Mathematics Commons^™

Contiguity Distance Between Simplicial Maps, Ayşe Borat, Mehmetci̇k Pamuk, Tane Vergi̇li̇

Turkish Journal of Mathematics

For simplicial complexes and simplicial maps, the notion of being in the same contiguity class is defined as the discrete version of homotopy. In this paper, we study the contiguity distance, $SD$, between two simplicial maps adapted from the homotopic distance. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion. Moreover, we present the behaviour of $SD$ under the barycentric subdivision, and its relation with strong collapsibility of a simplicial complex.

On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n

Turkish Journal of Mathematics

In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.

Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram

Turkish Journal of Mathematics

In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example.

Numerical Solutions Of Differential Equations Having Cubic Nonlinearity Using Boole Collocation Method, Kübra Erdem Bi̇çer, Hale Gül Dağ

Turkish Journal of Mathematics

The aim of the study is to develop a numerical method for the solution of cubic nonlinear differential equations in which the numerical solution is based on Boole polynomials. That solution is in the form of the truncated series and gives approximate solution for nonlinear equations of cubic type. In this method, firstly, the matrix form of the serial solution is set and the nonlinear differential equation is converted into a matrix equation system. By adding the effect of both the conditions of the problem and the collocation points to this system of equations, we obtain the new system of …

Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov

Turkish Journal of Mathematics

In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ and $Y$ are complex Banach spaces, and $\rho$ is a general binary relation on $Y$. We also analyze various classes of multidimensional Levitan almost periodic functions in general metric and multidimensional Bebutov uniformly recurrent functions in general metric. We provide several applications of our theoretical results to the abstract Volterra integro-differential equations and the partial differential equations.

Clairaut Riemannian Maps, Kiran Meena, Akhilesh Yadav

Turkish Journal of Mathematics

In this paper, first we define Clairaut Riemannian map between Riemannian manifolds by using a geodesic curve on the base space and find necessary and sufficient conditions for a Riemannian map to be Clairaut with a nontrivial example. We also obtain necessary and sufficient condition for a Clairaut Riemannian map to be harmonic. Thereafter, we study Clairaut Riemannian map from Riemannian manifold to Ricci soliton with a nontrivial example. We obtain scalar curvatures of $rangeF_\ast$ and $(rangeF_\ast)^\bot$ by using Ricci soliton. Further, we obtain necessary conditions for the leaves of $rangeF_\ast$ to be almost Ricci soliton and Einstein. We also …

Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu

Turkish Journal of Mathematics

This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems for Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay.

Generating Functions For Reciprocal Catalan-Type Sums: Approach To Linear Differentiation Equation And ($P$-Adic) Integral Equations, Damla Gün, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the $p$-adic Volkenborn integral …

Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran

Turkish Journal of Mathematics

In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of $T_{i}, i=0,1,2$, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and $T_{i}, i=1,2$, proximity spaces. Finally, we present Tietze extension theorem and Urysohn's lemma for proximity spaces.

Unipotence In Positive Characteristic For Groups Of Finite Morley Rank, Jules Gael Tindzogho Ntsiri

Turkish Journal of Mathematics

In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank $G$ has a definable connected subgroup $H$ whose derived subgroup $H'$ is a good unipotent subgroup of finite Morley rank.

Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz

Turkish Journal of Mathematics

In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help …

Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova

Turkish Journal of Mathematics

In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of …

Hart, Robert W., Papers, 1924-1966, Special Collections, Leonard H. Axe Library

Finding Aids

Personal documents, correspondence, and financial records of Robert W. Hart, former professor at Pittsburg State University.

