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Articles 1861 - 1890 of 27174
Full-Text Articles in Entire DC Network
Spherical Product Hypersurfaces In Euclidean Spaces, Sezgi̇n Büyükkütük, Günay Öztürk
Spherical Product Hypersurfaces In Euclidean Spaces, Sezgi̇n Büyükkütük, Günay Öztürk
Turkish Journal of Mathematics
Spherical product surfaces are obtained with the help of a special product by considering two curves inn−dimensional space. One of their special cases is rotational surface. The reason why the present study is significantthat the spherical product is used to construct hypersurfaces. (n−1)−curves are needed during this construction. Firstly,the spherical product hypersurfaces are defined in E4 , Gaussian and mean curvature are yielded and then conditionsbeing flat or minimal are examined. Moreover, superquadrics, which are associated with spherical product, are handledfor the first time in hypersurface form and give some examples. Finally, spherical product hypersurfaces are generalizedto n−dimensional Euclidean space …
Individual Stability Of Representations Of Abelian Semigroups, Heybetkulu Mustafayev
Individual Stability Of Representations Of Abelian Semigroups, Heybetkulu Mustafayev
Turkish Journal of Mathematics
Let S be a suitable subsemigroup of a locally compact abelian group and let T={T(s)}s(-S be a bounded and strongly continuous trepresentation of S on a Banach space X. In this note, we study the spectral conditions on T and the ergodic conditios on x in X which will imply that T(s)x-->0 strongly as s--> infinity through S.
Transmission Eigenvalues Problem Of A Schrödinger Equation, Emel Yildirim, Elgiz Bairamov
Transmission Eigenvalues Problem Of A Schrödinger Equation, Emel Yildirim, Elgiz Bairamov
Turkish Journal of Mathematics
In this paper, transmission eigenvalues of a Schrödinger equation have been studied by constructing a new inner product and using Weyl theory. Necessary conditions for these eigenvalues to be negative, real and finite have been examined. This method has provided a new framework related to transmission eigenvalue problems and investigation of their properties. The conclusions has been verified for special case of the problem.
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplicationoperations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally,the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonianconics are given. Additionally, examples were given and drawings were made to make the resulting characterizations andtheorems more memorable.
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 andthe ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connectionunder certain conditions.
Rings And Finite Fields Whose Elements Are Sums Or Differences Of Tripotents And Potents, Adel Abyzov, Stephen Cohen, Peter Danchev, Daniel Tapkin
Rings And Finite Fields Whose Elements Are Sums Or Differences Of Tripotents And Potents, Adel Abyzov, Stephen Cohen, Peter Danchev, Daniel Tapkin
Turkish Journal of Mathematics
We significantly strengthen results on the structure of matrix rings over finite fields and applythem to describe the structure of the so-called weakly n-torsion clean rings. Specifically, we establish that, forany field F with either exactly seven or strictly more than nine elements, each matrix over F is presentableas a sum of of a tripotent matrix and a q-potent matrix if and only if each element in F is presentable as asum of a tripotent and a q-potent, whenever q > 1 is an odd integer. In addition, if Q is a power of an oddprime and F is a field …
A Sufficient Condition For The Wildness Of An Automorphism Of A Free Leibnizalgebra, Zeynep Özkurt
A Sufficient Condition For The Wildness Of An Automorphism Of A Free Leibnizalgebra, Zeynep Özkurt
Turkish Journal of Mathematics
In this paper, we apply the criterion of Mikhalev and Umirbaev for the invertibility of an endomorphismof a finitely generated free Leibniz algebra via its Jacobian matrix to determine whether a given endomorphism is anautomorphism. Moreover, it is shown that the invertibility of the determinant of the Jacobian matrix of an automorphismimplies its wildness.
Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saito
Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saito
Journal of Stochastic Analysis
No abstract provided.
Minimal Separating Sets In Surfaces, Christopher Nelson Aagaard
Minimal Separating Sets In Surfaces, Christopher Nelson Aagaard
Dissertations and Theses
Given a connected topolgical space X, we say that L ⊆ X is a minimal separating set if removing L from X gives a disconnected surface, butremoving any proper subset of L leaves the surface connected. We classify which embeddings of topological graphs are minimal separating in an orientable surface X with genus g, and construct a computer program to compute the number of such embeddings, and the number of topological graphs which admit such an embedding for g ≤ 5.
