Mathematics Commons^™

Covering Of Objects Related To Rupert Property, Pongbunthit Tonpho

Chulalongkorn University Theses and Dissertations (Chula ETD)

One problem related to covering problem is whether one object has Rupert property. An object K in R³ has the Rupert property if a hole could be cut through one copy of K with the same size to permit another copy to pass through it. There are objects in R³ which have Rupert property, such as a cube. But not all of objects in R³ has Rupert property, such as a sphere. It is interesting to check that a given object has Rupert property. In this work, we construct useful lemmas for studying this problem. Furthermore, we apply these lemmas …

Noncommutative Reality-Based Algebras Of Rank 6, Allen Herman, Mikhael Muzychuk, Bangteng Xu

EKU Faculty and Staff Scholarship

We show that noncommutative standard reality-based algebras (RBAs) of dimension 6 are determined up to exact isomorphism by their character tables. We show that the possible character tables of these RBAs are determined by seven real numbers, the first four of which are positive and the remaining three real numbers can be arbitrarily chosen up to a single exception. We show how to obtain a concrete matrix realization of the elements of the RBA-basis from the character table. Using a computer implementation, we give a list of all noncommutative integral table algebras of rank 6 with orders up to 150. …

Quasi-Gorenstein Modules, Alexander York

Electronic Theses and Dissertations

This thesis will study the various roles that quasi-Gorenstein modules and their properties play in the study of homological dimensions and linkage of modules. To that effect we begin by studying these modules in their own right. An R-module M of grade g will be quasi-Gorenstein if ExtiR(M, R) = 0 for i 6= g and there is an isomorphism M ∼= ExtgR(M, R). Such modules have many nice properties which we will explore throughout this thesis. We will show they help extend a characterization of diagonalizable matrices over principal ideal domains to more general rings. We will use their …

Weierstrass Vertices And Divisor Theory Of Graphs, Ajani Ruwandhika Chulangi De Vas Gunasekara

Electronic Theses and Dissertations

Chip-firing games and divisor theory on finite, connected, undirected and unweighted graphs have been studied as analogs of divisor theory on Riemann Surfaces. As part of this theory, a version of the one-dimensional Riemann-Roch theorem was introduced for graphs by Matt Baker in 2007. Properties of algebraic curves that have been studied can be applied to study graphs by means of the divisor theory of graphs. In this research, we investigate the property of a vertex of a graph having the Weierstrass property in analogy to the theory of Weierstrass points on algebraic curves. The weight of the Weierstrass vertices …

Cyclic Clique Decompositions Of Powerof Cycles, Apiwat Peereeyaphat

Chulalongkorn University Theses and Dissertations (Chula ETD)

A clique decomposition P of a graph G is a collection of cliques of G such that each edge of G belongs to exactly one clique in the collection. We say that P is cyclic if there is an isomorphism : V (G)→ V (G) such that Kk{α (v₁), α (v₂), α (v₃), ... , α (vk)g is a clique in P whenever Kk{v₁; v₂; v₃; :::; vk} is. The k-power of an n-cycle, Ck n, is the graph having the same vertex set as Cn and uv is an edge in Ck n if and only if dCn(u; v) …

Defective Colorings On Complete Bipartite And Multipartite K-Uniform Hypergraphs, Artchariya Muaengwaeng

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the definition of a defective coloring and a defective chromatic number on graphs to a defective coloring and a defective chromatic number on hypergraphs. First, we find the defective chromatic number on a complete bipartite k-uniform hypergraph and the defective chromatic number on a complete bipartite k-uniform hypergraph of which each color class is acyclic. Second, we determine the defective chromatic number and the defective chromatic number of which each color class is acyclic on a complete k-partite k-uniform hypergraph whose each edge has k vertices from k different partite sets. Finally, we determine the …

Critical Exponent For Nonlinear Nonlocal Equations, Auttawich Manui

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study the nonlinear nonlocal equation ∂t u=J*u-u+u¹+p where p>0 and J is nonnegative, bounded, and radially symmetric with unit integral. The Fourier transform of J satisfies J ̂(ξ)=1-A|ξ|^β (ln1/|ξ| 〗 )^μ+o(〖|ξ|〗^β (ln〖1/(|ξ|)〗 )^μ ) as ξ→0, for 0<β≤2, μ∈R, and A>0. In this study, we establish the local existence, uniqueness, and the comparison principle of solutions. Furthermore, we show that the Fujita critical exponent for this equation is β/n when μ<0. For the case μ>1, we discover that the critical exponent is β/n , and the solutions belong to the global to the small initial data regime.

