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2019

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Middle School Mathematics Teachers' Perceptions Of Opportunities And Challenges, Shelby Eversole Jan 2019

Middle School Mathematics Teachers' Perceptions Of Opportunities And Challenges, Shelby Eversole

Masters Theses

This study investigates the perspectives of opportunities and challenges of middle school mathematics’ teachers. To gain these perspectives, an ethnographic study was conducted by interviewing four middle school mathematics teachers in central Illinois. The results of this study imply that teachers of different backgrounds and teaching environments have varying perspectives about challenges and opportunities in the classroom. Limitations of this study include but are not limited to, the researcher having one year to conduct the research, only four teachers from two schools being interviewed, interviewees teaching different grade levels, no rural setting involvement, one educator having little teaching experience, teachers’ …

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Impacts Of Plant-Microbe Interactions On Seedling Performance In A Riparian Forest Invaded By Lonicera Maackii, Taylor E. K. Strehl Jan 2019

Impacts Of Plant-Microbe Interactions On Seedling Performance In A Riparian Forest Invaded By Lonicera Maackii, Taylor E. K. Strehl

Masters Theses

Soil microbes have profound impacts on plant growth and survival and can either promote or inhibit plant dominance. Exotic plants are often strongly invasive because they have escaped their natural enemies, potentially including antagonistic soil microbes. I examined how the invasive shrub Lonicera maackii and a common native tree, Acer negundo, responded to soil microbial communities to determine the role of soil microbes in regulating invasion success. This was done by growing both species with microbes from invaded (L. maackii) and uninvaded (A. negundo) soils collected from three locations within a riparian forest. Seedlings were …

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Identifying Priority Conservation Areas And Strategies For Myotis Sodalis (Chiroptera: Vespertilionidae) Via Habitat And Connectivity Modeling, Ashleigh B. Cable Jan 2019

Identifying Priority Conservation Areas And Strategies For Myotis Sodalis (Chiroptera: Vespertilionidae) Via Habitat And Connectivity Modeling, Ashleigh B. Cable

Masters Theses

Myotis sodalis, the Indiana bat, is a federally endangered bat species in the United States of America (USA). Conservation efforts are typically focused at identified maternity sites at local scales, however, the species is a regional migrant that interacts with its environment at multiple spatial scales. We are limited in our knowledge of landscape-level requirements of this species, especially in large areas such as Illinois, USA, where a wide range of environmental and landscape conditions exist. Many previous M. sodalis habitat studies have limited their focus to smaller spatial scales. Due to limitations in funding, personnel, and time, it …

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Synthesis Toward A Molecular Container Based On P-Tert-Butylcalix[4]Arene With Gate Features, Balasooriya Appuhamilage Dinesh Madushan Balasooriya Jan 2019

Synthesis Toward A Molecular Container Based On P-Tert-Butylcalix[4]Arene With Gate Features, Balasooriya Appuhamilage Dinesh Madushan Balasooriya

Masters Theses

Nowadays molecular and supramolecular chemistry have endless examples for the development of smart devices. Among those applications, nano-baskets of calixarenes play vital roles in host-guest chemistry. One of the main appealing concepts of this field is the development of host molecules with gate features. These hosts are designed and constructed for the delivery of chemical or biochemical species that are volatile, or reactive, or sensitive to normal solution environment and they are mainly functioned by predefined groups that are responsive toward stimuli such as concentration, temperature, pH and so on. In our previous study, we found that benzyl bromides can …

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Complex Varieties As Minima, Richard Koss Jan 2019

Complex Varieties As Minima, Richard Koss

Masters Theses

We will explore various numeric methods of finding roots of an analytic function over some open set of the complex plane. We will discuss a method of visually observing the roots, a gradient descent method for finding the roots of an analytic function, a gradient descent method for solving systems of analytic functions, and finally a method of descent that uses osculating circles to find roots of an analytic function. Of particular interest to this thesis are roots of complex polynomials. There will be examples, code snippets, and outputs of programs to illustrate all of these methods.

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The Impact Of Dutch Disease: The Case Of Nigeria, Halimat Atinuke Laguda Jan 2019

The Impact Of Dutch Disease: The Case Of Nigeria, Halimat Atinuke Laguda

Masters Theses

Nigeria, over the years, has been showing a rapid appreciation of the domestic currency, a rise in real wages and the service sector and a slow-down in the industrial production which are all signs of presence of Dutch disease which predicts that a country with large natural resource rents may experience a de-industrialization and a lower long term economic growth. This paper analyses the impact of Dutch disease in Nigeria Ordinary Least square method, Two-Stage Least Square and Autoregressive Distributed Lag with a system of equation from 1981 to 2017 and found that the real wage rate emphasizes on the …

