Physical Sciences and Mathematics Commons^™

Adding Depth To The Discussion Of Capital Budgeting Techniques, Tom Arnold, Terry D. Nixon

Finance Faculty Publications

The subject of capital budgeting generally encompasses a significant percentage of any beginning finance course with net present value (NPV) often receiving the most attention. Even after this substantial time allotment, critical assumptions and comparisons of the different techniques (such as payback period, discounted payback period, NPV and IRR) are frequently glossed over due to time constraints. Consequently, the goal of this paper is to present these non-NPV techniques in a manner that allows the beginning finance student to expeditiously see the intuition, inherent assumptions, and any connection with the more popular NPV calculation. A small portion of this paper …

Detectable Coloring Of Graphs, Henry E. Escuadro

Dissertations

A basic problem in graph theory is to distinguish the vertices of a connected graph from one another in some manner. In this study, we investigate the problemof coloring the edges of a graph in a manner that distinguishes the vertices of the graph. The method we use combines many of the features of previously introduced methods.

Let G be a connected graph of order n ≥ 3 and let c : E (G ) [arrow right] {1,2,...,k } be a coloring of the edges of G (where adjacent edges may be colored the same). For each vertex …

Bayesian Wavelet Estimation Of Partially Linear Models, Leming Qu

Leming Qu

A Bayesian wavelet approach is presented for estimating a partially linear model (PLM). A PLM consists of a linear part and a nonparametric component. The nonparametric component is represented with a wavelet series where the wavelet coefficients have assumed prior distributions. The prior for each coefficient consists of a mixture of a normal distribution and a point mass at 0. The linear parameters are assumed to have a normal prior. The hyperparameters are estimated by the marginal maximum likelihood estimator using the direct maximization. The model selection and model averaging methods give different estimates of the model parameters. MCMC computation …

Admissible Sequences, Preprojective Modules, And Reduced Words In The Weyl Group Of A Quiver, Mark Kleiner, Allen Pelley

Mathematics - All Scholarship

This paper studies connections between the preprojective modules over the path algebra of a finite connected quiver without oriented cycles, the (+)-admissible sequences of vertices, and the Weyl group. For each preprojective module, there exists a unique up to a certain equivalence shortest (+)-admissible sequence annihilating the module. A (+)-admissible sequence is the shortest sequence annihilating some preprojective module if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. These statements have the following application that strengthens known results of Howlett and Fomin-Zelevinsky. For any fixed …

Quadratic Forms And Height Functions, Lenny Fukshansky

CMC Faculty Publications and Research

The effective study of quadratic forms originated with a paper of Cassels in 1955, in which he proved that if an integral quadratic form is isotropic, then it has non-trivial zeros of bounded height. Here height stands for a certain measure of arithmetic complexity, which we will make precise. This theorem has since been generalized and extended in a number of different ways. We will discuss some of such generalizations for quadratic spaces over a fixed number field as well as over the field of algebraic numbers. Specifically, let K be either a number field or its algebraic closure, and …

Hole Dynamics In Polymer Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Lu Zou

All HMC Faculty Publications and Research

This article develops a model for the closing of a gaseous hole in a liquid domain within a two-dimensional fluid layer coupled to a Stokesian subfluid substrate, and compares this model to experiments following hole dynamics in a polymer Langmuir monolayer. Closure of such a hole in a fluid layer is driven by the line tension at the hole boundary and the difference in surface pressure within the hole and far outside it. The observed rate of hole closing is close to that predicted by our model using estimates of the line tension obtained by other means, assuming that the …

Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon

Faculty Publications

The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular materials, for example collagen and fibrin, are modelled as continua, while fibroblasts are considered as discrete units. Within this model framework, we have explored the effects that different parameters have on the alignment process, and we have used the model to investigate how manipulation of transforming growth factor-b levels can reduce scar tissue formation. We briefly review this body of work, then extend the modelling framework to investigate the role played …

