Physical Sciences and Mathematics Commons^™

Wang Tilings In Arbitrary Dimensions, Ian Tassin

Rose-Hulman Undergraduate Mathematics Journal

This paper makes a new observation about arbitrary dimensional Wang Tilings,
demonstrating that any d -dimensional tile set that can tile periodically along d − 1 axes must be able to tile periodically along all axes.
This work also summarizes work on Wang Tiles up to the present day, including
definitions for various aspects of Wang Tilings such as periodicity and the validity of a tiling. Additionally, we extend the familiar 2D definitions for Wang Tiles and associated properties into arbitrary dimensional spaces. While there has been previous discussion of arbitrary dimensional Wang Tiles in other works, it has been …

Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz

Turkish Journal of Mathematics

Let H be a supersolvable Hall π -subgroup of a finite group G. We prove that G has a normal π -complement if and only if H controls G-fusion in H.

Algorithmic Design And Computational Modeling Using Dynamic Spectrum Allocation Techniques To Optimize Bandwidth Management In Wireless Communication Systems, Ankit Walishetti

Distinguished Student Work

This study aims to address the pressing need for efficient spectrum management methodologies in wireless communication systems by developing innovative sorting and allocation algorithms. Leveraging Dynamic Spectrum Allocation (DSA) techniques, this research devises strategies to optimize the utilization of bandwidth within existing spectrum space, ultimately reducing the need for network infrastructure expansion.

Ensuring thorough coverage of DSA techniques, 5 distinct transmitter sorting algorithms were programmed and tested across 8 performance metrics designed to measure specific capabilities. For consistency, a single bandwidth allocation program was designed to ‘pack’ transmitters starting from the left endpoint of the spectrum space. Progressively varying the …

Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik

Turkish Journal of Mathematics

Let Xn denote the chain {1, 2, . . . , n} under its natural order. We denote the semigroups consisting of all order-preserving transformations and all orientation-preserving transformations on Xn by On and OPn , respectively. We denote by E(U) the set of all idempotents of a subset U of a semigroup S . In this paper, we first determine the cardinalities of Er(On) = {α ∈ E(On) : |im(α)| = |fix(α)| = r}, E ∗ r (On) = {α ∈ Er(On) : 1, n ∈ fix(α)}, Er(OPn) = {α ∈ E(OPn) : |fix(α)| = r}, E ∗ r …

Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin

Turkish Journal of Mathematics

This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.

On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan

Turkish Journal of Mathematics

This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.

Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova

Turkish Journal of Mathematics

We study the duality and norm completeness in the new classes of limitedly L-weakly compact and Dunford–Pettis L-weakly compact operators from Banach spaces to Banach lattices.

An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ

Turkish Journal of Mathematics

Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).

Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Turkish Journal of Mathematics

Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance { − (HDγu ) (t) = f(t, u(t)), t ∈ (1, e), u(1) = 0, u(e) = ∫ e 1 u(t)dA(t), where 1 < γ < 2, f : [1, e]×R2 → R satisfies Carathéodory conditions, ∫ e 1 u(t)dA(t) is the Riemann–Stieltjes integration, and (HDγu ) is the Hadamard fractional derivation of u of order γ . An example is included to illustrate our result.

Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi

Turkish Journal of Mathematics

For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves.

Special Subdiagrams Of Young Diagrams And Numerical Semigroups, Meral Süer, Mehmet Yeşi̇l

Turkish Journal of Mathematics

In this study, Young diagrams and their corresponding numerical sets are considered, and a new notion called special subdiagrams is described. Characterizations of special subdiagrams and their corresponding numerical sets, as well as the conditions when they are numerical semigroups, are provided. Young diagrams of symmetric, almost symmetric and Arf numerical semigroups are also considered and properties of their special subdiagrams are given.

Laguerre Type Twice-Iterated Appell Polynomials, Nesli̇han Bi̇ri̇ci̇k, Mehmet Ali̇ Özarslan, Bayram Çeki̇m

Turkish Journal of Mathematics

In this study, we use discrete Appell convolution to define the sequence of Laguerre type twice-iterated Appell polynomials. We obtain explicit representation, recurrence relation, determinantal representation, lowering operator, integro-partial raising operator and integro-partial differential equation. In addition, the special cases of this new family are investigated using Euler and Bernoulli numbers. We also state their corresponding characteristic properties.

