Bargraphs In Bargraphs,
2018
TÜBİTAK
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.
The Productively Lindelöf Property In The Remainders Of Topological Spaces,
2018
TÜBİTAK
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.
Self Regulation In College-Level Mathematics Classes,
2018
Claremont Colleges
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 …
Math Department Newsletter, 2017-2018,
2018
Sacred Heart University
Math Department Newsletter, 2017-2018, Mathematics Department
Mathematics Newsletter
No abstract provided.
Global Dynamic Scenarios For Competitive Maps In The Plane,
2018
Sacred Heart University
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 ...
Global Dynamics Of Higher-Order Transcendental-Type Generalized Beverton–Holt Equations,
2018
Sacred Heart University
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.
Extensions Of The Morse-Hedlund Theorem,
2018
Bucknell University
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. …
Launch-Explore-Summarize In High School Calculus,
2018
Bucknell University
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 …
Reply To "Comment On 'Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence"',
2018
Technological University Dublin
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.
Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$,
2018
TÜBİTAK
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 $\xi$.
On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term,
2018
TÜBİTAK
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.
On A Biharmonic Equation Involving Slightly Supercritical Exponent,
2018
TÜBİTAK
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.
On Radial Solutions For Monge-Ampére Equations,
2018
TÜBİTAK
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.
$R$-Submodules And $Sr$-Submodules,
2018
TÜBİTAK
$R$-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.
Accelerating Diffusion By Incompressible Drift On The Two-Dimensional Torus,
2018
TÜBİTAK
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.
If $4$-Convex Vectors Are Closed In Uniform Norms Then Their Second Derivatives Are Also Closed In Weighted $L^2$-Norm,
2018
TÜBİTAK
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
Formal Residue And Computer-Assisted Proofs Of Combinatorial Identities,
2018
TÜBİTAK
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.
On The Higher Derivatives Of The Inverse Tangent Function,
2018
TÜBİTAK
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.
The Wright Message, 2018-2019,
2018
University of Northern Iowa. Department of Mathematics.
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
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport,
2018
Skidmore College
How Often Does The Best Team Win? A Unified Approach To Understanding Randomness In North American Sport, Michael J. Lopez, Gregory J. Matthews, Benjamin Baumer
Mathematics Sciences: Faculty Publications
Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variability of team …
