang, Xin. “Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models.” 2016. Doctoral Dissertation, Purdue University. Accessed March 07, 2021.
https://docs.lib.purdue.edu/open_access_dissertations/894.
MLA Handbook (7th Edition):
Zhang, Xin. “Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models.” 2016. Web. 07 Mar 2021.
Vancouver:
Zhang X. Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2021 Mar 07].
Available from: https://docs.lib.purdue.edu/open_access_dissertations/894.
Council of Science Editors:
Zhang X. Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/894
Universiteit Utrecht
16.
Hepkema, T.M.
Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks.
Degree: 2016, Universiteit Utrecht
URL: http://dspace.library.uu.nl:8080/handle/1874/335278
► This study aims to contribute to a better understanding of physical mechanisms in tidal channels as present in, for example, the Dutch Wadden Sea. Understanding…
(more)
▼ This study aims to contribute to a better understanding of physical mechanisms in tidal channels as present in, for example, the Dutch Wadden Sea. Understanding these mechanisms will contribute to effective management of the Wadden Sea and help preventing flooding in coastal areas. In this study we consider a tidal channel with tidal flats on both sides, that is connected on two sides to an open sea. The model is an idealized version of the channel connecting the Marsdiep and the Vlie in the Netherlands.
The specific mechanism studied is that of momentum dissipation on tidal flats.
Rising water level leads to water masses flowing onto the flats, carrying momentum. The water flows back into the channel during the falling tide after being temporarily stored on the flats. However, due to large friction on the shallow flats, the momentum dissipates rapidly. This is a momentum sink. The terms arising from the mass storage and the momentum dissipation are nonlinear and give rise to overtides of the primary (semi-diurnal lunar) tide, which in turn affect net sediment transport.
Here, we build on and extend a recent numerical study so as to better understand
the effect of momentum sink on characteristics of the primary tide and of its overtides. This is done by constructing an asymptotic approximation to the solution of the cross sectionally averaged shallow water equations that model the hydrodynamics in a tidal channel. The analytic approach enables assessment of the effect of the momentum sink and quantification of the differences between solutions that do or do not account for it. Multiple effects of the momentum sink on the hydrodynamics are found. In particular, when the tidal flats are approximately of the same width as the main channel no significant effects of momentum sink are found. However, when the tidal channel has wide tidal flats compared to the main channel, the momentum sink causes significant tidal distortion.
Advisors/Committee Members: Swart, H. E. de, Zagaris, A..
Subjects/Keywords: asymptotics; tidal channel; shallow water equations; momentum sink.
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APA (6th Edition):
Hepkema, T. M. (2016). Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/335278
Chicago Manual of Style (16th Edition):
Hepkema, T M. “Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks.” 2016. Masters Thesis, Universiteit Utrecht. Accessed March 07, 2021.
http://dspace.library.uu.nl:8080/handle/1874/335278.
MLA Handbook (7th Edition):
Hepkema, T M. “Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks.” 2016. Web. 07 Mar 2021.
Vancouver:
Hepkema TM. Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks. [Internet] [Masters thesis]. Universiteit Utrecht; 2016. [cited 2021 Mar 07].
Available from: http://dspace.library.uu.nl:8080/handle/1874/335278.
Council of Science Editors:
Hepkema TM. Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks. [Masters Thesis]. Universiteit Utrecht; 2016. Available from: http://dspace.library.uu.nl:8080/handle/1874/335278
Dalhousie University
17.
Vargas, Antonio.
Zeros of Sections of Some Power Series.
Degree: MS, Department of Mathematics & Statistics - Math
Division, 2012, Dalhousie University
URL: http://hdl.handle.net/10222/15394
► 62+x pages, 24 figures
For a power series which converges in some neighborhood of the origin in the complex plane, the zeros of its partial…
(more)
▼ 62+x pages, 24 figures
For a power series which converges in some
neighborhood of the origin in the complex plane, the zeros of its
partial sums often behave in a controlled manner. We give an
overview of some of the major results in the study of this
phenomenon in the past century, focusing on recent developments
which build on the theme of asymptotic analysis. Inspired by this
work, we study the asymptotic behavior of the zeros of partial sums
of power series for entire functions defined by exponential
integrals of a certain type. Most of the zeros of the n'th partial
sum travel outwards from the origin at a rate comparable to n, so
we rescale the variable by n and explicitly calculate the limit
curves of these normalized zeros. We discover that the zeros'
asymptotic behavior depends on the order of the critical points of
the integrand in the aforementioned exponential
integral.
Advisors/Committee Members: (None) (external-examiner), Keith Johnson (graduate-coordinator), Theodore Kolokolnikov (thesis-reader), Keith Taylor (thesis-reader), Karl Dilcher (thesis-supervisor), Not Applicable (ethics-approval), Not Applicable (manuscripts), Not Applicable (copyright-release).
Subjects/Keywords: zeros; roots; polynomials; power series; sections; asymptotics; szego curve; complex analysis
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APA (6th Edition):
Vargas, A. (2012). Zeros of Sections of Some Power Series. (Masters Thesis). Dalhousie University. Retrieved from http://hdl.handle.net/10222/15394
Chicago Manual of Style (16th Edition):
Vargas, Antonio. “Zeros of Sections of Some Power Series.” 2012. Masters Thesis, Dalhousie University. Accessed March 07, 2021.
http://hdl.handle.net/10222/15394.