Some Significant Results In The Classification Analysis Of The Spectroscopic Evaluation Of Cervical Cancer, C Shen

Mathematics Theses

Cervical Cancer is the second most common type of cancer in women worldwide (500,000 cases/year) and one of the leading causes of cancer-related mortality in women in developing countries (230,000 cases/year). The Spectrx LightTouch™ device uses light to detect chemical and structural changes in cervical tissue. Light responds differently when exposed to normal cells and cancerous cells. The purpose of this research is to find the best model that can be used to diagnose the early cervical cancerous conditions. To achieve this goal, we first tried to reduce the number of variables. We use statistical and non-statistical methods to search …

François Viète, Between Analysis And Cryptanalysis, Marco Panza

MPP Published Research

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same …

Algebraic Concepts In The Study Of Graphs And Simplicial Complexes, Christopher Michael Zagrodny

Mathematics Theses

This paper presents a survey of concepts in commutative algebra that have applications to topology and graph theory. The primary algebraic focus will be on Stanley-Reisner rings, classes of polynomial rings that can describe simplicial complexes. Stanley-Reisner rings are defined via square-free monomial ideals. The paper will present many aspects of the theory of these ideals and discuss how they relate to important constructions in commutative algebra, such as finite generation of ideals, graded rings and modules, localization and associated primes, primary decomposition of ideals and Hilbert series. In particular, the primary decomposition and Hilbert series for certain types of …

Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational …

Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar

Mathematics Faculty Publications

We investigate algorithms for reconstructing a convex body K in Rⁿ from noisy measurements of its support function or its brightness function in k directions u₁, . . . , u_k. The key idea of these algorithms is to construct a convex polytope P_k whose support function (or brightness function) best approximates the given measurements in the directions u₁, . . . , u_k (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, …

The Thermodynamic Formalism For Almost-Additive Sequences, Anna Mummert

Mathematics Faculty Research

We study the nonadditive thermodynamic formalism for the class of almost-additive sequences of potentials. We define the topological pressure PZ(Φ) of an almost-additive sequence Φ, on a set Z. We give conditions which allow us to establish a variational principle for the topological pressure. We state conditions for the existence and uniqueness of equilibrium measures, and for subshifts of finite type the existence and uniqueness of Gibbs measures. Finally, we compare the results for almost-additive sequences to the thermodynamic formalism for the classical (additive) case [10] [11] [3], the sequences studied by Barreira [1], Falconer [5], and that of Feng …

Timelike Surfaces Of Constant Mean Curvature ±1 In Anti-De Sitter 3-Space H31), Sungwook Lee

Faculty Publications

It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space H³ ₁(−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL₂R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E ³ ₁. The hyperbolic Gauß map of timelike surfaces in H³ ₁(−1), which is a close analogue of the classical …

Linear And Log-Linear Models Based On Generalized Inverse Sampling Scheme, Soumi Lahiri

Dissertations

This dissertation explores the development of novel statistical techniques and the applications in modeling rare events using generalized inverse sampling scheme. The Poisson model can be used for independent frequency count data. Also negative binomial and negative multinomial (NMn) models are applicable when there is only one rare category in the population. Here, a new model, based on generalized inverse sampling scheme, is introduced to study several rare events simultaneouly. The generalized inverse sampling scheme is used to study several rare categories of a population. Samples are drawn until a predetermined number of the total of the rare events occur. …

Mathematical Problems Arising In Interfacial Electrohydrodynamics, Dmitri Tseluiko

Dissertations

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order …

Basic Properties Of Sobolev's Spaces On Time Scales, Ravi P. Agarwal, Victoria Otero-Espinar, Kanishka Perera, Dolores R. Vivero

Mathematics and System Engineering Faculty Publications

We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of functions defined on an arbitrary open interval of the real numbers are derived.

Design Of Iteration On Hash Functions And Its Cryptanalysis., Mridul Nandi Dr.

Doctoral Theses

No abstract provided.