Twisted Sasaki Metric On The Unit Tangent Bundle And Harmonicity, Liana Lotarets

Turkish Journal of Mathematics

The paper deals with the twisted Sasaki metric on the unit tangent bundle of n–dimensional Riemannian manifold Mn . The main purpose of the research is to find deformations that preserve the existence harmonic left-invariant unit vector fields on 3-dimensional unimodular Lie groups G with the left invariant metric and harmonic maps G → T1G in case of twisted Sasaki metric on the unit tangent bundle. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map Mn → T1Mn are obtained. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map M2 …

Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo

Turkish Journal of Mathematics

In this paper, we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces.

Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar

Turkish Journal of Mathematics

Our main aim in the current study is to examine the mathematical properties of a generalized 2-component Camassa-Holm system with a weakly dissipative term. Firstly, we acquire the theorem of well-posedness in locally for the generalized system with weak dissipation. Then, we demonstrate that this system can reveal the blow-up phenomenon. Finally, we acquire the theorem of global existence utilizing a method of the Lyapunov function.

Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman

Turkish Journal of Mathematics

In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL2(C) . In particular, given a finitely generated purely loxodromic free Kleinian group Γ = ⟨ξ1, ξ2, . . . , ξn⟩ for n ≥ 2, we show that |trace2(ξi) − 4| + |trace(ξiξjξ −1 i ξ −1 j ) − 2| ≥ 2 sinh2 ( 1 4 log αn ) for some ξi and ξj for i ̸= j in Γ provided that certain conditions on the hyperbolic displacements given by ξi , ξj and their length 3 conjugates formed by …

On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang

Turkish Journal of Mathematics

We consider the integro-differential Dirac operator with parameter-dependent nonlocal integral boundary conditions. We derive the asymptotic expressions for the eigenvalues and the zeros of eigenfunctions (nodal points or nodes) and develop a constructive procedure for solving the inverse nodal problem for this operator.

Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva

Turkish Journal of Mathematics

In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way, we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge …

Strongly I-Bicritical Graphs, Michelle Edwards, Gary Macgillivray, Shahla Nasserasr

Theory and Applications of Graphs

A graph $G$ is \emph{strongly $i$-bicritical} if it has independent domination number $i(G) \geq 3$, and $i(G - \{x, y\}) = i(G) - 2$ whenever $x$ and $y$ are two non-adjacent vertices of $G$. We describe five constructions of strongly $i$-bicritical graphs. For four of them, necessary and sufficient conditions for the graph produced by the construction to be strongly $i$-bicritical are given. The strongly $i$-bicritical graphs with independent domination number $i(G) = 3$ are characterized, and it is shown that the strongly $i$-bicritical graphs with independent domination number $i(G) \geq 5$ may be hard to characterize. It is shown …

A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

The Distinguishing Number Of Some Special Kind Of Graphs, Arti Salat, Amit Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In the present study, the distinguishing number of some different graphs is examined where different graphs like the coconut tree graph, firecracker graph, jellyfish graph, triangular book graph, and banana tree graph have been taken into account. The major goal of the proposed study is to understand the distinguishing number of different graphs for better insights. It is evident from the results that the distinguishing numbers and automorphism groups of the above-mentioned graphs have been carried out successfully.

Construction Of Normal Polynomials Using Composition Of Polynomials Over Finite Fields Of Odd Characteristic, Shalini Gupta, Manpreet Singh, Rozy Sharma

Applications and Applied Mathematics: An International Journal (AAM)

A monic irreducible polynomial is known as a normal polynomial if its roots are linearly independent over Galois field. Normal polynomials over finite fields and their significance have been studied quite well. Normal polynomials have applications in different fields such as computer science, number theory, finite geometry, cryptography and coding theory. Several authors have given different algorithms for the construction of normal polynomials. In the present paper, we discuss the construction of the normal polynomials over finite fields of prime characteristic by using the method of composition of polynomials.

Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, And Rarely Of Other Directions: A Geometric Explanation, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In time, pavements deteriorate, and need maintenance. One of the most typical pavement faults are cracks. Empirically, the most frequent cracks are longitudinal, i.e., following the direction of the road; less frequent are transversal cracks, which are orthogonal to the direction of the road. Sometimes, there are cracks in different directions, but such cracks are much rarer. In this paper, we show that simple geometric analysis and fundamental physical ideas can explain these observed relative frequencies.

