Applied Mathematics Commons^™

Computational Modeling In Applied Problems: Collected Papers On Econometrics, Operations Research, Game Theory And Simulation, Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan

Branch Mathematics and Statistics Faculty and Staff Publications

Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.

Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

Markov Switching And Jump Diffusion Models With Applications In Mathematical Finance, Shengkun Xie

Theses and Dissertations (Comprehensive)

In this thesis, we study some jump diffusion models with Markov switching and transition densities for Markov switching diffusion processes with and without an absorbing barrier. We work out some analytical results, which have useful applications in mathematical finance and other related fields. The first-passage time problem for a Markov switching model is also studied and European type options and lookback options are computed in closed-form as examples to show that these models can be applied in practice. We apply optimization methods and kernel smoothing techniques to produce some important numerical results that show that jump diffusion with Markov switching …

Classifying Quadratic Number Fields Up To Arf Equivalence, Jeonghun Kim

LSU Doctoral Dissertations

Two number fields K and L are said to be Arf equivalent if there exists a bijection T : ­Ω_K → Ω_­L of places of K and of L such that K_P and L_TP are locally Arf equivalent for every place P ε Ω_K. That is, |K^*_p/K^*2_p| = |L^*_TP/L^*2_TP|, type[( , )_P] = type[( , )_TP], and Arf(r_P ) = Arf(r_TP ) for every place P ε Ω_K, where r_P is the local …

Limit Theorems For Weighted Stochastic Systems Of Interacting Particles, Jie Wu

LSU Doctoral Dissertations

The goal of this dissertation is to (a) establish the weak convergence of empirical measures formed by a system of stochastic differential equations, and (b) prove a comparison result and compactness of support property for the limit measure. The stochastic system of size n has coefficients that depend on the empirical measure determined by the system. The weights for the empirical measure are determined by a further n-system of stochastic equations. There is a random choice among N types of weights. The existence and uniqueness of solutions of the interacting system, weak convergence of the empirical measures, and the identification …

Representation Properties Of Definite Lattices In Function Fields, Jean Edouard Bureau

LSU Doctoral Dissertations

This work is made of two different parts. The first contains results concerning isospectral quadratic forms, and the second is about regular quadratic forms. Two quadratic forms are said to be isospectral if they have the same representation numbers. In this work, we consider binary and ternary definite integral quadratic form defined over the polynomial ring F[t], where F is a finite field of odd characteristic. We prove that the class of such a form is determined by its representation numbers. Equivalently, we prove that there is no nonequivalent definite F[t]-lattices of rank 2 or 3 having the same theta …

An Inverse Homogenization Design Method For Stress Control In Composites, Michael Stuebner

LSU Doctoral Dissertations

This thesis addresses the problem of optimal design of microstructure in composite materials. The work involves new developments in homogenization theory and numerical analysis. A computational design method for grading the microstructure in composite materials for the control of local stress in the vicinity of stress concentrations is developed. The method is based upon new rigorous multiscale stress criteria connecting the macroscopic or homogenized stress to local stress fluctuations at the scale of the microstructure. These methods are applied to three different types of design problems. The first treats the problem of optimal distribution of fibers with circular cross section …

Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari

LSU Doctoral Dissertations

The thesis is mainly concerned about properties of the so-called Filippov operator that is associated with a differential inclusion x'(t) ε F(x(t)) a.e. t ε [0,T], where F : Rⁿ → Rⁿ is given set-valued map. The operator F produces a new set-valued map F[F], which in effect regularizes F so that F[F] has nicer properties. After presenting its definition, we show that F[F] is always upper-semicontinuous as a map from Rⁿ to the metric space of compact subsets of Rⁿ endowed with the Hausdorff metric. Our main approach is to study the …

Integral Cohomology Of The Siegel Modular Variety Of Degree Two And Level Three, Mustafa Arslan

LSU Doctoral Dissertations

In this thesis work Deligne's spectral sequence E^p,q_r with integer coefficients for the embedding of the Siegel modular variety of degree two and level three, A₂(3) into its Igusa compactification, A₂(3)*, is investigated. It is shown that E₃ = E_∞ and this information is applied to compute the cohomology groups of A₂(3) over the integers.

Topics In Quantum Topology, Khaled Moham Qazaqzeh

LSU Doctoral Dissertations

In chapter 1, which represents joint work with Gilmer, we define an index two subcategory of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes the result of [9] where surfaces are equipped with Lagrangian subspaces of their rational first homology. To define such subcategory, we give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over R. In chapter 2, we find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus …

On Moment Conditions For The Girsanov Theorem, See Keong Lee

LSU Doctoral Dissertations

In this dissertation, the well-known Girsanov Theorem will be proved under a set of moment conditions on exponential processes. Our conditions are motivated by the desire to avoid using the local martingale theory in the proof of the Girsanov Theorem. Namely, we will only use the martingale theory to prove the Girsanov Theorem. Many sufficient conditions for the validity of the Girsanov Theorem have been found since the publication of the result by Girsanov in 1960. We will compare our conditions with some of these conditions. As an application of the Girsanov Theorem, we will show the nonexistence of an …

The Convergence Of V-Cycle Multigrid Algorithms For Axisymmetric Laplace And Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknowns. This is contrary to suggestions in the existing literature that line relaxations and semicoarsening are needed in multigrid algorithms to overcome difficulties caused by the singularities in the axisymmetric Maxwell problems. Our multigrid analysis proceeds by applying the well known regularity …