Streaming Data Classification Method Using Scalable Hyper-Ellipsoids With Linear Discriminant Projection Distance Ratio, Perasut Rungcharassang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Learning streaming data with limited size of memory storage becomes an interesting problem. Although there have been several learning methods recently proposed, based on the interesting concept of discard-after-learn, the performance of these issues: the learning speed, number of redundant neurons, and classification accuracy of these methods can be further improved in terms of faster speed, less number of neurons, and higher accuracy. The following new four concepts and approaches were proposed in this dissertation: (1) a more generic structure of hyper-ellipsoidal function called Scalable Hyper-Ellipsoidal Function (SHEF) capable of handling the problem of curse of dimensionality by introducing a …

Generalized Symplectic Graphs And Generalized Orthogonal Graphs Over Finite Commutative Rings, Siripong Sirisuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let R be a finite commutative ring with identity, n ∈ N and β a bilinear form on Rⁿ. In this dissertation, we count the numbers of free submodules and totally isotropic free submodules of Rⁿ of rank s by using the lifting idea. We define the generalized bilinear form graph whose vertex set is the set of totally isotropic free submodules of Rⁿ of rank s and the adjacency condition is given by some rank conditions. We study this graph when (Rⁿ, β) is a symplectic space and an orthogonal space. We can determine the degree of each vertex …

Variant Of D'Alembert Functional Equation On Compact Homogeneous Space, Sorawit Viwanthananut

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, we introduce a new functional equation on compact homogeneous spaces based on the d'Alembert functional equation on compact groups. We solve the functional equation by using tools from harmonic analysis.

Thin Cloud Removal Using Local Minimization And Image Transformation In Hsi Color Space, Thanet Markchom

Chulalongkorn University Theses and Dissertations (Chula ETD)

In the use of satellite images, clouds can be an obstacle due to their opacity property that can block the visibility of ground objects in case of thick clouds and can also be blended with the underlying details in case of thin clouds. In this research, we propose a novel method to remove thin clouds and retrieve the actual information by taking the advantage of HSI color space instead of RGB color space. The proposed method aims to estimate the cloud appearance called the scattering light, remove thin clouds from intensity channel to avoid an effect to the original color, …

กลยุทธ์การลงทุนส่วนบุคคลบนพื้นฐานเกณฑ์การจัดเก็บภาษีเงินได้, ปิยวดี สุขชาติ

Chulalongkorn University Theses and Dissertations (Chula ETD)

ตามที่กรมสรรพากรได้ระบุไว้ใน แบบแสดงรายการภาษีเงินได้บุคคลธรรมดา ปีภาษี 2559 สำหรับผู้มีเงินได้ตามมาตรา 40 (1) - (8) แห่งประมวลรัษฎากร (ภ.ง.ด.90) จะสามารถนำเงินไปลงทุนในแหล่งต่าง ๆ เพื่อลดเงินได้สุทธิก่อนที่จะนำไปคำนวณภาษี ในที่นี้ผู้ทำวิจัยสนใจการวางแผนการลงทุนเพื่อจะได้รับประโยชน์ทางภาษีและผลตอบแทนสูงสุดโดยการนำเงินไปลงทุนใน 3 แหล่ง ประกอบด้วย ประกันชีวิต (Life insurance) กองทุนรวมเพื่อการเลี้ยงชีพ (Retirement Mutual Fund : RMF) และกองทุนรวมหุ้นระยะยาว (Long Term Equity Fund : LTF) โดยการหากลยุทธ์การลงทุนเพื่อแนะนำแหล่งลงทุนและหาสัดส่วนจำนวนเงินที่เหมาะสมที่ใช้ในการลงทุนในแหล่งต่าง ๆ ที่สอดคล้องกับแผนการลงทุนที่มีอยู่ในตลาดและนำเสนอแผนการลงทุนที่เหมาะสมสำหรับแต่ละบุคคล โดยที่ผู้ลงทุนไม่เสียสภาพคล่องทางการเงิน อีกทั้งยังได้รับประโยชน์ทางภาษีและผลตอบแทน นั่นคือการเสียภาษีน้อยลงจากเดิมและได้ผลตอบแทนจากการลงทุนสูงสุด เริ่มจากการหาแหล่งลงทุนที่เหมาะสมสำหรับแต่ละบุคคลตามระดับความเสี่ยงที่รับได้ สร้างตัวแบบทางคณิตศาสตร์เพื่อทำนายราคากองทุนต่าง ๆ แล้วทำนายผลตอบแทนกองทุนต่าง ๆ ตามแหล่งลงทุนที่เหมาะสมนั้นเพื่อหาว่ากองทุนใดให้ผลตอบแทนที่เหมาะสมที่สุดที่เหมาะกับบางช่วงของรายได้ เพื่อคำนวณสัดส่วนจำนวนเงินที่เหมาะสมสำหรับแต่ละบุคคลที่จะต้องใช้ในการลงทุนในแหล่งต่าง ๆ และนำเสนอแผนการลงทุนที่ให้ผลตอบแทนสูงสุดสามอันดับของแต่ละแหล่งลงทุน เพื่อให้ผู้ลงทุนใช้ประกอบการตัดสินใจ เมื่อผู้มีเงินได้นำเงินได้สุทธิไปลงทุนแล้วนั้น จะเป็นการลดเงินได้สุทธิให้น้อยลงหรือปรับลดขั้นเงินได้สุทธิ ทำให้อัตราภาษีที่จะต้องเสียในปีนั้น ๆ ลดลงและได้ผลตอบแทนสูงสุด

