Browsing by Department "Mathematics"
Now showing items 120 of 340

(20230505)For many physical problems, robust numerical methods for solving the compressible Euler equations are essential. For the Euler equations to accurately describe the fluid behavior a suitable equation of state (EOS), which ...

(20130515)The motivating question behind this body of research is Smale’s 17th problem: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? While ...

(20180524)Multiscale modeling of complex physical phenomena in many areas, including hydrogeology, material science, chemistry and biology, consists of solving problems in highly heterogeneous porous media. In many of these applications, ...

(20170718)Many problems in application involve media with multiple scale, for example, in composite materials, porous media. These problems are usually computationally challenging since fine grid computation is extremely expensive. ...

(20120716)We examine the amalgamated free product of hyperfinite von Neumann algebras. First we describe the amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras. In this case the result ...

(20191030)When building cryptosystems, cryptographers focus on finding problems that are not believed to be solvable in polynomialtime. Some of the most popular problems they have found are the Discrete Logarithm Problem and Integer ...

(20230417)Many biological systems are modeled mathematically using systems of differential equations. Descartes’ rule of signs is a common tool for analyzing these systems. In this thesis we explore a new perspective on Descartes’ ...

(20090515)We study computational theory and methods for finding multiple unstable solutions (corresponding to saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. We ...

(20100114)We consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a ...

(20140429)Many species of birds migrate nocturnally. In nocturnally migrating birds, endogenous circadian and circannual rhythms serve as biological pacemakers (clocks). They are responsible for an individual’s migratory behavioral ...

Analysis of finite element approximation and iterative methods for timedependent Maxwell problems (Texas A&M University, 20040930)In this dissertation we are concerned with the analysis of the finite element method for the timedependent Maxwell interface problem when Nedelec and RaviartThomas finite elements are employed and preconditioning ...

(20111021)We study the integral equation related to the three and higher dimensional superradiance problem. Collective radiation phenomena has attracted the attention of many physicists and chemists since the pioneering work of R. ...

(20130506)A surface reconstruction and image enhancement nonlinear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally ...

(20090602)In recent years, new approaches to the problem of Automated Target Recognition using techniques of shape theory and algebraic geometry have been explored. The power of this shape theoretic approach is that it allows one ...

This research aims to investigate the impact of various Neural Architectures (NAs) on the performance of machine learning models in the context of the deterministic game of Othello, with the goal of providing insights into ...

(20140707)In the dissertation, we apply classical potential theory to study Property (P_(q)) and its relation with the compactness of the ∂ ̅Neumann operator N_(q). The main results in the dissertation consist of four parts. In ...

Approximation and interpolation employing divergencefree radial basis functions with applications (Texas A&M University, 20040930)Approximation and interpolation employing radial basis functions has found important applications since the early 1980's in areas such as signal processing, medical imaging, as well as neural networks. Several ...

(Texas A&M University, 20040930)The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as ...

(20111021)We study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous ...

(1981)This report concludes a year of investigative research in artificial intelligence. Artificial intelligence is a field of computer science in which recreating human behavior in machines is the main subject; the field is ...