Mathematics | Open Access Articles | Digital Commons Network™

Optimal Combined Divided And Proportional Reinsurance Policy, Eriyoti Chikodza, Julius N Esunge

Communications on Stochastic Analysis

No abstract provided.

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Expert Opinions And Logarithmic Utility Maximization In A Market With Gaussian Drift, Abdelali Gabih, Hakam Kondakji, Jörn Sass, Ralf Wunderlich

Communications on Stochastic Analysis

No abstract provided.

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Portfolio Optimization Under Partial Information With Expert Opinions: A Dynamic Programming Approach, Rüdiger Frey, Abdelali Gabih, Ralf Wunderlich

Communications on Stochastic Analysis

No abstract provided.

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Optimal Premium Policy Of An Insurance Firm With Delay And Stochastic Interest Rate, Charles Wilson Mahera, Olivier Menoukeu-Pamen, Moses Mwale

Communications on Stochastic Analysis

No abstract provided.

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Modelling Financial Information By Conditioning, Dennis Ikpe, Sure Mataramvura, Ronnie Becker

Communications on Stochastic Analysis

No abstract provided.

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Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman

Journal of Humanistic Mathematics

This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.

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Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry

Journal of Humanistic Mathematics

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.

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Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta

Journal of Humanistic Mathematics

Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.

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Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson

Journal of Humanistic Mathematics

This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …

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Quantitative K-Theory And Spin Chern Numbers [Dataset], Terry A. Loring

Math and Statistics Datasets

We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this is two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine what values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to …

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A Sampling Of Popular Books For Numeracy Readers, Michael T. Catalano

Numeracy

Popular books on quantitative themes are seemingly more available than ever. In this book review, we look at five such books from a wide range of authors. Although the books are written for diverse audiences, all provide examples and discussion of concepts that could be used in courses with quantitative literacy objectives. The books are Guesstimation and Guesstimation 2.0 by Lawrence Weinstein and John A. Adam, and Weinstein, respectively; Turning Numbers into Knowledge: Mastering the Art of Problem Solving, by Jonathan G. Koomey; How to Measure Anything: Finding The Value of “Intangibles” in Business, by Douglas W. Hubbard; and …

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Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde

STAR Program Research Presentations

This project explores the stability analysis of a given flow field. Specifically, where the peak disturbance occurs in a flow as this is the disturbance that is most likely to occur. In rocket combustion, it is important to understand where the maximum disturbance occurs so that the mixing of fuel can be stabilized. The instabilities are the results of frequencies in the area surrounding the flow field. The linear stability governing equations are employed to better understand the disturbance. The governing equations for continuity and momentum in the x and y directions are used to form an equation for the …

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A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek

HMC Senior Theses

The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.

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The Most-Perfect 4*4 Puzzle Game, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Draft of the 'Solution Page' for Jeremiah's puzzle "The Most Perfect 4*4 Puzzle Game", which was exchanged at the 2014 London International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exhange them. Includes e-mail correspondence with editor of the book.

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A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach

Department of Math & Statistics Faculty Publications

We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.

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Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

We discuss the boundary behavior of functions in star invariant subspaces (BH²)¹, where B is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of B where B does not admit a derivative in the sense of Carathéodory.

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A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus

Department of Math & Statistics Faculty Publications

Every link in R³ can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.

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On The Dimension Of A Certain Measure Arising From A Quasilinear Elliptic Partial Differential Equation, Murat Akman

Theses and Dissertations--Mathematics

We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution of a certain quasilinear elliptic partial differential equation in a simply connected domain in the plane. We also assume that the solution vanishes on the boundary of the domain. Then it is shown that the Hausdorff dimension of this measure is less than one, equal to one, greater than one depending on the homogeneity of the certain function. This work generalizes the work of Makarov when the partial differential equation is the usual Laplace's equation and the work of Lewis and his coauthors when …

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On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding noncommutative L2 of sample-space. We define a stochastic integral for our family of free processes.

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Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza

MPP Published Research

We follow two of the many paths leading from Newton’s to Euler’s scientific productions, and give an account of Euler’s role in the reception of some of Newton’s ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton’s conceptions within a new conceptual frame also influenced by Descartes’s views sand Leibniz’s formalism.

