Mathematics Commons^™

Cybersecurity Of The Artificial Pancreas, D. J. Cooke, Andres Guzman, Robert Kinney, Christine Patterson, Josh Stone

Mathematics Senior Showcase 2020

We live in a world of cyber-enabled devices that enhance many aspects of life, including the treatment of diabetes. Type I Diabetes is a chronic autoimmune disorder characterized by destruction of pancreatic cells and subsequent deficiency of insulin - a crucial hormone in regulating blood glucose levels. The development of an Artificial Pancreas System is automating the maintenance of this disease by integrating wireless devices to continuously balance blood glucose levels without patient interaction. An integral part of this system is the Continuous Glucose Monitor (CGM) which wirelessly transmits blood glucose measurements every 5 minutes. CGMs and other Implantable Medical …

Construction Of A First Order Logic Theorem Prover, Luke Philip Tyler

Mathematics Senior Showcase 2020

There are many systems that have been researched in the past on automating the process of theorem proving in first-order logic. This research explores one of these systems, the tableau method. A point of interest within the tableau method is whether or not the method is sound and complete. This research was done in tandem with a computer implementation of the tableau method written in Haskell. The basic design of the implementation was to construct a fair rule for tableau expansion and expand the tableau until it was found to be closed, open, or infinite, thereby proving or disproving of …

Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …

The Lattice Of Intuitionistic Fuzzy Topologies Generated By Intuitionistic Fuzzy Relations, Soheyb Milles

Applications and Applied Mathematics: An International Journal (AAM)

We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice.

Introduce Gâteaux And Frêchet Derivatives In Riesz Spaces, Abdullah Aydın, Erdal Korkmaz

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the Gâteaux and Frêchet differentiations of functions on Riesz space are introduced without topological structure. Thus, we aim to study Gâteaux and Frêchet differentiability functions in vector lattice by developing topology-free techniques, and also, we give some relations with other kinds of operators.

An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit

Applications and Applied Mathematics: An International Journal (AAM)

In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution.

A New Approach To The Q-Conjugacy Character Tables Of Finite Groups, Ali Moghani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the Q-conjugacy character table of an arbitrary finite group and introduce a general relation between the degrees of Q-conjugacy characters with their corresponding reductions. This could be accomplished by using the Hermitian symmetric form. We provide a useful technique to calculate the character table of a finite group when its corresponding Qconjugacy character table is given. Then, we evaluate our results in some useful examples. Finally, by using GAP (Groups, Algorithms and Programming) package, we calculate all the dominant classes of the sporadic Conway group Co₂ enabling us to find all possible the integer-valued …

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulated two types of higher-order dual models for such optimization problem.Weak, strong and strict converse duality theorems are derived under higherorder generalized invexity.

On Submoduloids Of A Moduloid On Nexus, Reza Kamranialiabad, Abbas Hasankhani, Masoud Bolourian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the submoduloid of a moduloid on nexus that is generated by a subset, cyclic submoduloid and bounded sets are defined and the properties of structures on it are investigated. Also, the fractions of a moduloid on nexus are defined and shown to be isomorphic with a moduloid on nexus.

Dual Pole Indicatrix Curve And Surface, Süleyman Senyurt, Abdussamet Çalıskan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the vectorial moment vector of the unit Darboux vector, which consists of the motion of the Frenet vectors on any curve, is reexpressed in the form of Frenet vectors. According to the new version of this vector, the parametric equation of the ruled surface corresponding to the unit dual pole indicatrix curve is given. The integral invariants of this surface are rederived and illustrated by presenting with examples.