MLA Handbook (7th Edition):
Vargas, Antonio. “Zeros of Sections of Some Power Series.” 2012. Web. 07 Mar 2021.
Vancouver:
Vargas A. Zeros of Sections of Some Power Series. [Internet] [Masters thesis]. Dalhousie University; 2012. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/10222/15394.
Council of Science Editors:
Vargas A. Zeros of Sections of Some Power Series. [Masters Thesis]. Dalhousie University; 2012. Available from: http://hdl.handle.net/10222/15394
Penn State University
18.
Misiats, Oleksandr.
Asymptotic analysis of Ginzburg-landau superconductivity model.
Degree: 2012, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/16044
► The thesis is devoted to variational problems and PDEs related to the Ginzburg-Landau superconductivity theory and consists of two parts. In the first part we…
(more)
▼ The thesis is devoted to variational problems and PDEs related to the Ginzburg-Landau superconductivity theory and consists of two parts. In the first part we establish the existence of minimizers of the magnetic Ginzburg-Landau energy functional with prescribed degrees and unit modulus on the boundary (so called semi-stiff boundary conditions) in both simply connected and doubly connected domains. In simply connected domains we show that the vortices of these minimizers are located strictly inside the domain for certain values of Ginzburg-Landau parameter, while in doubly connected domains we have nearboundary vortices in the same parameter regime. We also establish the necessary conditions for the existence of local minimizers of the simplified Ginzburg-Landau functional in doubly connected domains with semi-stiff boundary conditions. The second part of the thesis studies vortex pinning (i.e., fixing the positions of vortices), which is done through introducing inclusions into a homogeneous superconductor. We use the homogenization techniques to model a composite superconductor obtained by introducing a large number of superconducting inclusions in superconducting media. Next, we focus on modeling a superconductor with finitely many small superconducting inclusions in the vortex state. We show that even the inclusions of negligibly small size (e.g. shrinking to single points) capture the vortices of minimizers, and therefore, the problem of finding the locations of the vortices of minimizers may be reduced to a discrete minimization problem for a finite-dimensional functional.
Advisors/Committee Members: Leonid Berlyand, Dissertation Advisor/Co-Advisor, Alberto Bressan, Committee Member, Anna L Mazzucato, Committee Member, Qiang Du, Committee Member, Sarah Elizabeth Shandera, Special Member.
Subjects/Keywords: Ginzburg-Landau theory; asymptotics; vortices; degree boundary conditions; vortex pinning
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APA (6th Edition):
Misiats, O. (2012). Asymptotic analysis of Ginzburg-landau superconductivity model. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16044
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Misiats, Oleksandr. “Asymptotic analysis of Ginzburg-landau superconductivity model.” 2012. Thesis, Penn State University. Accessed March 07, 2021.
https://submit-etda.libraries.psu.edu/catalog/16044.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Misiats, Oleksandr. “Asymptotic analysis of Ginzburg-landau superconductivity model.” 2012. Web. 07 Mar 2021.
Vancouver:
Misiats O. Asymptotic analysis of Ginzburg-landau superconductivity model. [Internet] [Thesis]. Penn State University; 2012. [cited 2021 Mar 07].
Available from: https://submit-etda.libraries.psu.edu/catalog/16044.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Misiats O. Asymptotic analysis of Ginzburg-landau superconductivity model. [Thesis]. Penn State University; 2012. Available from: https://submit-etda.libraries.psu.edu/catalog/16044
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Colorado
19.
Chen, Yan.
Asymptotic Series Solutions to One-Dimensional Helmholtz Equation.
Degree: MS, Applied Mathematics, 2014, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/54
► We present a variation of the method of Berry & Howls, which eliminates some of the inherent error in their approach. Using Dingle's change…
(more)
▼ We present a variation of the method of Berry & Howls, which eliminates some of the inherent error in their approach. Using Dingle's change of variables we transform the Airy differential equation into a new ODE that is exact, for all positive z. After reformulating the ODE as an integral equation, we solve the integral equation (exactly) with a recurrent series that converges absolutely for all positive z. Each term in our series can be expanded as an asymptotic series with the error term under our control because of the bound we develop for it. Comparing with other techniques, our solution maintains all the original function's information.
We discover a type of oscillation behavior hidden in the hyperasymptotic series. This behavior ought to be in the structure because of the way that the hyperseries is constructed. Each term in the hyperseries is in the form that consists of indexes and arguments. Each index changes discretely, whereas each argument changes continuously. This is the fundamental reason that causes the oscillation phenomenon. The other researchers have not addressed this issue in their related work because they only approximate the solution when the argument is at a single value.
Advisors/Committee Members: Harvey Segur, Keith Julien, Sujeet Bhat.
Subjects/Keywords: Airy function; Asymptotics; Hyperasymptotics; Modeling; Oscillation; Series; Applied Mathematics
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APA (6th Edition):
Chen, Y. (2014). Asymptotic Series Solutions to One-Dimensional Helmholtz Equation. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/54
Chicago Manual of Style (16th Edition):
Chen, Yan. “Asymptotic Series Solutions to One-Dimensional Helmholtz Equation.” 2014. Masters Thesis, University of Colorado. Accessed March 07, 2021.
https://scholar.colorado.edu/appm_gradetds/54.