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A Proof-Theoretic Semantic Analysis Of Dynamic Epistemic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimić

Engineering Faculty Articles and Research

The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which have been successfully applied to diverse scientific disciplines, but the proof theoretic treatment of which presents many difficulties. After an illustration of the proof-theoretic semantic principles most relevant to the treatment of logical connectives, we turn to illustrating the main features of display calculi, a proof-theoretic paradigm which has been successfully employed to give a proof-theoretic semantic account of modal and substructural …

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New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …

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Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.

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Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does …

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Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder

Senior Independent Study Theses

An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …

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Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

College of Graduate Studies: Theses & Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …

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Elements Of Convergence Approach Theory, William D. Trott

College of Graduate Studies: Theses & Dissertations

We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.

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Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

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Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel

University Faculty and Staff Publications

In this paper we investigate the relation between the multiplicities of split strongly abelian p-chief factors of finite-dimensional restricted Lie algebras and first degree restricted cohomology. As an application we obtain a characterization of solvable restricted Lie algebras in terms of the multiplicities of split strongly abelian p-chief factors. Moreover, we derive some results in the representation theory of restricted Lie algebras related to the principal block and the projective cover of the trivial irreducible module of a finite-dimensional restricted Lie algebra. In particular, we obtain a characterization of finite-dimensional solvable restricted Lie algebras in terms of the second Loewy …

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A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi

Publications

As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e., we restrict the discussion to the so called European options. Now, for a simple illustration of …

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Full-Text Articles in Mathematics

Optimal Combined Divided And Proportional Reinsurance Policy, Eriyoti Chikodza, Julius N Esunge

Communications on Stochastic Analysis

Expert Opinions And Logarithmic Utility Maximization In A Market With Gaussian Drift, Abdelali Gabih, Hakam Kondakji, Jörn Sass, Ralf Wunderlich

Communications on Stochastic Analysis

Portfolio Optimization Under Partial Information With Expert Opinions: A Dynamic Programming Approach, Rüdiger Frey, Abdelali Gabih, Ralf Wunderlich

Communications on Stochastic Analysis

Optimal Premium Policy Of An Insurance Firm With Delay And Stochastic Interest Rate, Charles Wilson Mahera, Olivier Menoukeu-Pamen, Moses Mwale

Communications on Stochastic Analysis

Modelling Financial Information By Conditioning, Dennis Ikpe, Sure Mataramvura, Ronnie Becker

Communications on Stochastic Analysis

Game Theory Meets The Humanities And Both Win Or Book Review: Game Theory And The Humanities: Bridging Two Worlds, By Steven J. Brams, Karl-Dieter Crisman

Journal of Humanistic Mathematics

Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry

Journal of Humanistic Mathematics

Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta

Journal of Humanistic Mathematics

Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson

Journal of Humanistic Mathematics

Quantitative K-Theory And Spin Chern Numbers [Dataset], Terry A. Loring

Math and Statistics Datasets

A Sampling Of Popular Books For Numeracy Readers, Michael T. Catalano

Numeracy

Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde

STAR Program Research Presentations

A Mathematical Framework For Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek

HMC Senior Theses

The Most-Perfect 4*4 Puzzle Game, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

A Twisted Dimer Model For Knots, Heather M. Russell, Moshe Cohen, Oliver Dasbach

Department of Math & Statistics Faculty Publications

Bad Boundary Behavior In Star Invariant Subspaces I, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

A Reduced Set Of Moves On One-Vertex Ribbon Graphs Coming From Links, Heather M. Russell, Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Neal W. Stoltzfus

Department of Math & Statistics Faculty Publications

On The Dimension Of A Certain Measure Arising From A Quasilinear Elliptic Partial Differential Equation, Murat Akman

Theses and Dissertations--Mathematics

On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon

Mathematics, Physics, and Computer Science Faculty Articles and Research

Euler, Reader Of Newton: Mechanics And Algebraic Analysis, Sébastien Maronne, Marco Panza

MPP Published Research

A Proof-Theoretic Semantic Analysis Of Dynamic Epistemic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimić

Engineering Faculty Articles and Research

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder

Senior Independent Study Theses

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

College of Graduate Studies: Theses & Dissertations

Elements Of Convergence Approach Theory, William D. Trott

College of Graduate Studies: Theses & Dissertations

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel

University Faculty and Staff Publications

A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi

Publications