Mathematics Commons^™

Taylor Expansions And Castell Estimates For Solutions Of Stochastic Differential Equations Driven By Rough Paths, Qi Feng, Xuejing Zhang

Journal of Stochastic Analysis

No abstract provided.

Origins Of Atrophy In Parkinson Linked To Early Onset And Local Transcription Patterns, Pedro D. Maia, Sneha Pandya, Benjamin Freeze, Justin Torok, Ajay Gupta, Yashar Zeighami, Ashish Raj

Mathematics Faculty Publications - Archive

There is enormous clinical value in inferring the brain regions initially atrophied in Parkinson disease for individual patients and understanding its relationship with clinical and genetic risk factors. The aim of this study is to leverage a new seed-inference algorithm demonstrated for Alzheimer’s disease to the Parkinsonian context and to cluster patients in meaningful subgroups based on these incipient atrophy patterns. Instead of testing brain regions separately as the likely initiation site for each patient, we solve an L1-penalized optimization problem that can return a more predictive heterogeneous, multi-locus seed patterns. A cluster analysis of the individual seed patterns reveals …

Solvability Of Boundary Value Problem With A Conormal Derivative For An Equation Of Mixed Elliptic-Parabolic Type, Marguba H. Akbarova, Surayyo H. Akbarova

Scientific Bulletin. Physical and Mathematical Research

This article is devoted to the formulation and study of a nonlocal boundary value problem with a conormal derivative for an equation of mixed elliptic-parabolic type. Here the existence and uniqueness of the solution of the problem is proved. Uniqueness of the solution is shown by the method of energy integrals, and existence of a solution is based on the theory of integral equations. Existence of a solution of a nonlocal boundary value problem is equivalently led to a solvability of a system of singular integral equations of normal type with zero index.

On The Stability Of Some Non-Stationary Nonlinear Systems, Rustamjon V. Mullajonov, Shakhodathon N. Abdugapparova, Jumagul V. Mirzaahmedova

Scientific Bulletin. Physical and Mathematical Research

The objective of the theory of stability of motion is to establish signs that make it possible to judge whether the motion in question is stable or unstable. Since in reality perturbing factors always inevitably exist, it becomes clear that the problem of stability of movement assumes very important theoretical and practical significance.

Mathematical modeling of processes and phenomena in animate and inanimate nature always involves a certain classification of them in accordance with their complexity. Many processes and phenomena are modeled by large-scale systems (CMS), which consist of separate subsystems, united by communication functions. In many cases, CMS is …

Solve The Diophante`S Equations, Tulanboy T. Ibaydullayev, Alisher L. Abdulvohidov

Scientific Bulletin. Physical and Mathematical Research

This article is based on the lectures for gifted students of the faculty of Physics and Mathematics on the solution of Diophantine equations in science circles.

If the number of unknowns involved in a system of equations exceeds the number of equations, such equations are called Diophantine equations or indeterminate equations. Specifically, equations of the form

3x-5y=8, x²+3xy-y²=12,

x³+y²-3x+5=0, x³+y³=z³,… are indefinite equations.

Many of the equation or system of equations determine all the numbers to find solutions to the most common examples. Short multiplication formulas, …

Rota-Baxter Operators On 3-Dimensional Nilpotent Associative Algebras, Jamila R. Aliyeva, Hushruyahon M. Karimjanova, Ziyodahon B. Holmirzayeva

Scientific Bulletin. Physical and Mathematical Research

Associative algebras are introduced into mathematics of the 19th century and are still intensively studied. The classification of associative algebras of small dimensions first appeared in the works of Pierce in 1881. In 2018, the German scientist William de Graf gave a classification of nilpotent associative algebras of small sizes. The article describes all the Rota-Baxter operators on 3-dimensional nilpotent associative algebras.

Rota-Baxter operators were defined by Baxter to solve an analytic formula in probability. It has been related to other areas in mathematical physics and mathematics.

Throughout this paper algebras are considered over the field of complex numbers.

A …

Some Innovative Statistical Tools For Sustainability Of The Research Production Process, Kamola S. Ablazova

Scientific Bulletin. Physical and Mathematical Research

New control charts and their assessments determining the normality of the quality criterion are carried out in the article. Using these charts, the degree of stability of the production process is studied using one example.

In practice, the stability of the process under study is important. It depends on ordinary (random) and special (nonrandom) reasons. These reasons strongly affect the distribution of the process under study. Distributions may vary in position, spread, and shape. They can be checked using asymmetry and excess coefficients. If only the usual causes of variations occur, then the results of the process form a distribution …

On Abattle Over The ‘Ebbinghaus Forgetting Curve’ Using Control Charts, Sohibjon A. Ahmedov, Hushnudbek D. Yuldashev

Scientific Bulletin. Physical and Mathematical Research

Studying the laws of memorization, the German experimental psychologist German Ebbinghaus statistically proved that if a person does not repeat the material studied, then the storage of material in memory decreases almost exponentially with respect to time. He called these arcs the “Curve of Forgetting”. In this case, the information is forgotten at first very quickly, and then slower.