MLA Handbook (7th Edition):
Chen, Yan. “Asymptotic Series Solutions to One-Dimensional Helmholtz Equation.” 2014. Web. 07 Mar 2021.
Vancouver:
Chen Y. Asymptotic Series Solutions to One-Dimensional Helmholtz Equation. [Internet] [Masters thesis]. University of Colorado; 2014. [cited 2021 Mar 07].
Available from: https://scholar.colorado.edu/appm_gradetds/54.
Council of Science Editors:
Chen Y. Asymptotic Series Solutions to One-Dimensional Helmholtz Equation. [Masters Thesis]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/appm_gradetds/54
University of Oxford
20.
Seifert, David H.
Extensions of the Katznelson-Tzafriri theorem for operator semigroups.
Degree: PhD, 2014, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:cf8adfa4-b280-4cd8-b213-404d541ff651
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618461
► This thesis is concerned with extensions and refinements of the Katznelson-Tzafriri theorem, a cornerstone of the asymptotic theory of operator semigroups which recently has received…
(more)
▼ This thesis is concerned with extensions and refinements of the Katznelson-Tzafriri theorem, a cornerstone of the asymptotic theory of operator semigroups which recently has received renewed interest in the context of damped wave equations. The thesis comprises three main parts. The key results in the first part are a version of the Katznelson-Tzafriri theorem for bounded C_0-semigroups in which a certain function appearing in the original statement of the result is allowed more generally to be a bounded Borel measure, and bounds on the rate of decay in an important special case. The second part deals with the discrete version of the Katznelson-Tzafriri theorem and establishes upper and lower bounds on the rate of decay in this setting too. In an important special case these general bounds are then shown to be optimal for general Banach spaces but not on Hilbert space. The third main part, finally, turns to general operator semigroups. It contains a version of the Katznelson-Tzafriri theorem in the Hilbert space setting which relaxes the main assumption of the original result. Various applications and extensions of this general result are also presented.
Subjects/Keywords: 515.7; Functional analysis (mathematics); Operator semigroups; asymptotics; Katznelson-Tzafriri theorem
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APA (6th Edition):
Seifert, D. H. (2014). Extensions of the Katznelson-Tzafriri theorem for operator semigroups. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:cf8adfa4-b280-4cd8-b213-404d541ff651 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618461
Chicago Manual of Style (16th Edition):
Seifert, David H. “Extensions of the Katznelson-Tzafriri theorem for operator semigroups.” 2014. Doctoral Dissertation, University of Oxford. Accessed March 07, 2021.
http://ora.ox.ac.uk/objects/uuid:cf8adfa4-b280-4cd8-b213-404d541ff651 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618461.
MLA Handbook (7th Edition):
Seifert, David H. “Extensions of the Katznelson-Tzafriri theorem for operator semigroups.” 2014. Web. 07 Mar 2021.
Vancouver:
Seifert DH. Extensions of the Katznelson-Tzafriri theorem for operator semigroups. [Internet] [Doctoral dissertation]. University of Oxford; 2014. [cited 2021 Mar 07].
Available from: http://ora.ox.ac.uk/objects/uuid:cf8adfa4-b280-4cd8-b213-404d541ff651 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618461.
Council of Science Editors:
Seifert DH. Extensions of the Katznelson-Tzafriri theorem for operator semigroups. [Doctoral Dissertation]. University of Oxford; 2014. Available from: http://ora.ox.ac.uk/objects/uuid:cf8adfa4-b280-4cd8-b213-404d541ff651 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618461
University of Oxford
21.
O'Kiely, Doireann.
Mathematical models for the glass sheet redraw process.
Degree: PhD, 2017, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:3788de4d-8254-4fba-9cd0-4bec32409d1e
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729103
► In this thesis we derive mathematical models for the glass sheet redraw process for the production of very thin glass sheets. In the redraw process,…
(more)
▼ In this thesis we derive mathematical models for the glass sheet redraw process for the production of very thin glass sheets. In the redraw process, a prefabricated glass block is fed into a furnace, where it is heated and stretched by the application of draw rollers to reduce its thickness. Redrawn sheets may be used in various applications including smartphone and battery technology. Our aims are to investigate the factors determining the final thickness profile of a glass sheet produced by this process, as well as the growth of out-of-plane deformations in the sheet during redraw. Our method is to model the glass sheet using NavierâStokes equations and free-surface conditions, and exploit small aspect ratios in the sheet to simplify and solve these equations using asymptotic expansions. We first consider a simple two-dimensional sheet to determine which physical effects should be taken into account in modelling the redraw process. Next, we derive a mathematical model for redraw of a thin threedimensional sheet. We consider the limits in which the heater zone is either short or long compared with the sheet half-width. The resulting reduced models predict the thickness profile of the redrawn sheet and the initial shape required to redraw a product of uniform thickness. We then derive mathematical models for buckling of thin viscous sheets during redraw. For buckling of a two-dimensional glass sheet due to gravity-induced compression, we predict the evolution of the centreline and investigate the early- and late-time behaviour of the system. For a three-dimensional glass sheet undergoing redraw, we use numerical solutions to investigate the behaviour of the sheet mid-surface.