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Gifted Education In Elementary Schools, Danielle Wilkinson Jan 2019

Gifted Education In Elementary Schools, Danielle Wilkinson

Masters Theses

Gifted students have enormous potential, yet there are few consistent opportunities for gifted students to receive challenging instruction. Drawing upon literature detailing the history of gifted education nationally and in Illinois, this study sought to find what services were currently offered to Illinois students, and if the opportunities for gifted students were related to a district’s state funding tier. Findings indicated that the elementary gifted services being offered and the ways in which eligibility is determined were inconsistent among districts. In addition, many districts who offer gifted services are using local/community funds in order to provide services regardless of their …

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Farm To Label: A Critique Of Consumer Activism In The Sustainable Food Movement, Olivia Whitener Jan 2019

Farm To Label: A Critique Of Consumer Activism In The Sustainable Food Movement, Olivia Whitener

Pomona Senior Theses

“Local,” “organic,” “natural,” and “Fairtrade” are just several of the many claims adorning the food products that line grocery store shelves. These promises of environmental sustainability and social responsibility are pillars of the “good food revolution” sweeping the nation as consumers demand alternatives to the products of the industrial food system. Green consumerism, the premise that consumer demand for environmentally sustainable goods will bring about ecologically beneficial outcomes, is at the heart of the sustainable food movement. This thesis takes a critical look at the operation of green consumerism in the food system. It explores the ideology and shortcomings of …

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In The Eye Of The Storm: Houston After Hurricane Harvey, Brandon Tolentino-Serrano Jan 2019

In The Eye Of The Storm: Houston After Hurricane Harvey, Brandon Tolentino-Serrano

Pomona Senior Theses

Situated in one of the wettest climates in America, Houston, TX has had a long history of heavy rains and unprecedented floods. Unfortunately, floods have become more common over the last few decades as climate change increases the frequency and intensity of hurricanes around the globe. To complicate matters further, Houston has quickly sprawled to accommodate over 2.5 billion people. Rapid urbanization has rendered the landscape even more susceptible to floods through excess concretization and watershed disturbance. This thesis traces the history of the Bayou City in relation to the damages caused by Hurricane Harvey. By mapping out the original …

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Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou Jan 2019

Companion Sequences Associated To The$R$-Fibonacci Sequence: Algebraic And Combinatorial Properties, Sadjia Abbad, Hacene Belbachir, Benali Benzaghou

Turkish Journal of Mathematics

It is well known that the companion sequence of the Fibonacci sequence is Lucas's sequence. For the generalized Fibonacci sequences, the companion sequence is not unique. Several authors proposed different definitions, and they are in a certain sense all good. Our purpose is to introduce a family of companion sequences for some generalized Fibonacci sequence: the $r$-Fibonacci sequence. We evaluate the generating functions and give some applications, and we exhibit convolution relations that generalize some known identities such as Cassini's. Afterwards, we calculate the sums of their terms using matrix methods. Next, we propose a $q$-analogue and extend the definition …

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Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n Jan 2019

Nonnegative Integer Solutions Of The Equation $F_{N}-F_{M}=5^{A}$, Fati̇h Erduvan, Refi̇k Keski̇n

Turkish Journal of Mathematics

In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq 2$ and $p>7$ is prime, then the equation $F_{n}-F_{m}=p^{a}$ has no solutions in nonnegative integers $m,n.$

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On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan Jan 2019

On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan

Turkish Journal of Mathematics

The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.

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A New Solution Of Pair Matrix Equations With Arbitrary Triangular Fuzzy Numbers, Wan Suhana Wan Daud, Nazihah Ahmad, Ghassan Malkawi Jan 2019

A New Solution Of Pair Matrix Equations With Arbitrary Triangular Fuzzy Numbers, Wan Suhana Wan Daud, Nazihah Ahmad, Ghassan Malkawi

Turkish Journal of Mathematics

Pair matrix equations have numerous applications in control system engineering, such as for stability analysis of linear control systems and also for reduction of nonlinear control system models. There are some situations in which the classical pair matrix equations are not well equipped to deal with the uncertainty problem during the process of stability analysis and reduction in control system engineering. Thus, this study presents a new algorithm for solving fully fuzzy pair matrix equations where the parameters of the equations are arbitrary triangular fuzzy numbers. The fuzzy Kronecker product and fuzzy $Vec$-operator are employed to transform the fully fuzzy …

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Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez Jan 2019

Multiplication Alteration By Two-Cocycles For Bialgebras With Weak Antipode, Jose Nicanor Alonso, José Manuel Fernandez Vilaboa, Ramon Gonzalez Rodriguez

Turkish Journal of Mathematics

In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weak antipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special case of the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.

