Mathematics Commons^™

Minimizing Graph Of The Connected Graphs Whose Complements Are Bicyclic With Two Cycles, Muhammad Javaid

Turkish Journal of Mathematics

In a certain class of graphs, a graph is called minimizing if the least eigenvalueof its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, we characterize the minimizinggraph among all the connected graphs that belong to a class of graphs whose complements are bicyclic with two cycles.

A Note On The Conjugacy Problem For Finite Sylow Subgroups Of Linear Pseudofinite Groups, Pinar Uğurlu Kowalski̇

Turkish Journal of Mathematics

We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.

On The Extended Spectrum Of Some Quasinormal Operators, Meltem Sertbaş, Fati̇h Yilmaz

Turkish Journal of Mathematics

In this paper we consider some extended eigenvalue problems for some quasinormal operators. The spectrum of an algebra homomorphism defined by a compact normal operator is also investigated.

More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic

Turkish Journal of Mathematics

In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive.The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.

Some Notes On $Gqn$ Rings, Long Wang, Junchao Wei

Turkish Journal of Mathematics

A ring $R$ is called ageneralized quasinormal ring (abbreviated as $GQN$ ring) if $ea∈N(R)$ for each $e∈ E(R)$ and $a∈ N(R)$. The class of $GQN$ rings is a proper generalization of quasinormal rings and $NI$ rings. Many properties of quasinormal rings are extended to $GQN$ rings. For a$GQN$ ring $R$ and $a∈ R$, it is shown that:1) if $a$ is a regular element, then $a$ is a strongly regular element;2) if $a$ is an exchange element, then $a$ is clean;3) if $R$ is a semiperiodic ring with $J(R)\neq N(R)$, then $R$ is commutative;4) if $R$ is an $MVNR$, then $R$ …

A Novel Kind Of Akns Integrable Couplings And Their Hamiltonian Structures, Yu-Juan Zhang, Wen-Xiu Ma, Ömer Ünsal

Turkish Journal of Mathematics

We present a novel hierarchy of AKNS integrable couplings based on a specific semidirect sum of Lie algebras associated with sl$(2)$. By applying the variational identity, we derive a bi-Hamiltonian structure of the resulting coupling systems, thereby showing their Liouville integrability.

Modules Satisfying Double Chain Condition On Nonfinitely Generated Submodules Have Krull Dimension, Maryam Davoudian

Turkish Journal of Mathematics

We prove the result in the title. We study submodules $N$ of a module $M$ such that whenever $\frac{M}{N}$ satisfies the double infinite chain condition so does $M$.Moreover, we observe that an $\alpha $-atomic module, where $\alpha\geq 2$ is an ordinal number, satisfies the previous chain if and only if it satisfies the descending chain condition on nonfinitely generated submodules.

Arf Numerical Semigroups, Sedat İlhan, Hali̇l İbrahi̇m Karakaş

Turkish Journal of Mathematics

The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup$S$ and its Lipman semigroup $L(S).$ This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.

On Hölder Continuity Of Approximate Solution Maps To Vector Equilibrium Problems, Lam Quoc Anh, Kien Trung Nguyen, Tran Ngoc Tam

Turkish Journal of Mathematics

In this article, we considerparametric vector equilibrium problems in normed spaces. Sufficientconditions for Hölder continuity of approximate solution mappingswhere they are set-valued are established. As applications of theseresults, the Hölder continuity of the approximate solutionmappings for vector optimization problems and vector variationalinequalities are derived at the end of the paper. Our results arenew and include the existing ones in the literature.

Universal Central Extensions Of $\Mathfrak{Sl}(M, N, A)$ Over Associative Superalgebras, Xabier García-Martínez, Manuel Ladra

Turkish Journal of Mathematics

We find the universal central extension of the matrix superalgebras $\mathfrak{sl}(m, n, A)$, where $A$ is an associative superalgebra and $m+n = 3, 4$, and its relation with the Steinberg superalgebra $\mathfrak{st}(m, n,A)).$ We calculate $H_2$ $(\mathfrak{sl}(m, n,A))$ and $H_2$ $(\mathfrak{st}(m, n,A))$. Finally, we introduce a new method using the nonabelian tensor product of Lie superalgebras to and the connection between $H_2$ $(\mathfrak{sl}(m, n, A))$ and the cyclic homology of associative superalgebras for $m+n \geq 3$.

Generalization Of The Gauss--Lucas Theorem For Bicomplex Polynomials, Mahmood Bidkham, Sara Ahamadi

Turkish Journal of Mathematics

The aim of this paper is to extend the domain of the Gauss—Lucas theorem from the set of complex numbers to the set of bicomplex numbers. We also discuss a bicomplex version of another compact generalization of the Gauss—Lucas theorem.

Piecewise Asymptotically Almost Periodic Solution Of Neutral Volterra Integro-Differential Equations With Impulsive Effects, Zhinan Xia

Turkish Journal of Mathematics

In this paper, we investigate the existence and uniqueness ofa piecewise asymptotically almost periodic mild solution tononautonomous neutral Volterra integro-differential equations withimpulsive effects in Banach space. The working tools are based onthe Krasnoselskii's fixed point theorem and semigroup theory. Inorder to illustrate our main results, we study the piecewiseasymptotically almost periodic solution of the impulsive partialdifferential equations with Dirichlet conditions.