Subjects/Keywords: 620.1; mathematical modelling; asymptotics; thin viscous sheet; industrial mathematics; glass
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APA (6th Edition):
O'Kiely, D. (2017). Mathematical models for the glass sheet redraw process. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:3788de4d-8254-4fba-9cd0-4bec32409d1e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729103
Chicago Manual of Style (16th Edition):
O'Kiely, Doireann. “Mathematical models for the glass sheet redraw process.” 2017. Doctoral Dissertation, University of Oxford. Accessed March 07, 2021.
https://ora.ox.ac.uk/objects/uuid:3788de4d-8254-4fba-9cd0-4bec32409d1e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729103.
MLA Handbook (7th Edition):
O'Kiely, Doireann. “Mathematical models for the glass sheet redraw process.” 2017. Web. 07 Mar 2021.
Vancouver:
O'Kiely D. Mathematical models for the glass sheet redraw process. [Internet] [Doctoral dissertation]. University of Oxford; 2017. [cited 2021 Mar 07].
Available from: https://ora.ox.ac.uk/objects/uuid:3788de4d-8254-4fba-9cd0-4bec32409d1e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729103.
Council of Science Editors:
O'Kiely D. Mathematical models for the glass sheet redraw process. [Doctoral Dissertation]. University of Oxford; 2017. Available from: https://ora.ox.ac.uk/objects/uuid:3788de4d-8254-4fba-9cd0-4bec32409d1e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729103
22.
Acosta, Jorge A.
Holonomy Limits of Cyclic Opers.
Degree: PhD, Natural Sciences, 2016, Rice University
URL: http://hdl.handle.net/1911/96525
► Given a Riemann surface X = (Σ, J), we find an expression for the dominant term for the asymptotics of the holonomy of opers over…
(more)
▼ Given a Riemann surface X = (Σ, J), we find an expression for the dominant term for the
asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form (0,0,∙s,tω
n). Moreover, we find an associated equivariant map from the universal cover (~{Σ},~{J}) to the symmetric space SL
n(ℂ) / {SU}(n) and show that limits of these maps tend to a sub-building in the asymptotic cone. That sub-building is explicitly constructed from the local data of ω
n.
Advisors/Committee Members: Wolf, Michael (advisor).
Subjects/Keywords: Representations; Asymptotics; Differential Equations
…asymptotics of
this map in [8]. That is, Dumas showed
Theorem 1.3.2 (Dumas [8… …the asymptotics of the solutions of the differential
1−n
2
)T
12
equation, we can… …use this information to compute the asymptotics of the resulting
holonomy. We relate the… …asymptotics of the holonomy to the local geometry of the
defining holomorphic differential and to… …λn−1 φ n )
we can compute the asymptotics of the holonomy in terms of the matrices Et…
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APA (6th Edition):
Acosta, J. A. (2016). Holonomy Limits of Cyclic Opers. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/96525
Chicago Manual of Style (16th Edition):
Acosta, Jorge A. “Holonomy Limits of Cyclic Opers.” 2016. Doctoral Dissertation, Rice University. Accessed March 07, 2021.
http://hdl.handle.net/1911/96525.
MLA Handbook (7th Edition):
Acosta, Jorge A. “Holonomy Limits of Cyclic Opers.” 2016. Web. 07 Mar 2021.
Vancouver:
Acosta JA. Holonomy Limits of Cyclic Opers. [Internet] [Doctoral dissertation]. Rice University; 2016. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1911/96525.
Council of Science Editors:
Acosta JA. Holonomy Limits of Cyclic Opers. [Doctoral Dissertation]. Rice University; 2016. Available from: http://hdl.handle.net/1911/96525
Delft University of Technology
23.
Sandilo, S.H.
On Aspects of Asymptotics for Axially Moving Continua.
Degree: 2013, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20
;
urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20
;
urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20
;
http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20
► In this thesis two models for axially moving continua have been studied: a string-like model and a beam-like model. Mathematically, a string-like model is described…
(more)
▼ In this thesis two models for axially moving continua have been studied: a string-like model and a beam-like model. Mathematically, a string-like model is described by a wave equation and a beam-like model is usually described by the Euler-Bernoulli beam equation. A string-like model has been used to describe the transversal vibrations of a vertically moving elevator cable system with time-varying length and a beam-like model has been used to describe the transversal vibrations of a constant length conveyor belt system between two supports. For the string model, a rigid body is attached to the lower end of the string, and the suspension of this body against the guide rails is assumed to be rigid. For the string model, it is assumed that the length changes linearly in time or that the length changes harmonically about a constant mean length. For the linear length-variations it is assumed that the axial velocity of the string is small compared to nominal wave velocity and the string mass is small compared to the mass of the rigid body and, for the harmonically length variations small oscillation amplitudes are assumed. The case with boundary excitations has also been investigated in detail, and interesting resonance conditions have been found. For the beam model, the axial velocity is assumed to be constant and relatively small compared to the wave speed. The case with boundary damping has been investigated in detail for the beam equation and interesting damping properties have been obtained. The corresponding initial boundary value problems have been formulated, and in all cases formal asymptotic approximations of the analytic solutions have been constructed by using the multiple timescales perturbation methods. For the string-like problem, it has been shown that Galerkin's truncation method can not be applied in order to obtain asymptotic approximations valid on long timescales. For boundary excitations the interesting phenomenon of autoresonance occurs when there is passage through (dynamic) resonance. The maximal amplitude of the autoresonant solution and the time of autoresonant growth of the amplitude of the modes of fast oscillations have been determined. Interior layer analysis has been provided systematically and it has been shown that there exists an unexpected timescale of order (1/?(?). For this reason three timescales have been introduced when constructing asymptotic results. For the beam-like problem, by using the energy integral, it has been shown that the solutions are bounded for times t of order 1/?. It has also been analytically and numerically shown that all solutions (up to order ?) are uniformly damped.
