Digital Commons Network^™

A Note On $Ss$-Supplement Submodules, Emi̇ne Önal Kir

Turkish Journal of Mathematics

In this paper, we describe $ss$-supplement submodules in terms of a special class of endomorphisms. Let $R$ be a ring with semisimple radical and $P$ be a projective $R-$module. We show that there is a bijection between ss-supplement submodules of $P$ and ss-supplement submodules of $End_{R}(P)$. Moreover, we define radical-s-projective modules as a generalization of projective modules. We prove that every $ss$-supplement submodule of a projective $R-$module is radical-s-projective over the ring $R$ with semisimple radical. We show that over $SSI$-ring $R$, every radical-s-projective $R-$module is projective. We provide that over a ring $R$ with semisimple radical, every $ss$-supplement submodule …

Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro

Turkish Journal of Mathematics

In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.

Numerical Solution For Benjamin-Bona-Mahony-Burgers Equation With Strang Time-Splitting Technique, Meli̇ke Karta

Turkish Journal of Mathematics

In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the …

Bi-Periodic Incomplete Horadam Numbers, Eli̇f Tan, Mehmet Dağli, Amine Belkhir

Turkish Journal of Mathematics

In this paper, we introduce bi-periodic~incomplete~Horadam numbers as a natural generalization of incomplete Horadam numbers. We study their basic properties and provide recurrence relations. In particular, we derive the generating function of these numbers.

On Solvability Of Homogeneous Riemann Boundary Value Problems In Hardy-Orlicz Classes, Yusuf Zeren, Fi̇dan A. Ali̇zadeh, Feyza Eli̇f Dal

Turkish Journal of Mathematics

This work deals with the Orlicz space and the Hardy-Orlicz classes generated by this space, which consist of analytic functions inside and outside the unit disk. The homogeneous Riemann boundary value problems with piecewise continuous coefficients are considered in these classes. New characteristic of Orlicz space is defined which depends on whether the power function belongs to this space or not. Relationship between this characteristic and Boyd indices of Orlicz space is established. The concept of canonical solution of homogeneous problem is defined, which depends on the argument of the coefficient. In terms of the above characteristic, a condition on …

On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel

Turkish Journal of Mathematics

In this paper, we deal with two-person zero-sum games with fuzzy goals. We investigated the cases where the membership functions of the players are nonlinear. We examined how the solutions should be if the membership functions of players were exponential functions. In case players' membership functions are exponential, we developed a new method for the maximin solution according to a degree of attainment of the fuzzy goals. An application was made to show the effectiveness of the method.

On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova

Turkish Journal of Mathematics

In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations.

Geodesics And Natural Complex Magnetic Trajectories On Tangent Bundles, Mohamed Tahar Kadaoui Abbassi, Noura Amri

Turkish Journal of Mathematics

In this paper, we investigate geodesics of the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ endowed with an arbitrary pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. Then considering a class of naturally defined almost complex structures on $TM$, constructed by V. Oproiu, we construct a class of magnetic fields and we characterize the corresponding magnetic curves on $TM$, when $(M,g)$ is a space form.

Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico

Turkish Journal of Mathematics

A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of a connected stick figure (or any reduced and connected curve) $X\subset \mathbb{P}^r$ such that $\deg (X)=d$ and $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem of obtaining all arithmetic genera below the maximal one.

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 …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice Price

Mathematics Sciences: Faculty Publications

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Linking In Cyclic Branched Covers And Satellite (Non)-Homomorphisms, Patricia Cahn, Alexandra Kjuchukova

Mathematics Sciences: Faculty Publications

Let K⊂S3 be a knot and η,γ⊂S3∖K be simple closed curves. Denote by Σq(K) the q-fold cyclic branched cover of K. We give an explicit formula for computing the linking numbers between lifts of η and γ to Σq(K). As an application, we evaluate, in a variety of cases, an obstruction to satellite operations inducing homomorphisms on smooth concordance.

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 …