Complex-Valued Time Series Modeling For Improved Activation Detection In Fmri Studies, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we …

The Kumaraswamy Weibull Geometric Distribution With Applications, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the kumaraswamy weibull geometric (Kw-WG) distribution which includes as special cases, several models such as the kumaraswamy weibull distribution, kumaraswamy exponential distribution, weibull geometric distribution, exponential geometric distribution, to name a few. This distribution was monotone and non-monotone hazard rate functions, which are useful in lifetime data analysis and reliability. We derive some basic properties of the Kw-WG distribution including non-central rth-moments, skewness, kurtosis, generating functions, mean deviations, mean residual life, entropy, order statistics and certain characterizations of our distribution. The method of maximum likelihood is used for estimating the model parameters and a simulation …

On Modified Burr Xii-Inverse Exponential Distribution: Prop¬Erties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Haitham M. Yousof, Azeem Ali, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, increasing and decreasing and modified bathtub hazard rate called Modified Burr XII-Inverse Exponential (MBXII-IE) is introduced. The density function of MBXII-IE has exponential, left-skewed, right-skewed and symmetrical shapes. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The MBXII-IE distribution is characterized via different techniques. Parameters of MBXII-IE distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the MBXII-IE distribution. The …

Question 1: Iceberg To Los Angeles, Question 2: Lost Luggage, Larry Weinstein

Physics Faculty Publications

How much fuel would it take to tow a large enough iceberg to Los Angeles to provide fresh water for the city for an entire year? (Thanks to John Adam of Old Dominion University and co-author of Guesstimation for suggesting the question.)

U.S.-based airlines lost 1.7 million pieces of luggage in 2016. How tall a mountain will this make? What is the probability an airline will lose our luggage on our next flight? (Thanks to John Adam of Old Dominion University and co-author of Guesstimation for suggesting the question.)

Course Portfolio For Math 407 Mathematics For High School Teaching: Refining Conceptual Understanding In A Mathematics Course For Pre-Service Teachers, Alexandra Seceleanu

UNL Faculty Course Portfolios

My intention in this portfolio is to present my approach to teaching an upper-level mathematics course for pre-service secondary level mathematics teachers. Several teaching strategies are discussed in the context of designing a coherent approach to this course, which emphasizes the need for conceptual reasoning above all other goals. These strategies are evaluated and assessed in connection to the learning outcomes using samples of student work from the course.

Also presented are samples of course materials that were used to lead students through an organized discussion of the relevant concepts. These materials convey some basic mathematical knowledge and therefore may …

Restriction Of A Quadratic Form Over A Finite Field To A Nondegenerate Affine Quadric Hypersurface, Edoardo Ballico

Turkish Journal of Mathematics

Let $h, h_M: \mathbb {F} _q^n\to \mathbb {F} _q$ be quadratic forms with $h$ not degenerate. Fix $k\in \mathbb {F} _q$ and set $C_n(k,h)_{\mathbb {F} _q}:= \{h(x_1,\dots ,x_n)=k\}\subset \mathbb {F}_q^n$. We compute (in many cases) the image of $h_{M C_n(k,h)_{\mathbb {F} _q}}$. This question is related to a question on the numerical range of matrices over a finite field.

A Coanalytic Menger Group That Is Not $\Sigma$-Compact, Seçi̇l Tokgöz

Turkish Journal of Mathematics

Under $V=L$ we construct coanalytic topological subgroups of reals, demonstrating that even for definable groups of reals, selection principles may differ.

The Equation ${Dd'+D'D=D^2}$ For Derivations On C$^*$-Algebras, Sayed Khalil Ekrami, Madjid Mirzavaziri

Turkish Journal of Mathematics

Let $\mathcal{A}$ be an algebra. A linear mapping $d:\mathcal{A}\to\mathcal{A}$ is called a derivation if $d(ab)=d(a)b+ad(b)$ for each $a,b\in\mathcal{A}$. Given two derivations $d$ and $d'$ on a C$^*$-algebra $\mathcal{A}$, we prove that there exists a derivation $D$ on $\mathcal A$ such that $dd'+d'd=D^2$ if and only if $d$ and $ d' $ are linearly dependent.