Advisors/Committee Members: Van Horssen, W.T., Heemink, A.W..
Subjects/Keywords: multiple-timescales; asymptotics; autoresonance; oscillations
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APA (6th Edition):
Sandilo, S. H. (2013). On Aspects of Asymptotics for Axially Moving Continua. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20
Chicago Manual of Style (16th Edition):
Sandilo, S H. “On Aspects of Asymptotics for Axially Moving Continua.” 2013. Doctoral Dissertation, Delft University of Technology. Accessed March 07, 2021.
http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20.
MLA Handbook (7th Edition):
Sandilo, S H. “On Aspects of Asymptotics for Axially Moving Continua.” 2013. Web. 07 Mar 2021.
Vancouver:
Sandilo SH. On Aspects of Asymptotics for Axially Moving Continua. [Internet] [Doctoral dissertation]. Delft University of Technology; 2013. [cited 2021 Mar 07].
Available from: http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20.
Council of Science Editors:
Sandilo SH. On Aspects of Asymptotics for Axially Moving Continua. [Doctoral Dissertation]. Delft University of Technology; 2013. Available from: http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; urn:NBN:nl:ui:24-uuid:4d02ddd6-90fe-490f-9385-77046375de20 ; http://resolver.tudelft.nl/uuid:4d02ddd6-90fe-490f-9385-77046375de20
Delft University of Technology
24.
Hijmissen, J.W.
On aspects of boundary damping for cables and vertical beams.
Degree: 2008, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
;
urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
;
urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
;
http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
► Elastic structures are susceptible to wind- and earthquake-induced vibrations. These vibrations can damage a structure or cause human discomfort. To suppress structural vibrations, various types…
(more)
▼ Elastic structures are susceptible to wind- and earthquake-induced vibrations. These vibrations can damage a structure or cause human discomfort. To suppress structural vibrations, various types of damping mechanisms, active or passive, can be applied. In this thesis the model of a weakly damped, standing Euler-Bernoulli beam in a (turbulent) wind-field and the model of a standing Timoshenko beam will be used as a simple model of a tall building. These models will be used to study the stabilizing effect of dampers which are installed at the top of the beam (the so-called boundary dampers), the self-weight effect of a beam on its stability, and the possibly destabilizing effect due to galloping (a dynamic wind response). In this thesis two passive control methods will be applied to the Euler-Bernoulli beam. Moreover, the string-equation will be used to study the dynamics of a cable with an end-mass and subjected to boundary damping. The model of a tensioned beam will be used to examine the damping behavior of a tensioned cable with small bending stiffness and an attached tuned mass damper. The vibrations of these beam and string models can be described by (stochastic) initial-boundary value problems. The problem will be stochastic if a beam in a turbulent wind-field is studied. It is assumed that the damping effect, the self-weight effect, and the wind-force in these problems are small but not negligible. The multiple-timescales perturbation method, the method of separation of variables, and a combination of the Galerkin truncation method and a numerical scheme, will be used to construct (explicit) approximations of the beam-like problems. The Laplace transform method will be applied tothe string-like problem. In this way a so-called characteristic equation has been obtained. This equation have been solved by using (adapted) classical perturbation methods. For both control methods, the uniform stability of an Euler-Bernoulli beam subjected to boundary damping has been established and it has been concluded that these strategies can be used effectively to damp the wind-induced vibrations of a standing Euler-Bernoulli beam. Furthermore, it has been found that the self-weight effect on the frequencies and damping rates of an Euler-Bernoulli and Timoshenko beam is small. For the string problem approximations of the damping rates have been constructed. These have been used to conclude that a string with an end-mass can be damped uniformly by applying boundary damping. Lastly, for the tensioned beam with attached damper it has been shown that small bending stiffness only slightly influences the damping rates of the cable.
Advisors/Committee Members: Heemink, A.W., Van Horssen, W.T..
Subjects/Keywords: perturbation methods; boundary damping; asymptotics
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APA ·
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MLA ·
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Export
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Manager
APA (6th Edition):
Hijmissen, J. W. (2008). On aspects of boundary damping for cables and vertical beams. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
Chicago Manual of Style (16th Edition):
Hijmissen, J W. “On aspects of boundary damping for cables and vertical beams.” 2008. Doctoral Dissertation, Delft University of Technology. Accessed March 07, 2021.
http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156.
MLA Handbook (7th Edition):
Hijmissen, J W. “On aspects of boundary damping for cables and vertical beams.” 2008. Web. 07 Mar 2021.