Fuzzy Software Reliability And Optimal Release Policy With Log-Logistic Testing Effort: An Analysis, Seema Rani, Jitendra Kumar, N. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

We will discuss a Software Reliability Growth Model (SRGM) using fuzzy and imperfect debugging environments; we integrate Log-Logistic (LL) Testing Effort Function (TEF) into fuzzy SRGMs. Estimation methods, such as Least Square and Maximum Likelihood, are used to obtain the value of Testing-Effort and SRGMs parameters. It is not always possible and is constantly required to quantify the exact value of parameters. Due to human conduct, the value of Testing-Effort and SRGM parameters cannot be exactly quantified. In this scenario, parameters are supposed to be vague or fuzzy. To make the software consistent, the developer needs to propose some quantity …

On Constructions Of Maximum Distance Separable Pascal-Like Rhotrices Over Finite Fields, Neetu Dhiman, Mansi Harish, Shalini Gupta, Arun Chauhan

Applications and Applied Mathematics: An International Journal (AAM)

Cryptography and coding theory are the important areas where Maximum Distance Separable (MDS) matrices are used extensively. The Pascal matrix plays vital role in combinatorics, matrix theory and its properties provide interesting combinatorial identities. Pascal matrices also have a wide range of applications in cryptography. In this paper, we define Pascal-like rhotrix, and further, we construct MDS Pascal-like rhotrices over finite fields.

Some Generalizations Of Corona Product Of Two Graphs, Aparajita Borah, Gajendra Pratap Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we are seeking to conceptualize the notion of corona product of two graphs to contrive some special types of graphs. That is, here our attempt is to regenerate a familiar graph as a product graph. We are considering seven familiar graphs here to reconstruct them with the help of corona product of two graphs. Such types of families of the graphs and operations can be used to study biological pathways as well as to find the optimal order and size for the special types of graphs.

Thermal Performance Of Forced Convection Of Water- Nepcm Nanofluid Over A Semi-Cylinder Heat Source, Xiaoming Wang, Rassol H. Rasheed, Babak Keivani, Dheyaa J. Jasim, Abbas J. Sultan, Sajad Hamedi, Hamed Kazemi-Varnamkhasti, Soheil Salahshour, Davood Toghraie

Mathematics and Statistics Faculty Research & Creative Works

1) Background: Phase change materials (PCMs) have been used statically, which has caused the use of these materials to face challenges. Encapsulating PCMs and combining them with the base fluid can significantly solve the problem of using PCMs in BTM systems. In the present study, based on computational fluid dynamics, forced convection heat transfer of nano-encapsulated phase change materials (NEPCM) in a BTM system are simulated. The main aim of the present research is to reduce the temperature at the surface of the hot cylinder. 2) Methods: In this research, we simulated lithium battery thermal management systems in both steady …

Machine Learning Application Of Generalized Gaussian Radial Basis Function And Its Reproducing Kernel Theory, Himanshu Singh

Math Faculty Publications and Presentations

Gaussian Radial Basis Function Kernels are the most-often-employed kernel function in artificial intelligence for providing the optimal results in contrast to their respective counterparts. However, our understanding surrounding the utilization of the Generalized Gaussian Radial Basis Function across different machine learning algorithms, such as kernel regression, support vector machines, and pattern recognition via neural networks is incomplete. The results delivered by the Generalized Gaussian Radial Basis Function Kernel in the previously mentioned applications remarkably outperforms those of the Gaussian Radial Basis Function Kernel, the Sigmoid function, and the ReLU function in terms of accuracy and misclassification. This article provides a …

Singular Cr Structures Of Constant Webster Curvature And Applications, Chiara Guidi, Ali Maalaoui, Vittorio Martino

Mathematics

We consider the sphere (Formula presented.) equipped with its standard contact form. In this paper, we construct explicit contact forms on (Formula presented.), which are conformal to the standard one and whose related Webster metrics have constant Webster curvature; in particular, it is positive if (Formula presented.). As main applications, we provide two perturbative results. In the first one, we prove the existence of infinitely many contact forms on (Formula presented.) conformal to the standard one and having constant Webster curvature, where (Formula presented.) is a small perturbation of (Formula presented.). In the second application, we show that there exist …

Why Two Fish Follow Each Other But Three Fish Form A School: A Symmetry-Based Explanation, Shahnaz Shahbazova, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Recent experiments with fish has shown an unexpected strange behavior: when two fish of the same species are placed in an aquarium, they start following each other, while when three fish are placed there, they form (approximately) an equilateral triangle, and move in the direction (approximately) orthogonal to this triangle. In this paper, we use natural symmetries -- such as rotations, shifts, and permutation of fish -- to show that this observed behavior is actually optimal. This behavior is not just optimal with respect to one specific optimality criterion, it is optimal with respect to any optimality criterion -- as …