On Constructions Of Maximum Distance Separable Pascal-Like Rhotrices Over Finite Fields,
2024
Himachal Pradesh University, Shimla, India
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,
2024
National Institute of Technology, Sikkim, India
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.
The Distinguishing Number Of Some Special Kind Of Graphs,
2024
Shri P.N. Pandya Arts, M.P. Pandya Science and Smt. D.P. Pandya Commerce College
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,
2024
Himachal Pradesh University
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.
Thermal Performance Of Forced Convection Of Water- Nepcm Nanofluid Over A Semi-Cylinder Heat Source,
2024
Missouri University of Science and Technology
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 …
Quantum Computing And U.S. Cybersecurity: A Case Study Of The Breaking Of Rsa And Plan For Cryptographic Algorithm Transition,
2024
University of Nebraska - Lincoln
Quantum Computing And U.S. Cybersecurity: A Case Study Of The Breaking Of Rsa And Plan For Cryptographic Algorithm Transition, Helena Holland
Honors Theses
The invention of a cryptographically relevant quantum computer would revolutionize computing power, transforming industry and national security. While a theoretical possibility at the time of this writing, the ability of quantum algorithms to solve the factoring and discrete logarithm problems, upon which all currently employed public-key cryptography depends, presents a serious threat to digital communications. This research examines both the mathematics and government policy behind these risks and their implications for cybersecurity. Specifically, a case study of RSA, Shor’s algorithm, and the American Intelligence Community’s plan to transition toward quantum-resistant algorithms is presented to analyze quantum threats and opportunities and …
Singular Cr Structures Of Constant Webster Curvature And Applications,
2024
Università di Bologna
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,
2024
Azerbaijan State University of Economics
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 …
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates,
2024
Communication University of Zhejiang
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li
Engineering Faculty Articles and Research
In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of …
Optimizing Buying Strategies In Dominion,
2024
Georgia Southern University
Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis
Rose-Hulman Undergraduate Mathematics Journal
Dominion is a deck-building card game that simulates competing lords growing their kingdoms. Here we wish to optimize a strategy called Big Money by modeling the game as a Markov chain and utilizing the associated transition matrices to simulate the game. We provide additional analysis of a variation on this strategy known as Big Money Terminal Draw. Our results show that player's should prioritize buying provinces over improving their deck. Furthermore, we derive heuristics to guide a player's decision making for a Big Money Terminal Draw Deck. In particular, we show that buying a second Smithy is always more optimal …
Finite Element Solution Of Crack-Tip Fields For An Elastic Porous Solid With Density-Dependent Material Moduli And Preferential Stiffness,
2024
The University of Texas Rio Grande Valley
Finite Element Solution Of Crack-Tip Fields For An Elastic Porous Solid With Density-Dependent Material Moduli And Preferential Stiffness, Hyun C. Yoon, S. M. Mallikarjunaiah, Dambaru Bhatta
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, the finite element solutions of crack-tip fields for an elastic porous solid with density-dependent material moduli are presented. Unlike the classical linearized case in which material parameters are globally constant under a small strain regime, the stiffness of the model presented in this paper can depend upon the density with a modeling parameter. The proposed constitutive relationship appears linear in the Cauchy stress and linearized strain independently. From a subclass of the implicit constitutive relation, the governing equation is bestowed via the balance of linear momentum, resulting in a quasi-linear partial differential equation (PDE) system. Using the …
Regular Functions On The Scaled Hypercomplex Numbers,
2024
Chapman University
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the regularity of R-differentiable functions on open connected subsets of the scaled hypercomplex numbers {Ht}t∈R by studying the kernels of suitable differential operators {∇t}t∈R, up to scales in the real field R.
Hadamard Matrices Of Orders 60 And 64 With Automorphisms Of Orders 29 And 31,
2024
Shizuoka University
Hadamard Matrices Of Orders 60 And 64 With Automorphisms Of Orders 29 And 31, Makoto Araya, Masaaki Harada, Vladimir Tonchev
Michigan Tech Publications, Part 2
A classification of Hadamard matrices of order 2p + 2 with an automorphism of order p is given for p = 29 and 31. The ternary self-dual codes spanned by the newly found Hadamard matrices of order 60 with an automorphism of order 29 are computed, as well as the binary doubly even self-dual codes of length 120 with generator matrices defined by related Hadamard designs. Several new ternary near-extremal self-dual codes, as well as binary near-extremal doubly even self-dual codes with previously unknown weight enumerators are found.