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A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson Jan 2019

A Fully Hadamard And Erdelyi-Kober-Type Integral Boundary Value Problem Of Acoupled System Of Implicit Differential Equations, Fatima Zohra Berrabah, Benaouda Hedia, Johnny Henderson

Turkish Journal of Mathematics

In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.

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On An Elliptic Boundary Value Problem With Critical Exponent, Khadijah Sharaf Jan 2019

On An Elliptic Boundary Value Problem With Critical Exponent, Khadijah Sharaf

Turkish Journal of Mathematics

We study a nonlinear critical second-order PDE with zero Dirichlet boundary condition. We prove existence and compactness results for the equation by using Bahri's method of critical points at infinity.

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On The Cohen-Macaulayness Of Tangent Cones Of Monomial Curves In $\Mathbb{A}^{4}(K)$, Sefa Feza Arslan, Anargyros Katsampekis, Meli̇ssa Nalbandi̇yan Jan 2019

On The Cohen-Macaulayness Of Tangent Cones Of Monomial Curves In $\Mathbb{A}^{4}(K)$, Sefa Feza Arslan, Anargyros Katsampekis, Meli̇ssa Nalbandi̇yan

Turkish Journal of Mathematics

In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the case where $C$ is a Gorenstein noncomplete intersection monomial curve and we generalize some results in the literature. Moreover, by using these results, we construct families supporting Rossi's conjecture, which is still open for monomial curves in 4-dimensional affine space.

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Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy Jan 2019

Generalized Helices In Three-Dimensional Lie Groups, Alexander Yampolsky, Anastasiya Opariy

Turkish Journal of Mathematics

We introduce three types of helices in three-dimensional Lie groups with left-invariant metric and give their geometrical description similar to that of Lancret. We generalize the results known for the case of three-dimensional Lie groups with bi-invariant metric.

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On Expansions Of Prime And 2-Absorbing Hyperideals In Multiplicative Hyperrings, Gülşen Ulucak Jan 2019

On Expansions Of Prime And 2-Absorbing Hyperideals In Multiplicative Hyperrings, Gülşen Ulucak

Turkish Journal of Mathematics

In this paper, we study $ \delta $-primary and 2-absorbing $ \delta $-primary hyperideals which are the extended classes of prime and 2-absorbing hyperideals, respectively. Assume that $R$ is a commutative multiplicative hyperring with nonzero identity. We call $ I \in \mathcal{I*(R)}$ a $\delta $-primary hyperideal if $a,b\in R$ and $a\circ b\subseteq I$ imply either $a\in I$ or $b\in \delta (I)$ and also, $ I $ is called 2-absorbing $\delta $-primary hyperideal if $a,b,c\in R $ and $a\circ b\circ c \subseteq I$ imply $a\circ b\subseteq I$ or $b\circ c\subseteq \delta (I)$ or $a\circ c\subseteq \delta (I)$. Moreover, we give the …

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Convolutionproperties For A Family Of Analytic Functions Involving $Q$-Analogue Ofruscheweyh Differential Operator, Khurshid Ahmad, Muhammad Arif, Jin Lin Liu Jan 2019

Convolutionproperties For A Family Of Analytic Functions Involving $Q$-Analogue Ofruscheweyh Differential Operator, Khurshid Ahmad, Muhammad Arif, Jin Lin Liu

Turkish Journal of Mathematics

The main object of the present paper is to investigate convolution properties for a new subfamily of analytic functions that are defined by $q$ -analogue of Ruscheweyh differential operator. Several consequences of the main results are also given.

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The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function, Faruk Temur Jan 2019

The Frequency Function And Its Connections To The Lebesgue Points And The Hardy-Littlewood Maximal Function, Faruk Temur

Turkish Journal of Mathematics

The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function $\mathcal{T}$, and further to investigate its relations to the Hardy-Littlewood maximal function $\mathcal{M}$, and to the Lebesgue points. We surmount the intricate issue of measurability of $\mathcal{T}f$ by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of $\mathcal{M}f$ for $f$ simple to the zeros …

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An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral Jan 2019

An Involution Of Reals, Discontinuous On Rationals, And Whose Derivative Vanishes A.E., Abdurrahman Muhammed Uludağ, Hakan Ayral

Turkish Journal of Mathematics

We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.

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Some Sufficient Conditions For A Group To Be Abelian, Gary Walls Jan 2019

Some Sufficient Conditions For A Group To Be Abelian, Gary Walls

Turkish Journal of Mathematics

A group is said to satisfy a word $w$ in the symbols $\{x, x^{-1}, y, y^{-1} \}$ provided that if the 'x' and 'y' are replaced by arbitrary elements of the group then the equation $w=1$ is satisfied. This paper studies certain equations in words, as above, which together with other conditions imply that groups which satisfy these equations and conditions must be abelian.