Coarse-Gridded Simulation Of The Nonlinear Schrödinger Equation With Machine Learning, Benjamin F. Akers, Kristina O. F. Williams
Coarse-Gridded Simulation Of The Nonlinear Schrödinger Equation With Machine Learning, Benjamin F. Akers, Kristina O. F. Williams
Faculty Publications
A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data …
Symmetric Laminations Of Degree D And Identity Return Triangles In Degree 3, Thomas Sirna
Symmetric Laminations Of Degree D And Identity Return Triangles In Degree 3, Thomas Sirna
All ETDs from UAB
Laminations of the unit disc were introduced by Thurston in the 1980s as a tool to study the Julia sets and the parameter spaces of complex polynomials. In general, a lamination will be the unit disc D (considered as a subset of the complex plane C, with the boundary of D denoted by S) along with a collection of chords in D that can only intersect at their endpoints on S. We call the chords of a lamination leaves. In most situations we also consider a map σd : S → S on the endpoints of the leaves defined by …
Meta-Analysis Of Set-Based Multiple Phenotype Association Test Based On Gwas Summary Statistics From Different Cohorts, Lirong Zhu, Shuanglin Zhang, Qiuying Sha
Meta-Analysis Of Set-Based Multiple Phenotype Association Test Based On Gwas Summary Statistics From Different Cohorts, Lirong Zhu, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications
Genome-wide association studies (GWAS) have emerged as popular tools for identifying genetic variants that are associated with complex diseases. Standard analysis of a GWAS involves assessing the association between each variant and a disease. However, this approach suffers from limited reproducibility and difficulties in detecting multi-variant and pleiotropic effects. Although joint analysis of multiple phenotypes for GWAS can identify and interpret pleiotropic loci which are essential to understand pleiotropy in diseases and complex traits, most of the multiple phenotype association tests are designed for a single variant, resulting in much lower power, especially when their effect sizes are small and …
Generalized Periodicity And Applications To Logistic Growth, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Generalized Periodicity And Applications To Logistic Growth, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for …
The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential, Alex H. Ardila, Jason Murphy
The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential, Alex H. Ardila, Jason Murphy
Mathematics and Statistics Faculty Research & Creative Works
We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.
A Full Description Of All Commutative Associative Polynomial Operations On Probabilities, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
A Full Description Of All Commutative Associative Polynomial Operations On Probabilities, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
When two events are independent, the probability that both events occur is equal to the product p1 * p2 of the probabilities of each of these events. The probability that at least one of these events will occur is equal to p1 + p2 − p1 * p2. In both cases, we have a commutative associative polynomial operation. A natural question is: how can we describe all possible operations of this type? These operations are described in this paper.
Why Kolmolgorov-Arnold Networks (Kan) Work So Well: A Qualitative Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva
Why Kolmolgorov-Arnold Networks (Kan) Work So Well: A Qualitative Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
In the usual deep neural network, weights are adjusted during training, but the activation function remains the same. Lately, it was experimentally shown that if, instead of using the same activation function always, we train the activation functions as well, we get a much better results -- i.e., for the networks with the same number of parameters, we get a much better accuracy. Such networks are called Kolmogorov-Arnold networks. In this paper, we provide a general explanation of why these new networks work so well.
How To Check Continuity Based On Approximate Measurement Results, Inese Bula, Vladik Kreinovich
How To Check Continuity Based On Approximate Measurement Results, Inese Bula, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, a reasonable conjecture is that, e.g., the dependence of some quantity on the spatial location is continuous, with an appropriate bounds on the difference between the values at nearby points. If we knew the exact values of the corresponding quantity, checking this conjecture would be very straightforward. In reality, however, measurement results are only approximations to the actual values. In this paper, we show how to check continuity based on the approximate measurement results.