Boolean Differential Operators, Luis Hernandez Encinas, Ángel Martín Del Rey

Turkish Journal of Mathematics

In this work the notion of boolean differential operator is revisited and some new properties are stated.

Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems, Youssef Raffoul

Turkish Journal of Mathematics

In this note, we investigate the existence of periodic and asymptotically periodic solutions of a system of coupled nonlinear Volterra integro-differential equations with infinite delay. We will make use of Schauder fixed point theorem to prove our maps have fixed points.

Regularity And Projective Dimension Of The Edge Ideal Of A Generalized Theta Graph, Seyyede Masoome Seyyedi, Farhad Rahmati

Turkish Journal of Mathematics

Let $k\geq 3$ and $G=\theta_{n_1,\ldots, n_k}$ be a graph consisting of $k$ paths that have common endpoints. In this paper, we show that the projective dimension of $R/I(G)$ equals $bight I(G)$ or $ bight I(G)+1$. For some special cases, we explain $depth(R/I(G))$ in terms of invariants of graphs. Moreover, we prove the regularity of $R/I(G)$ equals $c_G$ or $c_G+1$, where $c_G$ is the maximum number of 3-disjoint edges in $G$.

On A Class Of Unitary Operators On The Bergman Space Of The Right Half Plane, Namita Das, Jitendra Kumar Behera

Turkish Journal of Mathematics

In this paper, we introduce a class of unitary operators defined on the Bergman space $L_a^2(\mathbb{C}_+)$ of the right half plane $\mathbb{C}_+$ and study certain algebraic properties of these operators. Using these results, we then show that a bounded linear operator $S$ from $L_a^2(\mathbb{C}_+)$ into itself commutes with all the weighted composition operators $W_a, a \in \mathbb{D}$ if and only if $\widetilde{S}(w)=\langle Sb_{\overline{w}},b_{\overline{w}}\rangle, w \in \mathbb{C}_+ $ satisfies a certain averaging condition. Here for $a=c+id \in \mathbb{D}, f \in L_a^2(\mathbb{C}_+), W_af=(f \circ t_a) \frac{M^{\prime}}{M^{\prime} \circ t_a}, Ms=\frac{1-s}{1+s}, t_a(s)=\frac{-ids +(1-c)}{(1+c)s + id}$, and $b_{\overline{w}}(s)=\frac{1}{\sqrt{\pi}} \frac{1+w}{1+\overline{w}} \frac{2 \mbox {Re} w}{(s+w)^2}, w=M\overline {a}, …

The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski

Turkish Journal of Mathematics

How many linear connections are there with a prescribed Ricci tensor? The question is answered in the analytic case by using the Cauchy-Kowalevski theorem

Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

In this paper, by applying the $p$-adic $q$-integrals to a family of continuous differentiable functions on the ring of $p$-adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius-Euler numbers and polynomials, the Stirling numbers, and other …

An Inequality On The Hodge Number $H^{1,1}$ Of A Fibration And The Mordell-Weil Rank, Cheng Gong, Hao Sun

Turkish Journal of Mathematics

In this paper, we establish some formulas on the Mordell-Weil rank and the Hodge number $h^{1,1}$ for a fibration.

An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus, Muhammad Waseem, Muhammad Aslam Noor, Farooq Ahmed Shah, Khalida Inayat Noor

Turkish Journal of Mathematics

In this paper, we develop an efficient technique in the framework of multiplicative calculus and suggest a new class of numerical methods for solving multiplicative nonlinear equations \textit{g}(\textit{x}% ) = 1. We also develop the convergence criteria of the proposed methods. We solve the population growth model and minimization problem, which demonstrate the implementation and efficiency of the new techniques. We also show that these techniques perform much better as compared to the similar ordinary methods for solving ordinary nonlinear equations \textit{f}(\textit{x}) = 0.

An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar

Turkish Journal of Mathematics

The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.

Hyperplanes, Parallelism, And Related Problems In Veronese Spaces, Krzysztof Petelczyc, Krzysztof Prazmowski, Malgorzata Prazmowska, Mariusz Zynel

Turkish Journal of Mathematics

We determine hyperplanes in Veronese spaces associated with projective spaces and polar spaces, and we analyze the geometry of parallelisms induced by these hyperplanes. We also discuss whether or not parallelisms on Veronese spaces associated with affine spaces can be imposed.