Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators,
2018
TÜBİTAK
Onthe Global $L^{P}$ Boundedness Of A General Classof $H$-Fourier Integral Operators, Chafika Amel Aitemrar, Abderrahmane Senoussaoui
Turkish Journal of Mathematics
In this paper, we study the $L^{p}$-boundedness of a class of semiclassical Fourier integral operators.
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations,
2018
TÜBİTAK
Two Asymptotic Results Of Solutions For Nabla Fractional $(Q,H)$-Difference Equations, Feifei Du, Lynn Erbe, Baoguo Jia, Allan Peterson
Turkish Journal of Mathematics
In this paper we study the Caputo and Riemann--Liouville nabla $(q,h)$-fractional difference equation and obtain the following two main results: Assume $0
Spectral Expansion For The Singular Dirac System With Impulsive Conditions,
2018
TÜBİTAK
Spectral Expansion For The Singular Dirac System With Impulsive Conditions, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications,
2018
TÜBİTAK
Evaluations Of Some Terminating Hypergeometric $_2f_1(2)$ Series With Applications, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Turkish Journal of Mathematics
Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $ j \leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
Non-Science, Technology, Engineering, Mathematics Teachers' Efficacy For Integrating Mathematics Across The Curriculum,
2018
Walden University
Non-Science, Technology, Engineering, Mathematics Teachers' Efficacy For Integrating Mathematics Across The Curriculum, Sandra Charlene Burrell
Walden Dissertations and Doctoral Studies
The problem at a local science, technology, engineering, mathematics (STEM) charter high school in this study, was that non-STEM teachers lacked the self-efficacy and background knowledge to integrate mathematics into their content-specific instructional activities. The goal of this study was to explore non-STEM teachers' self-efficacy for integrating mathematics across the STEM charter high school's curriculum. The conceptual framework of self-efficacy informed the study. A case study research design was chosen to develop an in-depth understanding of the problem. . Twelve of the 16 local school's non-STEM teachers agreed to participate in the study. Personal interviews were conducted to access non-STEM …
The Beauty Of Numbers In Nature: Mathematical Patterns And Principles From The Natural World [Book Review],
2018
Old Dominion University
The Beauty Of Numbers In Nature: Mathematical Patterns And Principles From The Natural World [Book Review], John A. Adam
Mathematics & Statistics Faculty Publications
(First paragraph) It came as quite a shock at the time. I cannot recall exactly when it happened, but it certainly caught me by surprise. For most of my life, and certainly from elementary school (or “primary” school in the UK) through high school I had become used to seeing posters and books illustrating the “standard” map of the world: the Mercator projection. Of course, Greenwich, London, sat at longitude 0◦ (and still does!). And certainly I knew that planet Earth is spheroidal and that this flat projection distorted the shapes and areas (especially near the polar regions), but somehow …
Validation Of A Lottery,
2018
City University of New York (CUNY)
Validation Of A Lottery, Xiaona Zhou
Publications and Research
The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. The Chi-squared distribution gives us a number beyond which we reject fairness. However, there is another possibility. If the difference between the fair model and the observed frequency is too small, that …
Boundary Sentinels For The Resolution Of A Geometrical Problem,
2018
TÜBİTAK
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Turkish Journal of Mathematics
The present paper aims to investigate a class of linear positive operators by combining Szász-Jain operators and Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-type results and establish Grüss-Voronovskaja-type theorem. Furthermore, we show the rate of convergence for Szász-Jain-Brenke operators to functions having derivative of bounded variation and not having derivative of bounded variation by illustrative graphics using MATLAB.
On $N$-Absorbing $\Delta$-Primary Ideals,
2018
TÜBİTAK
On $N$-Absorbing $\Delta$-Primary Ideals, Gülşen Ulucak, Ünsal Teki̇r, Suat Koç
Turkish Journal of Mathematics
Let $R$ be a commutative ring with nonzero identity and $n$ be a positive integer. In this paper, we study the concepts of $n$-absorbing $\delta $-primary ideals and weakly $n$-absorbing $\delta$-primary ideals, which are the generalizations of $\delta$-primary ideals and weakly $\delta$-primary ideals, respectively. We introduce the concepts of $n$-absorbing $\delta$-primary ideals and weakly $n$-absorbing $\delta$-primary ideals. Moreover, we give many properties of these new types of ideals and investigate the relations between these structures.
Pythagorean Triples Containing Generalized Lucas Numbers,
2018
TÜBİTAK
Pythagorean Triples Containing Generalized Lucas Numbers, Zafer Şi̇ar, Refi̇k Keski̇n
Turkish Journal of Mathematics
Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper, we assume that $P$ and $Q$ are relatively prime odd positive integers and $P^{2}+4Q>0.$ We determine all indices $n$ such that $U_{n}=(P^{2}+4Q)x^{2}.$ Moreover, we determine all indices $n$ such that $(P^{2}+4Q)U_{n}=x^{2}.$ As a result, we show that the equation $V_{n}^{2}(P,1)+V_{n+1}^{2}(P,1)=x^{2}$ has solution only for $n=2,$ $P=1,$ $x=5$ and $V_{n+1}^{2}(P,-1)=V_{n}^{2}(P,-1)+x^{2}$ has no solutions. Moreover, we solve some Diophantine equations.
