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2018

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Articles 1081 - 1110 of 1332

Full-Text Articles in Mathematics

On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$, Murat Alan Jan 2018

On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$, Murat Alan

Turkish Journal of Mathematics

Let $m$ be a positive integer. We show that the exponential Diophantine equation $ (18m^2+1)^x+(7m^2-1)^y=(5m)^z $ has only the positive integer solution $(x,y,z)=(1,1,2)$ except for $m \equiv 23,47,63, 87 \pmod {120}$. For $m\not\equiv 0 \pmod5$ we use some elementary methods and linear forms in two logarithms. For $m \equiv 0 \pmod 5$ we apply a result for linear forms in $p$-adic logarithms.

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Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum Jan 2018

Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum

Turkish Journal of Mathematics

This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order $2

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The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi Jan 2018

The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi

Turkish Journal of Mathematics

Karoubi's density theorem was first proved in Benayat's thesis and then cited and used in several books and articles. As K-theory is a special case of hermitian $_{\varepsilon }L$-theory, a natural question is whether such a theorem is still true in the latter theory. The purpose of this article is to show that it is indeed the case.

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Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds, Tuna Bayrakdar, Abdullah Azi̇z Ergi̇n Jan 2018

Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds, Tuna Bayrakdar, Abdullah Azi̇z Ergi̇n

Turkish Journal of Mathematics

We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan's method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an $\{e\}$-structure on both total and base spaces.

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Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani Jan 2018

Bargraphs In Bargraphs, Toufik Mansour, Armend Shabani

Turkish Journal of Mathematics

Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.

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The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz Jan 2018

The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz

Turkish Journal of Mathematics

A topological space $X$ is called productively Lindelöf if $X\times Y$ is Lindelöf for every Lindelöf space $Y$. We study with remainders and investigate topological spaces with productively Lindelöf remainders.

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Self Regulation In College-Level Mathematics Classes, Jenny Lee Jan 2018

Self Regulation In College-Level Mathematics Classes, Jenny Lee

HMC Senior Theses

This thesis investigates the need for improvement in mathematics education at the college level in the US regarding equitable practices in instruction. In particular, it focuses on understanding the role self-regulation can play in the classroom dynamics, and how self-regulation can be a way to empower students. Also included is a case study in an introductory linear algebra class at a liberal arts college and is meant to provide a investigation into a way of incorporating self-regulation by using self-paced assessments. Results of this study suggest a possible question to consider in reforming mathematics education for a more equitable environment …

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Math Department Newsletter, 2017-2018, Mathematics Department Jan 2018

Math Department Newsletter, 2017-2018, Mathematics Department

Mathematics Newsletter

No abstract provided.

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Global Dynamic Scenarios For Competitive Maps In The Plane, Elliott J. Bertrand, M.R.S. Kulenovic Jan 2018

Global Dynamic Scenarios For Competitive Maps In The Plane, Elliott J. Bertrand, M.R.S. Kulenovic

Mathematics Faculty Publications

In this paper we present some global dynamic scenarios for general competitive maps in the plane. We apply these results to the class of second-order autonomous difference equations whose transition functions are decreasing in the variable \(x_{n}\) and increasing in the variable \(x_{n-1}\).We illustrate our results with the application to the difference equation ...

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Global Dynamics Of Higher-Order Transcendental-Type Generalized Beverton–Holt Equations, Elliott J. Bertrand, M.R.S. Kulenovic Jan 2018

Global Dynamics Of Higher-Order Transcendental-Type Generalized Beverton–Holt Equations, Elliott J. Bertrand, M.R.S. Kulenovic

Mathematics Faculty Publications

We investigate generalized Beverton–Holt difference equations of order k.

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Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell Jan 2018

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …

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Launch-Explore-Summarize In High School Calculus, Nate Mattis Jan 2018

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

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Reply To "Comment On 'Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence"', Rossen Ivanov, Emil Prodanov Jan 2018

Reply To "Comment On 'Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence"', Rossen Ivanov, Emil Prodanov

Articles

No abstract provided.

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Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi Jan 2018

Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi

Turkish Journal of Mathematics

We classify semisymmetric contact metric manifolds $M^{2n+1}(\varphi, \xi, \eta, g),~n\geq2$ with $\xi$-parallel tensor $h$, where $2h$ denotes the Lie derivative of the structure tensor $\varphi$ in the direction of the characteristic vector field $\xi$.

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On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk Jan 2018

On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk

Turkish Journal of Mathematics

The oscillation and nonoscillation theories for nonlinear systems have recently received a lot of attention. We consider a two-dimensional time-scale system and find the oscillation criteria for solutions of the system by using some improper integrals and inequalities. We also give a few examples in order to highlight our main results.

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On A Biharmonic Equation Involving Slightly Supercritical Exponent, Kamal Ould Bouh Jan 2018

On A Biharmonic Equation Involving Slightly Supercritical Exponent, Kamal Ould Bouh

Turkish Journal of Mathematics

We consider the biharmonic equation with supercritical nonlinearity $ (P_\varepsilon ):$ $\Delta^{2} u = K u ^{8/(n-4)+\varepsilon}u$ in $\Omega$, $\Delta u =u = 0$ on $\partial \Omega $, where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n $, $n \geq 5 $, $K$ is a $C^3$ positive function, and $\varepsilon$ is a positive real parameter. In contrast with the subcritical case, we prove the nonexistence of sign-changing solutions of $ (P_\varepsilon )$ that blow up at two near points. We also show that $(P_\varepsilon)$ has no bubble-tower sign-changing solutions.