Three Applications Of Geometric Reasoning: Why Metastasis Is Mostly Caused By Elongated Cancer Cells? How Body Shape Affects Curiosity? Why Ring Fractures In Ice?, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Three Applications Of Geometric Reasoning: Why Metastasis Is Mostly Caused By Elongated Cancer Cells? How Body Shape Affects Curiosity? Why Ring Fractures In Ice?, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we describe three applications of geometric reasoning to important practical problems ranging from micro- to macro-level. Specifically, we use geometric reasoning to explain why metastasis is mostly caused by elongated cancer cell, why curiosity in fish is strongly correlated with body shape, and why ring-shaped fractures appear in Antarctica.
To Which Interdisciplinary Research Collaborations Should We Pay More Attention?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
To Which Interdisciplinary Research Collaborations Should We Pay More Attention?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
Interdisciplinary research is very important in modern science. However, such a research is not easy, it often needs support and help. Resources that can be used for such a support are limited, so we need to decide which of many possible collaborations we should support. In this paper, we provide a natural simple model of collaboration effectiveness. Based on this model, we conclude that we should support collaborations for which the vector product of the participants' knowledge vectors attains the largest values.
Why Decisions Based On The Results Of Worst-Case, Most Realistic, And Best-Case Scenarios Work Well?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Chon Van Le
Why Decisions Based On The Results Of Worst-Case, Most Realistic, And Best-Case Scenarios Work Well?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
Often, to make an appropriate decision, people try three scenarios: the worst case, the most realistic case, and the best case. This three-scenarios approach often leads to reasonable decisions. A natural question is: why worst case and best case? These extreme cases mean that all numerous independent random factors work in the same direction: either are all stacked for or are all stacked against. Such stacking of random factors is highly improbable. So, at first glance, it would be more beneficial to use more realistic scenarios than the worst case and the best case. However, empirically, decisions based on the …
Why Green Wavelength Is Closer To Blue Than To Red And How It Is Related To Computations: Information-Based Explanation, Victor L. Timchenko, Yury P. Kondratenko, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Why Green Wavelength Is Closer To Blue Than To Red And How It Is Related To Computations: Information-Based Explanation, Victor L. Timchenko, Yury P. Kondratenko, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
In our previous papers, we analyzed the idea of using light signals of three basic color -- red, green, and blue -- to speed up computations, in particular fuzzy-related computations. A natural question is: why red, green, and blue? Why not select some other colors: e.g., from the wavelength viewpoint, green is much closer to blue than to green, so why not select colors whose distribution is more even? In this paper, we show that if we consider this problem from the information viewpoint, then the corresponding equal-information criterion indeed implies that the intermediate wavelength should be closer to the …
Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, Luc Jaulin
Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, Luc Jaulin
Departmental Technical Reports (CS)
In many practically useful numerical computations, training-and-then-using a neural network turned out to be a much faster alternative than running the original computations. When we applied a similar idea to take into account interval uncertainty, we encountered two unexpected results: (1) that while for numerical computations, it is usually better to represent an interval by its midpoint and half-width, for neural networks, it is more efficient to represent an interval by its endpoints, and (2) that while usually, it is better to train a neural network on the whole data processing algorithm, in our problems, it turned out to be …
Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts
Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts
Dissertations, Theses, and Capstone Projects
We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …
Twisted Alexander Polynomials And Ptolemy Varieties Of Knots And Surface Bundles, Michael R. Marinelli
Twisted Alexander Polynomials And Ptolemy Varieties Of Knots And Surface Bundles, Michael R. Marinelli
Dissertations, Theses, and Capstone Projects
The first focus of this dissertation is to compute Ptolemy varieties for triangulations of two infinite families of manifolds. Given an ideal triangulation of a cusped manifold, one can compute the Ptolemy variety and using it, obtain parabolic representations of the fundamental group. We compute certain obstruction classes for these manifolds, which are necessary to obtain the discrete faithful representation. This leads to our second focus of the dissertation, the twisted Alexander polynomial. The twisted Alexander polynomial (TAP) is a variation of the classical Alexander polynomial twisted by a representation of the fundamental group into a linear group. It was …