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators,
2018
TÜBİTAK
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Turkish Journal of Mathematics
In this paper, the authors study some subordination and superordination properties for classes of $p$-valent meromorphic, analytic, and univalent functions associated with a linear operator $\mathfrak{L}_{p,\lambda}^{m,\ell}(a,c,\mu)$ of the Erdélyi-Kober type. Connections with several earlier results are also pointed out.
A New Proof Of A Harnack Inequality For The Curve Shortening Flow,
2018
TÜBİTAK
A New Proof Of A Harnack Inequality For The Curve Shortening Flow, Mihai Bailesteanu
Turkish Journal of Mathematics
We offer a new approach for determining Harnack quantities for the curve shortening flow and we show how, following this procedure, one can obtain Hamilton's Harnack inequality for this flow $\kappa_t+\frac{1}{2t}\kappa\geq\frac{\kappa_s^2}{\kappa}$, where $\kappa$ is the curvature of the curve being deformed by the flow.
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales,
2018
TÜBİTAK
Convergence And Gundy's Decomposition For Noncommutative Quasi-Martingales, Congbian Ma, Ping Li, Youliang Hou
Turkish Journal of Mathematics
In this paper, we prove the bilaterally almost uniformly convergence of bounded $L_1(\mathcal{M})$-noncommutative quasi-martingales. We also prove Gundy's decomposition for noncommutative quasi-martingales. As an application, we prove that every relatively weakly compact quasi-martingale difference sequence in $L_1(\mathcal{M},\tau)$ whose sequence of norms is bounded away from zero is 2-co-lacunary.
Unconditional Wavelet Bases In Lebesgue Spaces,
2018
TÜBİTAK
Unconditional Wavelet Bases In Lebesgue Spaces, Yan Zhang, Yun Zhang Li
Turkish Journal of Mathematics
In this paper, we prove that an orthonormal wavelet basis associated with a general isotropic expansive matrix must be an unconditional basis for all $L^{p}$(ℝ${}^{d})$ with $1$<$p$<$\infty$, provided the wavelet functions satisfy some usual conditions.
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds,
2018
TÜBİTAK
Geometric Properties Of Rotation Minimizing Vector Fields Along Curves In Riemannian Manifolds, Fernando Etayo
Turkish Journal of Mathematics
Rotation minimizing (RM) vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even when the curvature vanishes. Nevertheless, many other geometric properties have not been studied. In the present paper, RM vector fields along a curve immersed into a Riemannian manifold are studied when the ambient manifold is the Euclidean 3-space, the hyperbolic 3-space, and a Kähler manifold.
On The $J$-Reflexive Operators,
2018
TÜBİTAK
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Banach space $X$ is $J$-reflexive if every bounded operator on $X$ that leaves invariant the sets $J(T,x)$ for all $x$ is contained in the closure of $orb(T)$ in the strong operator topology. We discuss some properties of $J$-reflexive operators. We also give and prove some necessary and sufficient conditions under which an operator is $J$-reflexive. We show that isomorphisms preserve $J$-reflexivity and some examples are considered. Finally, we extend the $J$-reflexive property in terms of subsets.
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$,
2018
TÜBİTAK
Prime-Valent Arc-Transitivebasic Graphs With Order $4p$ Or $4p^2$, Hailin Liu
Turkish Journal of Mathematics
A graph $\Ga$ is called $G$-basic if $G$ is quasiprimitive or bi-quasiprimitive on the vertex set of $\Ga$, where $G\leq\Aut\Ga$. In this paper, we complete the classification of $r$-valent arc-transitive basic graphs with order $4p$ or $4p^2$, where $p$ and $r$ are odd primes.
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator,
2018
TÜBİTAK
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
Turkish Journal of Mathematics
The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
A Machine Learning Exploration Of Human Connectome Data,
2018
Eastern Michigan University
A Machine Learning Exploration Of Human Connectome Data, Katrina Prantzalos
Senior Honors Theses and Projects
The intent of this project is to statistically examine the relationships between psychological traits, demographics, and physiological information provided by various brain scans. The Human Connectome Project dataset includes brain imaging data, demographics, and psychological data, from 1,206 individuals. Using this data, we performed exploratory data analysis, including an investigation of the distinctions in connectome data across participants with anxiety and/or depression as opposed to those without. Our aim was to predict the two mental disorders from given data via machine learning techniques such as Random Forest and Boosted Trees methods. Unfortunately, we were unable to reasonably predict anxiety or …