Vancouver:
Hijmissen JW. On aspects of boundary damping for cables and vertical beams. [Internet] [Doctoral dissertation]. Delft University of Technology; 2008. [cited 2021 Mar 07].
Available from: http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156.
Council of Science Editors:
Hijmissen JW. On aspects of boundary damping for cables and vertical beams. [Doctoral Dissertation]. Delft University of Technology; 2008. Available from: http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; urn:NBN:nl:ui:24-uuid:53fece0d-c512-4bd8-a0da-ea3311b35156 ; http://resolver.tudelft.nl/uuid:53fece0d-c512-4bd8-a0da-ea3311b35156
25.
Gtet, Abdelfatah.
Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities.
Degree: Docteur es, Mathématiques Appliquées, 2017, Université Grenoble Alpes (ComUE)
URL: http://www.theses.fr/2017GREAM096
► La diffraction d'une onde électromagnétique par une structure présentant des échelles d'espace petites devant la longueur d'onde est un phénomène complexe qui décrit à la…
(more)
▼ La diffraction d'une onde électromagnétique par une structure présentant des échelles d'espace petites devant la longueur d'onde est un phénomène complexe qui décrit à la fois l'interaction entre l'onde et la géométrie de la structure et la matière qui la constitue. Quand la fréquence n'est pas résonnante, l'onde incidente interagit faiblement avec des petites irrégularités de la structure. En langage mathématique, ceci se traduit par le fait que la différence entre les champs électromagnétiques de la structure perturbée et ceux de la structure de référence est de l'ordre de la perturbation. Par contre, quand la fréquence est résonante, le comportement de l'onde est très sensible aux petites déformations singulières de la géométrie de la structure. Cette sensibilité est susceptible d'être détectée dans les mesures du champ lointain, et est la brique de base de plusieurs capteurs et filtres plasmoniques. Dans ce projet de thèse nous nous sommes intéressés aux propriétés optiques de surfaces métalliques comportant des cavités sub-longueur d'onde distribués périodiquement ou non, et de couches métalliques minces. Ces structures possèdent des résonances électromagnétiques proches de l’axe réel, et sont capables de concentrer l’énergie électromagnétique dans des volumes bien inférieurs à la cubique de la longueur d’onde incidente. La compréhension de ce phénomène est un enjeu important pour le développement des spectroscoepies ultra-sensibles, mais aussi dans le domaine des bio-capteurs et de l’opto-électronique. En utilisant des techniques asymptotiques couplées avec des équations intégrales, nous avons déterminé le développement asymptotique des fréquences de résonance de ces structures quand le rapport entre l'échelle de la structuration spatiale et la longueur d'onde tend vers zéro. Les modèles asymptotiques dérivés sont beaucoup plus simples à étudier et à simuler et rendent parfaitement compte des résultats expérimentaux. Ils permettent de prédire les fréquences résonnantes, la quantité d’énergie localisée en fonction de la géométrie des structures et des propriétés des matériaux qui les constituent.
Rough metallic surfaces with subwavelength structurations possess extraordinary diffractive properties: at certain frequencies, one may observe fine localization and very large enhancement of the electromagnetic fields. The discovery of these phenomena has raised considerable interest as potential applications are numerous (optical switches, sensors, devices for microscopy). This behavior results from the combination of very complex interaction between the incident excitation, the geometry and the material properties of the scatterer. The main goal of this thesis is to better understand these phenomena from the mathematical point of view.In mathematical terms, the localization and concentration of the fields is the mark of a resonance phenomenon. In our context, the corresponding resonant field may be surface plasmons, i.e., waves that propagate along the interface of the grating, and that decay exponentially away…
Advisors/Committee Members: Triki, Faouzi (thesis director), Bonnetier, Eric (thesis director).
Subjects/Keywords: Calcul asymptotique; Représentation intégrale; Résonances plasmoniques; Asymptotics; Plasmonics; Integral equation; 510
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APA (6th Edition):
Gtet, A. (2017). Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2017GREAM096
Chicago Manual of Style (16th Edition):
Gtet, Abdelfatah. “Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities.” 2017. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed March 07, 2021.
http://www.theses.fr/2017GREAM096.
MLA Handbook (7th Edition):
Gtet, Abdelfatah. “Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities.” 2017. Web. 07 Mar 2021.
Vancouver:
Gtet A. Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2017. [cited 2021 Mar 07].
Available from: http://www.theses.fr/2017GREAM096.
Council of Science Editors:
Gtet A. Calcul asymptotique de résonances de plasmon de cavités rectangulaires : Asymptotics of plasmonic resonnances of rectangular cavities. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2017. Available from: http://www.theses.fr/2017GREAM096
University of Minnesota
26.
ZHOU, YU.
Quantile-optimal Treatment Regimes with Censored Data.