Categorical Chain Conditions For Étale Groupoid Algebras, Sunil Philip
Categorical Chain Conditions For Étale Groupoid Algebras, Sunil Philip
Dissertations, Theses, and Capstone Projects
Let R be a unital commutative ring and G an ample groupoid. Using the topology of the groupoid G, Steinberg defined an étale groupoid algebra RG. These étale groupoid algebras generalize various algebras, including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for étale groupoid algebras. In this work, we characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple étale groupoid algebras, thereby generalizing existing results for Leavitt path algebras and introducing new results for inverse …
A New Fractional Derivative Extending Classical Concepts: Theory And Applications, Mutaz Mohammad, Mohamed Saadaoui
A New Fractional Derivative Extending Classical Concepts: Theory And Applications, Mutaz Mohammad, Mohamed Saadaoui
All Works
In this paper, a novel general definition for the fractional derivative and fractional integral based on an undefined kernel function is introduced. For 0<α≤1, this definition aligns with classical interpretations and is applicable for calculating the derivative in an open negative interval I⊆[a,+∞),a∈R. Additionally, when α=1, the definition coincides with the classical derivative. Fundamental properties of the fractional integral and derivative, including the product rule, quotient rule, chain rule, Rolle's theorem, and the mean value theorem, are derived. These properties are illustrated through various applications to demonstrate their applicability. Furthermore, some applications of solving fractional nonlinear systems of integro-differential equations using framelets are presented.
A Staged Approach Using Machine Learning And Uncertainty Quantification To Predict The Risk Of Hip Fracture, Anjum Shaik, Kristoffer A. Larsen, Nancy E. Lane, Chen Zhao, Kuan Jui Su, Joyce H. Keyak, Qing Tian, Qiuying Sha, Hui Shen, Hong Wen Deng, Weihua Zhou
A Staged Approach Using Machine Learning And Uncertainty Quantification To Predict The Risk Of Hip Fracture, Anjum Shaik, Kristoffer A. Larsen, Nancy E. Lane, Chen Zhao, Kuan Jui Su, Joyce H. Keyak, Qing Tian, Qiuying Sha, Hui Shen, Hong Wen Deng, Weihua Zhou
Michigan Tech Publications
Hip fractures present a significant healthcare challenge, especially within aging populations, where they are often caused by falls. These fractures lead to substantial morbidity and mortality, emphasizing the need for timely surgical intervention. Despite advancements in medical care, hip fractures impose a significant burden on individuals and healthcare systems. This paper focuses on the prediction of hip fracture risk in older and middle-aged adults, where falls and compromised bone quality are predominant factors. The study cohort included 547 patients, with 94 experiencing hip fracture. To assess the risk of hip fracture, clinical variables and clinical variables combined with hip DXA …
On Deformation Rings Of Residual Galois Representations With Three Jordan–Hölder Factors, Xiaoyu Huang
On Deformation Rings Of Residual Galois Representations With Three Jordan–Hölder Factors, Xiaoyu Huang
Dissertations, Theses, and Capstone Projects
In this paper, we study Fontaine-Laffaille, self-dual deformations of a mod p non-semisimple Galois representation of dimension n with its Jordan–Hölder factors being three mutually non-isomorphic absolutely irreducible representations. We show that under some conditions regarding the orders of certain Selmer groups, the universal deformation ring is a discrete valuation ring. Given enough information on the Hecke algebra, we also prove an R = T theorem in the general context. We then apply our results to abelian surfaces with cyclic rational isogenies and certain 6-dimensional representations arising from automorphic forms congruent to Ikeda lifts. Assuming the Bloch-Kato conjecture, our result …
Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo
Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo
School of Mathematical & Statistical Sciences Faculty Publications
We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients. In each variant, white noise exhibits spatial uniformity, and the three categories include additive, multiplicative, and advection noise. Across all cases, the coefficients are time-dependent functions. Our discovery indicates that solving certain deterministic counterparts of KdV–Burgers equations and composing the solution with a solution of stochastic differential equations leads to the exact solution of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equations.
Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams
Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams
School of Mathematical & Statistical Sciences Faculty Publications
In this work, a new relationship is established between the solutions of higher order fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, derive d’Alembert’s formula and show the existence of explicit solutions for a general fractional wave equation with variable coefficients. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as …