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On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An Jan 2018

On Radial Solutions For Monge-Ampére Equations, Ronghua Liu, Fanglei Wang, Yukun An

Turkish Journal of Mathematics

In this paper,we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampére equations using the fixed point theorem.

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$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r Jan 2018

$R$-Submodules And $Sr$-Submodules, Suat Koç, Ünsal Teki̇r

Turkish Journal of Mathematics

In this article, we introduce new classes of submodules called $r$-submodule and special $r$-submodule, which are two different generalizations of $r$-ideals. Let $M $be an $R$-module, where $R $is a commutative ring$. $We call a proper submodule $N\ $of $M$ an $r$-submodule (resp., special $r$-submodule) if the condition $am\in N$ with $ann_{M}(a)=0_{M} $(resp., $ann_{R}(m)=0$) implies that $m\in N$ (resp., $a\in(N:_{R} M)$) for each $a\in R $and $m\in M. $ We also give various results and examples concerning $r$-submodules and special $r$-submodules.

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Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib Jan 2018

Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus, Yaakoubi Nejib

Turkish Journal of Mathematics

In this paper we construct an explicit sequence of divergence-free vector fields $\rm{b}_{n}$ that pushes the spectral gap of the nonself-adjoint operator $A_{\rm{b}_{n}}=\Delta +\rm{b}_{n}\cdot\nabla $ to infinity. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution.

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If $4$-Convex Vectors Are Closed In Uniform Norms Then Their Second Derivatives Are Also Closed In Weighted $L^2$-Norm, Muhammad Shoaib Saleem, Josip Pecaric, Hamood Ur Rehman, Mobeen Munir, Muhammad Wahab Khan Jan 2018

If $4$-Convex Vectors Are Closed In Uniform Norms Then Their Second Derivatives Are Also Closed In Weighted $L^2$-Norm, Muhammad Shoaib Saleem, Josip Pecaric, Hamood Ur Rehman, Mobeen Munir, Muhammad Wahab Khan

Turkish Journal of Mathematics

In this paper, we develop the weighted energy estimates for arbitrary 4-convex vectors and the vectors having both 4-convex and 4-concave functions as their arguments. To do this, we first develop these estimates for smooth 4-convex vectors and then, through mollification, extend the results for arbitrary 4-convex vectors. This type of estimates are valuable in problems of financial mathematics for the establishment of optimal investment strategies

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Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao Jan 2018

Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities, Jin Haitao

Turkish Journal of Mathematics

The coefficient of $x^{-1}$ of a formal Laurent series $f(x)$ is called the formal residue of $f(x)$. Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their $q$-analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.

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On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani Jan 2018

On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani

Turkish Journal of Mathematics

In this paper, we find explicit formulas for higher-order derivatives of the inverse tangent function. More precisely, we study polynomials that are induced from the higher-order derivatives of $\arctan(x)$. Successively, we give generating functions, recurrence relations, and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas, and matching polynomials are established.

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The Wright Message, 2018-2019, University Of Northern Iowa. Department Of Mathematics. Jan 2018

The Wright Message, 2018-2019, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside This Issue:
--New Faculty Faculty Spotlight Around Wright Hall
--Alumni Spotlight In Memoriam: Jack Wilkinson
--News from the CTLM
--Student Spotlights
--Donor Spotlight
--Alumni Updates
--Contributions to an Account – Recognition
--Department Funds
--Contribution Form

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Ancient Cultures + High School Algebra = A Diverse Mathematical Approach, Laryssa Byndas Jan 2018

Ancient Cultures + High School Algebra = A Diverse Mathematical Approach, Laryssa Byndas

Masters Essays

No abstract provided.

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Using Geogebra To Explore Properties Of Circles In Euclidean Geometry, Erin Hanna Jan 2018

Using Geogebra To Explore Properties Of Circles In Euclidean Geometry, Erin Hanna

Masters Essays

No abstract provided.

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College Algebra Through Problem Solving (2018 Edition), Danielle Cifone, Karan Puri, Debra Masklanko, Ewa Dabkowska Jan 2018

College Algebra Through Problem Solving (2018 Edition), Danielle Cifone, Karan Puri, Debra Masklanko, Ewa Dabkowska

Open Educational Resources

This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.

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Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross Jan 2018

Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper we examine the multipliers from one model space to another.

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Models For Decision-Making, Steven Cosares Jan 2018

Models For Decision-Making, Steven Cosares

Open Educational Resources

No abstract provided.

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Limits Of Julia Sets For Sums Of Power Maps And Polynomials, Micah Brame Jan 2018

Limits Of Julia Sets For Sums Of Power Maps And Polynomials, Micah Brame

Undergraduate Honors Thesis Collection

Suppose f_{n,c} is a complex-valued mapping of one complex variable given by f_{n,c}(z) = z^n + p(z) + c, where p is a polynomial such that p(0) = 0 and c is a complex parameter such that |c| < 1. We provide necessary and sufficient conditions that the geometric limit, as n approaches infinity, of the set of points that remain bounded under iteration by f_{n,c} is the disk of radius 1 centered at the origin.

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On Comparability Of Bigrassmannian Permutations, John Engbers, Adam Hammett Jan 2018

On Comparability Of Bigrassmannian Permutations, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let Sn and Gn denote the respective sets of ordinary and bigrassmannian (BG) permutations of order n, and let (Gn,≤) denote the Bruhat ordering permutation poset. We study the restricted poset (Bn,≤), first providing a simple criterion for comparability. This criterion is used to show that that the poset is connected, to enumerate the saturated chains between elements, and to enumerate the number of maximal elements below r fixed elements. It also quickly produces formulas for β(ω) (α(ω), respectively), the number of BG permutations weakly below (weakly above, respectively) a fixed ω ∈ B …

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