The Surface Diffusion And The Willmore Flow For Uniformly Regular Hypersurfaces, Jeremy Lecrone, Yuanzhen Shao, Gieri Simonett

Department of Math & Statistics Faculty Publications

We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The surface diffusion and Willmore flows each give rise to a fourth–order quasilinear parabolic equation with nonlinear terms satisfying a specific singular structure. We establish well–posedness of both flows for initial surfaces that are C^1+α–regular and parameterized over a uniformly regular hypersurface. For the Willmore flow, we also show long–term existence for initial surfaces which are C^1+α–close to a sphere, and we prove …

Nonlinear Multigrid Based On Local Spectral Coarsening For Heterogeneous Diffusion Problems, Chak Shing Lee, Francois Hamon, Nicola Castelletto, Panayot S. Vassilevski, Joshua A. White

Mathematics and Statistics Faculty Publications and Presentations

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of freedom and spectral decomposition of reference linear operators associated with the aggregates. For rapid convergence, it is important that the resulting coarse spaces have good approximation properties. In our approach, the approximation quality can be directly improved by including more spectral degrees of freedom in the coarsening process. Further, by exploiting local coarsening and a piecewise-constant approximation when evaluating the nonlinear component, the coarse level problems are assembled and …

On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, J. Brandes, Scott T. Parsell, C. Poulias, G. Shakan, R. C. Vaughn

Mathematics Faculty Publications

We obtain asymptotics for sums of the form

Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n),

involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has

sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon,

and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.

Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin, K. Summer Ware

Boise State University Theses and Dissertations

Memory is traditionally thought of as a biological function of the brain. In recent years, however, researchers have found that some stimuli-responsive molecules exhibit memory-like behavior manifested as history-dependent hysteresis in response to external excitations. One example is lysenin, a pore-forming toxin found naturally in the coelomic fluid of the common earthworm Eisenia fetida. When reconstituted into a bilayer lipid membrane, this unassuming toxin undergoes conformational changes in response to applied voltages. However, lysenin is able to "remember" past history by adjusting its conformational state based not only on the amplitude of the stimulus but also on its previous …

On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings, J. Sathiyaraj, A. Vadivel, O. U. Maheshwari

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate some new class of mappings called double fuzzy M-open map and double fuzzy M-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy open, double fuzzy θ semiopen, double fuzzy δ preopen, double fuzzy M open and double fuzzy e open and their respective closed mappings.

Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras, J. Z. Lobo, Y. S. Valaulikar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we shall apply symmetry analysis to some first order functional differential equations with constant coefficients. The approach used in this paper accounts for obtaining the inverse of the classification. We define the standard Lie bracket and make a complete classification of some first order linear functional differential equations with constant coefficients to solvable Lie algebras.We also classify some nonlinear functional differential equations with constant coefficients to solvable Lie algebras.

Generalized Smarandache Curves Of Spacelike And Equiform Spacelike Curves Via Timelike Second Binormal In 𝕽𝟏 𝟒, Emad Solouma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate spacelike Smarandache curves recording to the Frenet and the equiform Frenet frame of spacelike base curve with timelike second binormal vector in fourdimensional Minkowski space. Also, we compute the formulas of Frenet and equiform Frenet apparatus recording to the base curve. Furthermore, we give the geometric properties to these curves when is general helix.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Bayesian Variable Selection Methods For Genome-Wide Association Studies With Categorical Phenotypes, Benazir Rowe

UNLV Theses, Dissertations, Professional Papers, and Capstones

Genome-wide association studies (GWAS) attempt to find the associations between genetic markers and studied traits (phenotypes). The problem of GWAS is complex and various methods have been developed to approach it. One of such methods is Bayesian variable selection (BVS). We describe the BVS methods in detail and demonstrate the ability of BVS method Posterior Inference via Model Averaging and Subset Selection (piMASS) to improve the power of detecting phenotype-associated genetic loci, potentially leading to new discoveries from existing data without increasing the sample size.

We present several ways to improve and extend the applicability of piMASS for GWAS. The …

Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

A vertex coloring c : V(G) → N of a non-trivial graph G is called a sigma coloring if σ(u) is not equal to σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G)−σ(G−e) …