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Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina Jan 2019

Some Applications Of Differential Subordination For Certain Starlike Functions, Rahim Kargar, Lucyna Trojnar Spelina

Turkish Journal of Mathematics

Let $\mathcal{S}^*(q_c)$ denote the class of functions $f$ analytic in the open unit disc $\Delta$, normalized by the condition $f(0)=0=f'(0)-1$ and satisfying the following inequality $\left \left(\frac{zf'(z)}{f(z)}\right)^2-1\right < c \quad (z\in\Delta, 0

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The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico Jan 2019

The Matrix-Valued Numerical Range Over Finite Fields, Edoardo Ballico

Turkish Journal of Mathematics

In this paper we define and study the matrix-valued $k\times k$ numerical range of $n\times n$ matrices using the Hermitian product and the product with $n\times k$ unitary matrices $U$ (on the right with $U$, on the left with its adjoint $U^\dagger = U^{-1}$). For all $i, j=1,\dots ,k$ we study the possible $(i,j)$-entries of these $k\times k$ matrices. Our results are for the case in which the base field is finite, but the same definition works over $\mathbb {C}$. Instead of the degree $2$ extension $\mathbb {R}\hookrightarrow \mathbb {C}$ we use the degree $2$ extension $\mathbb {F} _q\hookrightarrow \mathbb …

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Further Results On The Join Graph Of A Finite Group, Zahra Bahrami, Bijan Taeri Jan 2019

Further Results On The Join Graph Of A Finite Group, Zahra Bahrami, Bijan Taeri

Turkish Journal of Mathematics

Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ is an undirected simple whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup $\Phi(G)$ of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=\langle H,K\rangle$. We classify finite groups whose join graphs have domination number $\leq 2$ and independence number $\leq 3$. We show that $\Delta(G)\cong \Delta(A_4)$ if and only if $G\cong A_4$. We also show that if the independence number of $\Delta(G)$ is less than $15$, …

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Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik Jan 2019

Relative Ranks Of Some Partial Transformation Semigroups, Ebru Yi̇ği̇t, Gonca Ayik, Hayrullah Ayik

Turkish Journal of Mathematics

Let $P_{n}$, $T_{n}$, $I_{n}$, and $S_{n}$ be the partial transformation semigroup, the (full) transformation semigroup, the symmetric inverse semigroup, and the symmetric group on $X_{n}=\{1,\ldots ,n \}$, respectively. For $1\leq r\leq n-1$, let $PK_{n,r}$ be the subsemigroup consisting $\alpha\in P_{n}$ such that $ \im\alpha \leq r$ and let $SPK_{n,r}=PK_{n,r}\setminus T_{n}$. In this paper, we first examine the subsemigroup $I_{n,r}=I_{n}\cup PK_{n,r}$ and we find the necessary and sufficient conditions for any nonempty subset of $PK_{n,r}$ to be a (minimal) relative generating set of the subsemigroup $I_{n,r}$ modulo $I_{n}$. Then we examine the subsemigroups $PI_{n,r}= SI_{n}\cup PK_{n,r}$ and $SI_{n,r}=SI_{n}\cup SPK_{n,r}$ for $1\leq …

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A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin Jan 2019

A Convergent Two-Level Linear Scheme For The Generalizedrosenau-Kdv-Rlw Equation, Ayhan Aydin

Turkish Journal of Mathematics

A new convergent two-level finite difference scheme is proposed for the numerical solution of initial value problem of the generalized Rosenau--KdV--RLW equation. The new scheme is second-order, linear, conservative, and unconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solution is studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence of the scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating the solitary wave graph of the equation. Wave generation subject to initial Gaussian condition has …

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On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇ Jan 2019

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher S. Hassan, Özkan Öztürk, İsmai̇l Uğur Ti̇ryaki̇

Turkish Journal of Mathematics

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

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On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev Jan 2019

On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev

Turkish Journal of Mathematics

We investigate the Schrödinger operator $L(q)$ in $L_{2}\left( \mathbb{R}^{d}\right) \ (d\geq1)$ with the complex-valued potential $q$ that is periodic with respect to a lattice $\Omega.$ Besides, it is assumed that the Fourier coefficients $q_{\gamma}$ of $q$ with respect to the orthogonal system $\{e^{i\left\langle \gamma x\right\rangle }:\gamma\in\Gamma\}$ vanish if $\gamma$ belongs to a half-space, where $\Gamma$ is the lattice dual to $\Omega.$ We prove that the Bloch eigenvalues are $\mid\gamma+t\mid^{2}$ for $\gamma\in\Gamma,$ where $t$ is a quasimomentum and find explicit formulas for \ the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions …

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