Degree: PhD, Statistics, 2018, University of Minnesota
URL: http://hdl.handle.net/11299/200262
► The problem of estimating an optimal treatment regime has received considerable attention recently. However, most of the earlier work in this area has focused on…
(more)
▼ The problem of estimating an optimal treatment regime has received considerable attention recently. However, most of the earlier work in this area has focused on estimating a mean-optimal treatment regime based on completely observed data. We investigate a new quantile criterion for estimating an optimal treatment regime with right-censored survival outcomes. When the outcome distribution is skewed or when the censoring is heavy, the quantile criterion is easy to interpret and provides an attractive measure of treatment effect. In contrast, the mean criterion often cannot be reliably estimated in such settings. We propose a nonparametric approach to robustly estimate the quantile-optimal treatment regime from a class of candidate treatment regimes without imposing an outcome regression model. We derive a nonstandard converge rate and a non-normal limiting distribution for the estimated parameters indexing the optimal treatment regime using advanced empirical processes theory. Such a theory has not been established in any earlier work for survival data. We also extend the method to a two-stage dynamic setting. We illustrate the practical utility of the proposed new method for single-stage estimation through Monte Carlo studies and an application to a clinical trial data set, and we also examine the performance of the proposed method for two-stage estimation through Monte Carlo studies.
Subjects/Keywords: M-estimation; Nonstandard asymptotics; Precision medicine; Quantile criterion; Survival analysis
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APA ·
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APA (6th Edition):
ZHOU, Y. (2018). Quantile-optimal Treatment Regimes with Censored Data. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/200262
Chicago Manual of Style (16th Edition):
ZHOU, YU. “Quantile-optimal Treatment Regimes with Censored Data.” 2018. Doctoral Dissertation, University of Minnesota. Accessed March 07, 2021.
http://hdl.handle.net/11299/200262.
MLA Handbook (7th Edition):
ZHOU, YU. “Quantile-optimal Treatment Regimes with Censored Data.” 2018. Web. 07 Mar 2021.
Vancouver:
ZHOU Y. Quantile-optimal Treatment Regimes with Censored Data. [Internet] [Doctoral dissertation]. University of Minnesota; 2018. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/11299/200262.
Council of Science Editors:
ZHOU Y. Quantile-optimal Treatment Regimes with Censored Data. [Doctoral Dissertation]. University of Minnesota; 2018. Available from: http://hdl.handle.net/11299/200262
Clemson University
27.
Steuber, Tara.
Inference in Reversible Markov Chains.
Degree: PhD, Mathematical Science, 2011, Clemson University
URL: https://tigerprints.clemson.edu/all_dissertations/756
► This dissertation describes the research that we have done concerning reversible Markov chains. We first present definitions for what it means for a Markov chain…
(more)
▼ This dissertation describes the research that we have done concerning reversible Markov chains. We first present definitions for what it means for a Markov chain to be reversible. We then give applications of where reversible Markov chains are used and give a brief history of Markov chain inference. Finally, two journal articles are found in the paper, one that is already published and another which is currently being submitted. The first article examines estimation of the one-step-ahead transition probabilities in a reversible Markov chain on a countable state space. A symmetrized moment estimator is proposed that exploits the reversible structure. Examples are given where the symmetrized estimator has superior asymptotic properties to those of a naive estimator, implying that knowledge of reversibility can sometimes improve estimation. The asymptotic mean and variance of the estimators are quantified. The results are proven using only elementary results such as the law of large numbers and the central limit theorem. The second article introduces two statistics that assess whether (or not) a sequence sampled from a time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.
Advisors/Committee Members: Kiessler, Peter C., Gallagher , Colin, Fralix , Brian.
Subjects/Keywords: asymptotics; inference; Markov chain; reversible; test statistic; Applied Mathematics
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APA (6th Edition):
Steuber, T. (2011). Inference in Reversible Markov Chains. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/756
Chicago Manual of Style (16th Edition):
Steuber, Tara. “Inference in Reversible Markov Chains.” 2011. Doctoral Dissertation, Clemson University. Accessed March 07, 2021.
https://tigerprints.clemson.edu/all_dissertations/756.
MLA Handbook (7th Edition):
Steuber, Tara. “Inference in Reversible Markov Chains.” 2011. Web. 07 Mar 2021.
Vancouver:
Steuber T. Inference in Reversible Markov Chains. [Internet] [Doctoral dissertation]. Clemson University; 2011. [cited 2021 Mar 07].
Available from: https://tigerprints.clemson.edu/all_dissertations/756.
Council of Science Editors:
Steuber T. Inference in Reversible Markov Chains. [Doctoral Dissertation]. Clemson University; 2011. Available from: https://tigerprints.clemson.edu/all_dissertations/756
University of Maryland
28.
Nam, Kijoeng.
DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION.
Degree: Mathematical Statistics, 2014, University of Maryland
URL: http://hdl.handle.net/1903/15776
► In high-dimensional data analysis, we often want to reduce the number of predictors without eliminating variables which are related to the response of interest. Inverse…
(more)
▼ In high-dimensional data analysis, we often want to reduce the number of predictors without eliminating variables which are related to the response of interest. Inverse regression methods use the response variable when performing dimension reduction so that information regarding the relation between the covariates and the response is not lost. However, it is common to assume that the inverse regression function is linear or to use some other ad hoc approach. Instead, we propose a new dimension reduction method which models the inverse regression function as a spline. We develop
asymptotics for our approach and demonstrate its performance through simulations and several data sets commonly found in the machine learning literature. We show that its performance is better than existing inverse regression based methods, especially when the dimension reduction space is a nonlinear manifold such as the Swiss roll example of Roweis and Saul (2000).
Advisors/Committee Members: Smith, Paul J. (advisor), Dolgopyat, Dmitry (advisor).
