Commognitive Conflicts In A Virtual Learning Environment: Exploring The Affordances Of Mobile Learning For Discourse Analysis,
2024
Ateneo de Manila University
Commognitive Conflicts In A Virtual Learning Environment: Exploring The Affordances Of Mobile Learning For Discourse Analysis, Mark N. Cumayas, Maria Alva Q. Aberin
Mathematics Faculty Publications
This paper explores the affordances of mobile learning in developing frameworks for discourse analysis. Specifically, this paper examines the commognitive analysis of classroom discourses in virtual learning environments (VLEs) and how it resolves the challenges of discourse analysis in face-to-face (F2F) settings. With the ongoing social turn of mathematics education research comes the widespread adoption of discourse analysis in educational research. The shift towards virtual learning technologies necessitated by the recent COVID-19 crisis has led to the development of various tools and processes that enable the teaching-learning process to occur in the virtual environment. While the initial drive to adapt …
Proving The Existence Of Equichordal Tight Fusion Frames Using The Newton–Kantorovich Theorem,
2024
Air Force Institute of Technology
Proving The Existence Of Equichordal Tight Fusion Frames Using The Newton–Kantorovich Theorem, Staci R. Davis
Theses and Dissertations
An equichordal tight fusion frame (ECTFF) is an example of an optimal packing of subspaces. In particular, an ECTFF is an optimal packing of points in the Grassmannian with respect to chordal distance. Equivalently, every ECTFF is an arrangement of subspaces that meet certain criteria; tightness and equichordality. The existence of an ECTFF can be rephrased as, a certain polynomial mapping as a root. Hence, one can prove the existence of an ECTFF by applying Newton–Kantorovich theorem to this polynomial mapping, given a close enough approximation of one. Newton–Kantorovich requires checking an inequality within a neighborhood of the approximate root, …
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 …
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.
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.
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.
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.
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 Program: Senior Projects (Public)
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 …
Fuzzy Software Reliability And Optimal Release Policy With Log-Logistic Testing Effort: An Analysis,
2024
T. M. Bhagalpur University, Bhagalpur
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 …
Geogebra Applets For Fostering Conceptual Understanding In Algebra,
2024
Ateneo de Manila University
Geogebra Applets For Fostering Conceptual Understanding In Algebra, Ma. Louise Antonette N. De Las Penas, Mark Anthony C. Tolentino, Maria Alva Q. Aberin, Agnes D. Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Debbie Marie B. Verzosa
Mathematics Faculty Publications
This paper discusses two GeoGebra applets, Radical and Parabola, that are designed to strengthen the conceptual understanding of specific topics in algebra. The design and pedagogical basis of the applets are presented. The integration of the applets in teaching Grade 9 mathematics in a partner high school in the Philippines is then discussed. Finally, we report feedback gathered from students and teachers during this integration. Their feedback indicates the potential of these applets for improving students’ learning of algebra.
Extensions Of Polynomial Plank Covering Theorems,
2024
The University of Texas Rio Grande Valley
Extensions Of Polynomial Plank Covering Theorems, Alexey Glazyrin, Roman Karasev, Alexandr Polyanskii
School of Mathematical & Statistical Sciences Faculty Publications
We prove the complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally symmetric and not necessarily round. We also prove a weaker version of the spherical polynomial plank covering conjecture for planks of different widths.
Nontrivial Invariant Subspaces Of Linear Operator Pencils,
2024
The University of Texas Rio Grande Valley
Nontrivial Invariant Subspaces Of Linear Operator Pencils, Jaewoong Kim, Jasang Yoon
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair T=(T1,T2) and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of T and the linear pencil of the original pair T of bounded operators with dense ranges.
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 & Statistical Sciences Faculty Publications
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
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.
Apollonian Packings And Kac-Moody Root Systems,
2024
Swarthmore College
Apollonian Packings And Kac-Moody Root Systems, Ian Whitehead
Mathematics & Statistics Faculty Works
We study Apollonian circle packings using the properties of a certain rank 4 indefinite Kac-Moody root system ϕ. We introduce the generating function Z(s) of a packing, an exponential series in four variables with an Apollonian symmetry group, which is a symmetric function for ϕ. By exploiting the presence of affine and Lorentzian hyperbolic root subsystems of ϕ, with automorphic Weyl denominators, we express Z(s) in terms of Jacobi theta functions and the Siegel modular form Δ₅. We also show that the domain of convergence of Z(s) is the Tits cone of ϕ, and discover that this domain inherits the …
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 & Statistical Sciences Faculty Publications
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 …
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 & Statistical Sciences Faculty Publications
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 …