Robert William Hart was born in 1896 to William and Sarah Hart and grew up in Crawford County, Kansas. In 1916 he graduated from the State Manual Training Normal School (now Pittsburg State University), and found early work as an engineer. Robert served as an ensign in the navy during World War I. He taught in the public schools in Fort Scott and Pittsburg from 1916-1918; 1921-1923. In 1920 he married Retta Statler and they had two children. In 1923 he was hired as …

Lattice Extensions And Zeros Of Multilinear Polynomials, Maxwell Forst

CGU Theses & Dissertations

We treat several problems related to the existence of lattice extensions preserving certain geometric properties and small-height zeros of various multilinear polynomials. An extension of a Euclidean lattice $L_1$ is a lattice $L_2$ of higher rank containing $L_1$ so that the intersection of $L_2$ with the subspace spanned by $L_1$ is equal to $L_1$. Our first result provides a counting estimate on the number of ways a primitive collection of vectors in a lattice can be extended to a basis for this lattice. Next, we discuss the existence of lattice extensions with controlled determinant, successive minima and covering radius. In …

Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel

Turkish Journal of Mathematics

In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]=E_1E_2-E_2E_1$ involving idempotents $E_1,E_2$ in certain subrings of $M_{2}(\mathbb{Z})$.

Precalculus, 3rd Edition, Thomas Tradler, Holly Carley

Open Educational Resources

This text, our third edition, contains notes for a course in precalculus as it is taught at New York City College of Technology, CUNY, where it is offered under the course number MAT 1375. Our approach is calculator-based. As of the third edition of this text, we use the Desmos graphing calculator to analyze and solve many of the examples studied in this course. An introduction to the Desmos graphing calculator appears in Chapter 4. Moreover, we are very grateful to be able to include in this edition many wonderful illustrations of the cartoon characters featured on the cover of …

The Magic Ratio Of Circles, Admin Stem For Success

STEM for Success Showcase

The ratio of a circle's circumference to diameter

• What pi is

Use logic to sense that the diameter and circumference of a circle will always be related

Platonic Solids Activity Plan, Admin Stem For Success

STEM for Success Showcase

No abstract provided.

Symbolic Logic, Tony Roy

Books

Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel's completeness and incompleteness theorems. The text naturally divides into two volumes, the first for reasoning in logic, the second for reasoning about it.

The first volume includes parts I and II of the text. Part I introduces the complete classical predicate calculus with equality, including both axiomatic and natural derivation systems. Part II transitions to methods for reasoning about logic, including direct reasoning from definitions and mathematical induction.

The second volume includes parts III and IV of the text. Part III develops basic results in …

A Clock Model For Planetary Conjunctions, Sunil Chebolu

Faculty Publications – Mathematics

[In lieu of an abstract, an excerpt from the introduction is presented]:

On 21 December 2020 the night sky offered a beautiful astronomical treat for stargazers worldwide. An exceptionally rare conjunction of Jupiter and Saturn brought them to 0.1 degrees of angular separation – a fifth of the full moon's diameter. It marked their closest approach since 1623 and the closest visible conjunction since 1226 (almost 800 years ago!). Astronomy enthusiasts crossed their fingers for clear skies and waited eagerly for this event. The internet and social media were inundated with pictures and news reports, celebrating the great conjunction of …

Measuring Racial Segregation In Los Angeles County Using Random Walks, Zarina Kismet Dhillon

CMC Senior Theses

As of now there is no universal quantitative measure used to evaluate racial segregation in different regions. This paper begins by providing a history of segregation, with an emphasis on the impact of redlining in the early 20th century. We move to its effect on the current population distribution in Los Angeles, California, and then provide an overview of the mathematical concepts that have been used in previous measurements of segregation. We then introduce a method that we believe encompasses the most representative aspects of preceding work, proposed by Sousa and Nicosia in their work on quantifying ethnic segregation in …

Counting Spanning Trees On Triangular Lattices, Angie Wang

CMC Senior Theses

This thesis focuses on finding spanning tree counts for triangular lattices and other planar graphs comprised of triangular faces. This topic has applications in redistricting: many proposed algorithmic methods for detecting gerrymandering involve spanning trees, and graphs representing states/regions are often triangulated. First, we present and prove Kirchhoff’s Matrix Tree Theorem, a well known formula for computing the number of spanning trees of a multigraph. Then, we use combinatorial methods to find spanning tree counts for chains of triangles and 3 × n triangular lattices (some limiting formulas exist, but they rely on higher level mathematics). For a chain of …