More than two centuries, research has been conducted on the functional abilities of the human brain. Nowadays, natural and artificial intelligence are being compared by researchers.

Our method on the “Ebbinghaus Forgetting Curve” is based on using Control Charts with exponentially …

Convex And Nonconvex Optimization Techniques For Multifacility Location And Clustering, Tuyen Dang Thanh Tran

Dissertations and Theses

This thesis contains contributions in two main areas: calculus rules for generalized differentiation and optimization methods for solving nonsmooth nonconvex problems with applications to multifacility location and clustering. A variational geometric approach is used for developing calculus rules for subgradients and Fenchel conjugates of convex functions that are not necessarily differentiable in locally convex topological and Banach spaces. These calculus rules are useful for further applications to nonsmooth optimization from both theoretical and numerical aspects. Next, we consider optimization methods for solving nonsmooth optimization problems in which the objective functions are not necessarily convex. We particularly focus on the class …

The Burning Number Of Directed Graphs: Bounds And Computational Complexity, Remie Janssen

Theory & Applications of Graphs

The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalizes naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for directed graphs, and we study bounds for the corresponding burning number and the hardness of finding this number. We derive sharp bounds from simple algorithms and examples. The hardness question yields more surprising results: finding the burning number of a directed tree with one indegree-0 node is NP-hard, but FPT; however, it is W[2]-complete for DAGs. Finally, we give a fixed-parameter …

A Minimal Congruence Lattice Representation For 𝕄ₚ₊₁, Roger Bunn, David E. Grow, Matt Insall, Philip Thiem

Mathematics and Statistics Faculty Research & Creative Works

Let p be an odd prime. The unary algebra consisting of the dihedral group of order 2p, acting on itself by left translation, is a minimal congruence lattice representation of 𝕄_p+1.

How Mathematics And Computing Can Help Fight The Pandemic: Two Pedagogical Examples, Julio Urenda, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

With the 2020 pandemic came unexpected mathematical and computational problems. In this paper, we provide two examples of such problems -- examples that we present in simplified pedagogical form. The problems are related to the need for social distancing and to the need for fast testing. We hope that these examples will help students better understand the importance of mathematical models.

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

New Results For Compatible Mappings Of Type A And Subsequential Continuous Mappings, Rajinder Sharma, Vishal Gupta, Mukesh Kushwaha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we corroborated some common fixed point theorems for two pairs of self mappings by using the impression of compatibility of type A and subsequential continuity (alternatively subcompatiblity and reciprocal continuity) in multiplicative metric spaces (MMS). The proven results are the improved version in a manner that the completeness, closedness and continuity of the mappings are relaxed.

On Fejér Type Inequalities For Convex Mappings Utilizing Generalized Fractional Integrals, A. Kashuri, R. Liko

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we first establish Hermite-Hadamard-Fejér type inequalities for convex function involving generalized fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some trapezoid type inequalities for these kind of generalized fractional integrals. The results given in this paper provide generalization of several inequalities obtained in earlier studies.

C# Application To Deal With Neutrosophic G(Alpha)-Closed Sets In Neutrosophic Topology, S. Saranya, M. Vigneshwaran, S. Jafari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have developed a C# Application for finding the values of the complement, union, intersection and the inclusion of any two neutrosophic sets in the neutrosophic field by using .NET Framework, Microsoft Visual Studio and C# Programming Language. In addition to this, the system can find neutrosophic topology, neutrosophic alpha-closed sets and neutrosophic g(alpha)-closed sets in each resultant screens. Also, this computer-based application produces the complement values of each neutrosophic closed sets.

Existence Of Resolvent For Conformable Fractional Volterra Integral Equations, Awais Younus, Khizra Bukhsh, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the conformable fractional Volterra integral equation. We study the existence of a resolvent kernel corresponding to conformable fractional Volterra integral equation. The technique of proof involves Lebesgue dominated convergence theorem. Our results improve and extend the results obtained in literature.

Some Operations Over Pythagorean Fuzzy Matrices Based On Hamacher Operations, I. Silambarasan, S. Sriram

Applications and Applied Mathematics: An International Journal (AAM)

Pythagorean fuzzy matrix is a powerful tool for describing the vague concepts more precisely. The Pythagorean fuzzy matrix based models provide more flexibility in handling the human judgment information as compared to other fuzzy models. The objective of this paper is to apply the concept of intuitionistic fuzzy matrices to Pythagorean fuzzy matrices. In this paper, we briefly introduce the Pythagorean fuzzy matrices and some theorems and examples are applied to illustrate the performance of the proposed methods. Then we define the Hamacher scalar multiplication (n._hA) and Hamacher exponentiation (A^^hn) operations on Pythagorean fuzzy matrices and …

A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …

Indexed Absolute Summability Factor Of Improper Integrals, L. N. Mishra, D. Acharya, S. K. Sahu, P. C. Nayak, U. K. Misra, S. Pandey

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have defined the summability for improper integrals and established a theorem on indexed absolute Cesaro summability factors of improper integral under sufficient conditions. Some auxiliary results (well known) have also been deduced from the main result under suitable conditions.