Automatic Recognition Of Printed And Handwritten Mathematical Expressions., Shri Sahadeb Garain Dr.

Doctoral Theses

This thesis presents a systematic study on recognition of printed and handwritten mathematical expressions. Automatic recognition of printed expressions is an essential requirement for efficient Optical Character Recognition (OCR) of scientific paper documents. On the other hand, recognition of handwritten expressions has been tried for online environment. Here expressions are written using electronic data tablet/stylus providing a convenient alternative to keyboard or mouse used for data entry into a computer.The previous studies dealing with different aspects of expression recognition are, at first, reviewed. Next, the scope of the present thesis, its layout and contributions are outlined. Discussion on OCR of …

Double Domination Edge Critical Graphs., Derrick Wayne Thacker

Electronic Theses and Dissertations

In a graph G=(V,E), a subset S ⊆ V is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uv ∈ E(G̅), the double domination number of G+uv is less than the double domination number of G. We investigate properties of double domination edge critical graphs. In particular, we characterize the double domination edge critical trees and …

On The Chromatic Number Of The Ao(2, K , K-1) Graphs., Navya Arora

Electronic Theses and Dissertations

The alphabet overlap graph is a modification of the well known de Bruijn graph. De Bruijn graphs have been highly studied and hence many properties of these graphs have been determined. However, very little is known about alphabet overlap graphs. In this work we determine the chromatic number for a special case of these graphs.

We define the alphabet overlap graph by G = AO(a, k, t, where a, k and t are positive integers such that 0 ≤ t ≤ k. The vertex set of G is the set of all k …

Trees With Unique Minimum Locating-Dominating Sets., Stephen M. Lane

Electronic Theses and Dissertations

A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.

Lecture Notes: Non-Standard Approach To J.F. Colombeau’S Theory Of Generalized Functions, Todor D. Todorov

Mathematics

In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physicists and engineers who do research on J. F. Colombeau’ theory of new generalized functions and its applications. The main purpose of our non-standard approach to Colombeau’ theory is the improvement of the properties of the scalars of the varieties of spaces of generalized functions: in our non-standard approach the sets of scalars of the functional spaces always form algebraically closed non-archimedean Cantor complete fields. In contrast, the scalars of the functional spaces in Colombeau’s theory are rings with zero divisors. The …

Pietro Paoli, Italian Algebraist, John L. Cuzzocrea, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Pietro Paoli was a leading Italian mathematician in the late 18th century. His signed letter pertaining to the death of astronomer Giuseppe Antonio Slop is translated from Italian to flowing (American) English.

Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Liouville’s 1846 introduction to the mathematical works of Galois is translated from French to flowing (American) English. It gave an overview of the tragic circumstances of the undergraduate mathematician whose originality led to major advances in abstract Algebra.

Variational Analysis In Nonsmooth Optimization And Discrete Optimal Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern methods of variational· analysis to constrained optimization and control problems generally formulated in infinite-dimensional spaces. The main attention is paid to the study of problems with nonsmooth structures, which require the usage of advanced tools of generalized differentiation. In this way we derive new necessary optimality conditions in optimization problems with functional and. operator constraints and then apply them to optimal control problems governed by discrete-time inclusions in infinite dimensions. The principal difference between finite-dimensional and infinite-dimensional frameworks of optimization and control consists of the "lack of compactness" in infinite dimensions, which …

Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov

Mathematics Faculty Publications

The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are …

Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov

Mathematics Faculty Publications

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Periodic Difference Equations, Population Biology And The Cushing-Henson Conjectures, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

We show that for a k-periodic difference equation, if a periodic orbit of period r is globally asymptotically stable (GAS), then r must be a divisor of k. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and which has a GAS periodic orbit with minimum period r. Our method uses the technique of skew-product dynamical systems. Our methods are then applied to prove two conjectures of J. Cushing and S. Henson concerning a non-autonomous Beverton-Holt equation which arises in the study of the response of a population to a periodically …