On Regular D-Handicap Tournaments, Bryan Freyberg, Melissa S. Keranen

Michigan Tech Publications, Part 1

k-regular d-handicap tournament is an incomplete tournament in which n teams, ranked according to the natural numbers, play exactly k < n − 1 different teams exactly once and the strength of schedule of the ith ranked team is d more than the (i − 1)st ranked team for some d ≥ 1. That is, strength of schedules increase arithmetically by d with strength of team. A d-handicap distance antimagic labeling of a graph (Formula Presented)forms an arithmetic sequence with difference d ≥ 1. A graph G which admits such a labeling is called a d-handicap graph. Constructing a k-regular d-handicap tournament on n teams is equivalent to finding a k-regular d-handicap graph of order n. For d = 1 and n even, the existence has recently been completely settled for all pairs (n, k), and some results are known for d = 2. For d > 2, the only known result is restricted to the case where n is divisible by 2d+2. In this paper, we construct infinite families of d-handicap graphs where the order is not restricted to a power of 2.

Festival Of Research Abstracts, 2023, College Of Science And Mathematics, Wright State University

Festival of Research

The collection of abstracts accepted for the 2023 Festival of Research hosted by the Wright State University College of Science and Mathematics.

More Properties Of Optimal Polynomial Approximants In Hardy Spaces, Raymond Cheng, Christopher Felder

Mathematics & Statistics Faculty Publications

We study optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, H^p (1 < p < ∞). For fixed f ∈ H^p and n ∈ N, the OPA of degree n associated to f is the polynomial which minimizes the quantity ∥qf −1∥_p over all complex polynomials q of degree less than or equal to n. We begin with some examples which illustrate, when p ≠ 2, how the Banach space geometry makes the above minimization problem interesting. We then weave through various results concerning limits and roots of these polynomials, including results which show that OPAs can be witnessed as solutions …

Looped Homology Theory Of Weighted Reflexive Graphs, Sahawat Wongkhunen

Chulalongkorn University Theses and Dissertations (Chula ETD)

In recent years, the notions of discrete homotopy for graphs, such as A-homotopy, x-homotopy and fundamental groupoid for graphs, have been introduced. Next, these theories are developed and extended for further studies, motivating us to study the discrete homology theory of graphs. This dissertation develops the notion of a looped fundamental groupoid for graphs to the isotropy group of the vertex v in the fundamental groupoid. We show that it is similar to the classical fundamental group of a topological space and the A-theory of graphs in some sense. Then, we apply this theory's idea to the looped fundamental group …

Analytical Formula For Conditional Moments Of Extended Heston-Cev Hybrid Model With Time-Dependent Parameters, Promsiri Anunak

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis proposes an analytical formula for the conditional moments of the extended Heston-CEV hybrid model, which is the combination of the Heston model and the March-Rosenfeld process, also known as the constant elasticity of variance (CEV) process, to model the price dynamics of the underlying asset. The formula is derived by solving a partial differential equation (PDE) that characterizes a two-dimensional process. This Monte Carlo simulation results to ensure its accuracy. Department formula is practical and more comprehensive than the existing results in the literature. The thesis also includes numerical validations by verifying the analytical formula against

On Symmetric Operator Ideals And S-Numbers, Daniel Akech Thiong

CGU Theses & Dissertations

Motivated by the well-known theorem of Schauder, we study the relationship between various s-numbers of an operator T and its adjoint T∗ between Banach spaces. For non-compact operator T ∈ L(X, Y ), we do not have a lot of information about the relationship between n-th s-number, sn(T), with sn(T∗ ), however, in chapter 2, by considering X and Y , with lifting and extension properties, respectively, we were able to obtain a relationship between sn(T) with sn(T∗ ) for certain …

Pura Vida Neutrosophic Algebra, Florentin Smarandache, Ranulfo Paiva Barbosa (Sobrinho)

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic …

A New Type Of Neutrosophic Set In Pythagorean Fuzzy Environment And Applications To Multi-Criteria Decision Making, Mahmut Can Bozyıgıt, Murat Olgun, Florentin Smarandache, Mehmet Unver

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker …