Involutive Automorphisms And Derivations Of The Quaternions,
2023
TÜBİTAK
Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman
Turkish Journal of Mathematics
Let $Q=(\frac{a,b}{{\Bbb R}})$ denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra $H$ of Hamilton's quaternions. We have presented explicitly in \cite{Kizil-Alagoz} the matrix of a typical derivation of $Q$. Given a derivation $d\in Der(H)$, we show that the matrix $D\in M_{3}({\Bbb R})$ that represents $d$ on the linear subspace $% H_{0}\simeq {\Bbb R}^{3}$ of pure quaternions provides a pair of idempotent matrices $AdjD$ and $-D^{2}$ that correspond bijectively to the involutary matrix $\Sigma $ of a quaternion involution $\sigma $ and present several equations involving these matrices. In particular, …
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product,
2023
TÜBİTAK
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev
Turkish Journal of Mathematics
The Berezin symbol $\tilde{A}$ of an operator $A$ on the reproducing kernel Hilbert space $\mathcal{H}\left( \Omega\right) $ over some set $\Omega$ with the reproducing kernel $k_{\lambda}$ is defined by \[ \tilde{A}(\lambda)=\left\langle {A\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}}\right\Vert }},\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}% }\right\Vert }}}\right\rangle ,\ \lambda\in\Omega. \] We study the existence of invariant subspaces for Bergman space operators in terms of Berezin symbols.
Some Congruences With $Q-$Binomial Sums,
2023
TÜBİTAK
Some Congruences With $Q-$Binomial Sums, Neşe Ömür, Zehra Betül Gür, Si̇bel Koparal, Lai̇d Elkhiri
Turkish Journal of Mathematics
In this paper, using some combinatorial identities and congruences involving $q-$harmonic numbers, we establish congruences that for any odd prime $p$ and any positive integer $\alpha$,% \begin{equation*} \text{ }\sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}\frac{% q^{-\alpha npk+ n\tbinom{k+1}{2}+2k}}{[k]_{q}}{\alpha p-1 \brack k}_{q}^{n} \pmod{[p]_{q}^{2}} , \end{equation*}% and \begin{equation*} \sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}q^{-\alpha npk+ n\tbinom{k+1}{2}+k}{\alpha p-1 \brack k}_{q}^{n}% \widetilde{H}_{k}(q)\pmod{[p]_{q}^{2}} ,\text{ } \end{equation*}% where $n$ is any integer.
Generalized Pell Graphs,
2023
TÜBİTAK
Generalized Pell Graphs, Vesna Irsi̇c, Sandi Klavzar, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, generalized Pell graphs $\Pi _{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi _{n,k}$ is a median graph, and that $\Pi _{n,k}$ embeds into a Fibonacci cube.
Interpolation Polynomials Associated To Linear Recurrences,
2023
TÜBİTAK
Interpolation Polynomials Associated To Linear Recurrences, Muhammad Syifa'ul Mufid, Laszlo Szalay
Turkish Journal of Mathematics
Assume that $(G_n)_{n\in\mathbb{Z}}$ is an arbitrary real linear recurrence of order $k$. In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by $(t,G_t)$ ($n_0\le t\le n_1$). The main result is an explicit formula depends on the explicit formula of $G_n$ and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of $(G_n)$. During the investigations, we developed certain formulae related to the finite differences.
Operator Index Of A Nonsingular Algebraic Curve,
2023
TÜBİTAK
Operator Index Of A Nonsingular Algebraic Curve, Anar Dosi̇
Turkish Journal of Mathematics
The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.
Dynamical Complexity Of A Predator-Prey Model With A Prey Refuge And Allee Effect,
2023
TÜBİTAK
Dynamical Complexity Of A Predator-Prey Model With A Prey Refuge And Allee Effect, Jianping Gao, Jianghong Zhang, Wenyan Lian
Turkish Journal of Mathematics
We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose …
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves,
2023
TÜBİTAK
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves, Karol Gryszka
Turkish Journal of Mathematics
We discuss dynamical systems that exhibit at least one weakly asymptotically periodic point. In the general case we prove that the system becomes trivial (it is either a periodic point or a fixed point) provided it is equicontinuous and transitive. This result can be used to provide a simple characterization of periodic points in transitive systems. We also discuss systems whose orbits are both proximal and weakly asymptotically periodic. As a result, we obtain a more general tool to detect mutual dynamics between two close orbits which need not be bounded (or have the empty limit set).
Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics,
2023
George Mason University
Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose,
2023
University of Tennessee, Knoxville
Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose, Charlotte Beckford
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
A Modeling Framework For Minimizing Spread Of Mathematics Anxiety In College Students,
2023
UMKC
A Modeling Framework For Minimizing Spread Of Mathematics Anxiety In College Students, Sara Sony, Majid Bani-Yaghoub
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Msis-Kadelka: On The Uniqueness Of Network Identification,
2023
University of Dayton
Msis-Kadelka: On The Uniqueness Of Network Identification, Alan Veliz-Cuba, Elena Dimitrova
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Langevin Dynamic Models For Smfret Dynamic Shift,
2023
Clemson University
Langevin Dynamic Models For Smfret Dynamic Shift, David Frost, Keisha Cook Dr, Hugo Sanabria Dr
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Geometry Of Competition And Stability For One-Host, Two-Parasitoid Systems With Application To Biocontrol,
2023
University of Richmond
Geometry Of Competition And Stability For One-Host, Two-Parasitoid Systems With Application To Biocontrol, Michael Kerckhove
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Msis-Kadelka: Algebraic Methods For Inferring Discrete Models Of Biological Networks,
2023
Southern Methodist University
Msis-Kadelka: Algebraic Methods For Inferring Discrete Models Of Biological Networks, Brandilyn Stigler
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Integrating Quantitative Skills Into Biology Courses,
2023
UMBC
Integrating Quantitative Skills Into Biology Courses, Kathleen Hoffman, Sarah Leupen, Hannah Pie, Michelle Starz-Gaiano, Patricia Turner, Tory Williams
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Msis-Kondrashov: Constrained Optimization: Maximizing Student Success Subject To Covering Required Calculus Content,
2023
College of the Holy Cross
Msis-Kondrashov: Constrained Optimization: Maximizing Student Success Subject To Covering Required Calculus Content, Reginald Mcgee
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
⊕-Supplemented Semimodules,
2023
Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
⊕-Supplemented Semimodules, Ahmed H. Alwan
Al-Bahir Journal for Engineering and Pure Sciences
In this paper, ⊕-Supplemented Semimodules are defined as generalizations of ⊕-Supplemented modules. Let S be a semiring. An S-semimodule A is named a ⊕-supplemented semimodule, if every subsemimodule of A has a supplement which is a direct summand of A. In this paper, we investigate some properties of ⊕-supplemented semimodules besides generalize certain results on ⊕-supplemented modules to semimodules.
Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions,
2023
Texas Tech University
Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Effects Of Persistent Post-Concussion Syndrome,
2023
Illinois State University
The Effects Of Persistent Post-Concussion Syndrome, Jackson Flemming, Olivia Schleifer, Megan Powell
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