Subjects/Keywords: Statistics; Asymptotics; High-dimensional data; Inverse regression methods
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APA (6th Edition):
Nam, K. (2014). DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/15776
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Nam, Kijoeng. “DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION.” 2014. Thesis, University of Maryland. Accessed March 07, 2021.
http://hdl.handle.net/1903/15776.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Nam, Kijoeng. “DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION.” 2014. Web. 07 Mar 2021.
Vancouver:
Nam K. DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION. [Internet] [Thesis]. University of Maryland; 2014. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1903/15776.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Nam K. DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION. [Thesis]. University of Maryland; 2014. Available from: http://hdl.handle.net/1903/15776
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Georgia
29.
Liao, Lina.
Developments of regularized approaches in non-standard paradigm.
Degree: 2015, University of Georgia
URL: http://hdl.handle.net/10724/33159
► This dissertation proposes new regularized approaches to two different topics. The first topic revisits the autocovariance function estimation, a fundamental problem in statistical inference for…
(more)
▼ This dissertation proposes new regularized approaches to two different topics. The first topic revisits the autocovariance function estimation, a fundamental problem in statistical inference for time series data. We convert the function
estimation problem into constrained penalized regression with a generalized penalty that provides us with flexible and accurate estimation, and study the asymptotic properties of the proposed estimator. In case of a nonzero time series, we apply a
penalized regression technique to a differenced time series, which does not require a separate detrending procedure. We propose four different data-driven criteria to determine the tuning parameters, whose selection is critical in penalized regression. A
simulation study shows that the proposed approach is superior to three existing methods and the tuning parameter selection is effective. We also briefly discuss the extension of the proposed approach to interval-valued time series. The second topic
concerns the study of the entire conditional distribution of a response given predictors in a regression setting. A usual approach to address heterogenous data is quantile regression, but it has some drawbacks and is computationally challenging due to
the L1 norm. As an alternative to quantile regression, we consider expectile regression that relies on the minimization of the asymmetric L2 norm. We assume that only a small set of predictors is relevant to the response, and develop penalized
expectile regression with SCAD and adaptive LASSO penalties. With properly chosen tuning parameters, we show that the proposed estimators enjoy the oracle properties. A numerical study using simulated and real examples demonstrates the superior
performance of the proposed penalized expectile regression over penalized quantile regression.
Subjects/Keywords: Asymptotics, Autocovariance function; Expectile regression; Penalized regression; Time series; Variable selection
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APA ·
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Export
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Manager
APA (6th Edition):
Liao, L. (2015). Developments of regularized approaches in non-standard paradigm. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/33159
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Liao, Lina. “Developments of regularized approaches in non-standard paradigm.” 2015. Thesis, University of Georgia. Accessed March 07, 2021.
http://hdl.handle.net/10724/33159.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Liao, Lina. “Developments of regularized approaches in non-standard paradigm.” 2015. Web. 07 Mar 2021.
Vancouver:
Liao L. Developments of regularized approaches in non-standard paradigm. [Internet] [Thesis]. University of Georgia; 2015. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/10724/33159.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Liao L. Developments of regularized approaches in non-standard paradigm. [Thesis]. University of Georgia; 2015. Available from: http://hdl.handle.net/10724/33159
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Canterbury
30.
de Jong, Jamie Victoria.
Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts.
Degree: MS, Mathematics, 2015, University of Canterbury
URL: http://dx.doi.org/10.26021/3473
► A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods…
(more)
▼ A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for the reconstruction of trees, it is crucial to understand the size and structure of neighbourhoods of trees under tree rearrangement operations. The diameter and size of the immediate neighbourhood of a tree has been well-studied, however little is known about the number of trees at distance two, three or (more generally) k from a given tree. In this thesis we explore previous results on the size of these neighbourhoods under common tree rearrangement operations (NNI, SPR and TBR). We obtain new results concerning the number of trees at distance k from a given tree under the Robinson-Foulds (RF) metric and the Nearest Neighbour Interchange (NNI) operation, and the number of trees at distance two from a given tree under the Subtree Prune and Regraft (SPR) operation. We also obtain an exact count for the number of pairs of binary phylogenetic trees that share a first RF or NNI neighbour.
Subjects/Keywords: Phylogenetic tree; splits; Robinson-Foulds metric; tree rearrangements; asymptotics
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APA ·
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APA (6th Edition):
de Jong, J. V. (2015). Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts. (Masters Thesis). University of Canterbury. Retrieved from http://dx.doi.org/10.26021/3473
Chicago Manual of Style (16th Edition):
de Jong, Jamie Victoria. “Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts.” 2015. Masters Thesis, University of Canterbury. Accessed March 07, 2021.
http://dx.doi.org/10.26021/3473.
MLA Handbook (7th Edition):
de Jong, Jamie Victoria. “Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts.” 2015. Web. 07 Mar 2021.
Vancouver:
de Jong JV. Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts. [Internet] [Masters thesis]. University of Canterbury; 2015. [cited 2021 Mar 07].
Available from: http://dx.doi.org/10.26021/3473.
Council of Science Editors:
de Jong JV. Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts. [Masters Thesis]. University of Canterbury; 2015. Available from: http://dx.doi.org/10.26021/3473
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Open Access Theses and Dissertations