Using A Two-Way Engagement Community- And Family-Centered Pedagogy To Prepare Pre-Service Mathematics Teachers In A Hispanic-Serving Institution,
2024
The University of Texas Rio Grande Valley
Using A Two-Way Engagement Community- And Family-Centered Pedagogy To Prepare Pre-Service Mathematics Teachers In A Hispanic-Serving Institution, Olga Ramirez, Mayra Ortiz Galarza, Luis M. Fernandez
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Research on effective methods to prepare pre-service teachers (PSTs) in teaching mathematics to K-12 Latin* students has been gaining significant momentum. These efforts have focused, in part, on promoting pedagogical practices that recognize and incorporate the culture and language that K-12 Latin* students and their communities share. As teacher educators, we argue that if we are to further prepare PSTs to serve the needs of such increasingly diversifying K-12 student population, the same pedagogical focus on the learner’s cultural wealth should also be applied to the preparation of PSTs themselves, especially among Latin* PSTs in Hispanic Serving Institutions (HSI) like …
Functional Data Learning Using Convolutional Neural Networks,
2024
The University of Texas Rio Grande Valley
Functional Data Learning Using Convolutional Neural Networks, Jose Galarza, Tamer Oraby
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we show how convolutional neural networks (CNNs) can be used in regression and classification learning problems for noisy and non-noisy functional data (FD). The main idea is to transform the FD into a 28 by 28 image. We use a specific but typical architecture of a CNN to perform all the regression exercises of parameter estimation and functional form classification. First, we use some functional case studies of FD with and without random noise to showcase the strength of the new method. In particular, we use it to estimate exponential growth and decay rates, the bandwidths of …
Spacetime Geometry Of Acoustics And Electromagnetism,
2024
Chapman University
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials,
2024
University Bordeaux
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, Roger Gay, Ahmed Sebbar
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how the classical polylogarithm function Lis (z) and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution (x +i0)s .We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemann’s zeta function, Master of Science, Ohio State University, Mathematics (1975)].
Gauss Circle Problem Over Smooth Integers,
2024
The University of Texas Rio Grande Valley
Gauss Circle Problem Over Smooth Integers, Ankush Goswami
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
For a positive integer 𝑛, let 𝑟2(𝑛) be the number of representations of 𝑛 as sums of two squares (of integers), where the convention is that different signs and different orders of the summands yield distinct representations. A famous result of Gauss shows that 𝑅(𝑥) ∶= ∑ 𝑛≤𝑥 𝑟2(𝑛) ∼ 𝜋𝑥. Let 𝑃(𝑛) denote the largest prime factor of 𝑛 and let 𝑆(𝑥, 𝑦) ∶= {𝑛 ≤ 𝑥 ∶ 𝑃(𝑛) ≤ 𝑦}. In this paper, we study the asymptotic behavior of 𝑅(𝑥, 𝑦) ∶= ∑ 𝑛∈𝑆(𝑥,𝑦) 𝑟2(𝑛) for various ranges of 2 ≤ 𝑦 ≤ 𝑥. For 𝑦 in a …
An Icosahedron For Two: A Many-Sided Look At Making A Duet,
2024
Alfred University
An Icosahedron For Two: A Many-Sided Look At Making A Duet, Colleen T. Wahl
LASER Journal
The space around our bodies is not empty or neutral. In fact, the space around our bodies is loaded with meaning and important. When we move through it, whether it be in our daily lives or a choreographer making specific choices in order to convey a message, we activate new understandings in our lives. As a dancer and choreographer, I created a duet from improvisational climbs on an icosahedron. This article discusses choreographing from the form icosahedron and connects Laban's theories of space harmony with the activation of meaning in my life.
Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins,
2024
Università di Roma Tor Vergata, Roma I-00133, Italy
Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich
Journal of Stochastic Analysis
No abstract provided.