Evaluation Of Euler-Like Sums Via Hurwitz Zeta Values, Ayhan Di̇l, Istvan Mezo, Mehmet Cenkci̇

Turkish Journal of Mathematics

In this paper we collect two generalizations of harmonic numbers (namelygeneralized harmonic numbers and hyperharmonic numbers) under one roof.Recursion relations, closed-form evaluations, and generating functions of thisunified extension are obtained. In light of this notion we evaluate someparticular values of Euler sums in terms of odd zeta values. We alsoconsider the noninteger property and some arithmetical aspects of this unifiedextension.

On The Bounds Of The Forgotten Topological Index, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami

Turkish Journal of Mathematics

The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph $G.$ In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus--Gaddum-type inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.

On Armendariz-Like Properties In Amalgamated Algebras Along Ideals, Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi

Turkish Journal of Mathematics

Let $f: A\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ)$ introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for $A\bowtie^fJ$ to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.

On Generalized Kropina Change Of $M$Th Root Finsler Metrics With Special Curvature Properties, Bankteshwar Tiwari, Ghanashyam Kr. Prajapati

Turkish Journal of Mathematics

In the present paper, we consider generalized Kropina change of $m$th root Finsler metrics and prove that every generalized Kropina change of $m$th root Finsler metrics with isotropic Berwald curvature, isotropic mean Berwald curvature, relatively isotropic Landsberg curvature, and relatively isotropic mean Landsberg curvature reduces to the Berwald metric, weakly Berwald metric, Landsberg metric, and weakly Landsberg metric, respectively. We also show that every generalized Kropina change of $m$th root Finsler metrics with almost vanishing $\textbf{H}$-curvature has vanishing $\textbf{H}$-curvature.

Sine, Cosine, And Tangent Table: 0 To 360 Degrees, Paul Royster

Department of Mathematics: Class Notes and Learning Materials

In helping with my high school student's math homework, I was astonished to find no trig tables in the 800-page textbook. I was further astonished to find no printable version online that extended beyond 90°.

While most smartphones will tell you the sine of an angle, they will not necessarily tell you the angle for which the sine is x. And since multiple angles may have the same sine (e.g. 59° and 121°), it seems useful to see the numerical progression of the functions in addition to their graphical representation.

Here is a printable sine-cosine-tangent table for all integer angle …

The Element Spectrum Of A Graph, Milisha Hart-Simmons

Electronic Theses and Dissertations

Characterizations of graphs and matroids that have cycles or circuits of specified cardinality have been given by authors including Edmonds, Junior, Lemos, Murty, Reid, Young, and Wu. In particular, a matroid with circuits of a single cardinality is called a Matroid Design. We consider a generalization of this problem by assigning a weight function to the edges of a graph. We characterize when it is possible to assign a positive integer value weight function to a simple 3-connected graph G such that the graph G contains an edge that is only in cycles of two different weights. For example, as …

Orthosymmetric Maps And Polynomial Valuations, Stephan Christopher Roberts

Electronic Theses and Dissertations

We present a characterization of orthogonally additive polynomials on vector lattices as orthosymmetric multilinear maps. Our proof avoids partitionaly orthosymmetric maps and results that represent orthogonally additive polynomials as linear maps on a power. We also prove band characterizations for order bounded polynomial valuations and for order continuous polynomials of order bounded variation. Finally, we use polynomial valuations to prove that a certain restriction of the Arens extension of a bounded orthosymmetric multilinear map is orthosymmetric.

Hybrid Stochastic Systems: Numerical Methods, Limit Results, And Controls, Tuan A. Hoang

Wayne State University Dissertations

This dissertation is concerned with the so-called stochastic hybrid systems, which are

featured by the coexistence of continuous dynamics and discrete events and their interactions. Such systems have drawn much needed attentions in recent years. One of the main reasons is that such systems can be used to better reflect the reality for a wide range of applications in networked systems, communication systems, economic systems, cyber-physical systems, and biological and ecological systems, among others. Our main interest is centered around one class of such hybrid systems known as switching diffusions. In such a system, in addition to the driving force …

01: Quadratic Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.

03: Poly Basics 2, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.

17: Plotting S(N), Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.

01: Creating Derivative, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

CreatingDerivative.nb takes any function and an x-window and animates a tangent line while plotting the value of the derivative.

04: Ivt, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

IVT.nb allows the user to examine the Intermediate Value Theorem. Consider the graphs to examine whether or not the conclusions of the theorem hold.

07: Riemann Sums, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RiemannSums.nb allows the user to input a function, and x-interval, and a maximum value of n, the number of rectangles. This animates Riemann and trapezoidal sums.

14: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.

A Comprehensive Analysis Of Team Streakiness In Major League Baseball: 1962-2016, Paul H. Kvam, Zezhong Chen

Department of Math & Statistics Faculty Publications

A baseball team would be considered “streaky” if its record exhibits an unusually high number of consecutive wins or losses, compared to what might be expected if the team’s performance does not really depend on whether or not they won their previous game. If an average team in Major League Baseball (i.e., with a record of 81-81) is not streaky, we assume its win probability would be stable at around 50% for most games, outside of peculiar details of day-to-day outcomes, such as whether the game is home or away, who is the starting pitcher, and so on.

In this …

Multipliers Of Sequence Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

This paper is selective survey on the space l_A^p and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality.

Birkhoff–James Orthogonality And The Zeros Of An Analytic Function, Raymond Cheng, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space ℓ^p with p ∈ (1,∞), along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.