Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, 2021 Missouri University of Science and Technology

#### Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace

*Mathematics and Statistics Faculty Research & Creative Works*

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

The Structure Of Functional Graphs For Functions From A Finite Domain To Itself For Which A Half Iterate Exists, 2021 Institute of Mathematics Pedagogical University of Krakow

#### The Structure Of Functional Graphs For Functions From A Finite Domain To Itself For Which A Half Iterate Exists, Paweł Marcin Kozyra

*Theory and Applications of Graphs*

The notion of a replica of a nontrivial in-tree is defined. A result enabling to determine whether an in-tree is a replica of another in-tree employing an injective mapping between some subsets of sources of these in-trees is presented. There are given necessary and sufficient conditions for the existence of a functional square root of a function from a finite set to itself through presenting necessary and sufficient conditions for the existence of a square root of a component of the functional graph for the function and for the existence of a square root of the union of two components ...

Berry-Esseen Bounds For Approximate Maximum Likelihood Estimators In The Α-Brownian Bridge, 2021 Kuwait University, Kuwait City, Kuwait

#### Berry-Esseen Bounds For Approximate Maximum Likelihood Estimators In The Α-Brownian Bridge, Khalifa Es-Sebaiy, Jabrane Moustaaid, Idir Ouassou

*Journal of Stochastic Analysis*

No abstract provided.

Career And Technology Connections To Enhance The Teaching & Learning Of Mathematics, 2021 Illinois Mathematics and Science Academy

#### Career And Technology Connections To Enhance The Teaching & Learning Of Mathematics, Kelly W. Remijan

*Publications & Research*

No abstract provided.

Pixel Math Across All Levels, 2021 Illinois Mathematics and Science Academy

#### Pixel Math Across All Levels, Kelly W. Remijan

*Publications & Research*

No abstract provided.

Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, 2021 Southern Illinois University, Carbondale, IL 62901, USA

#### Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz

*Journal of Stochastic Analysis*

No abstract provided.

A Math Without Words Puzzle, 2021 Stephen F. Austin State University

#### A Math Without Words Puzzle, Jane H. Long, Clint Richardson

*Journal of Math Circles*

A visual puzzle by James Tanton forms the basis for a session that has been successfully implemented with various audiences. Designed to be presented with no directions or description, the puzzle requires participants to discover the goals themselves and to generate their own questions for investigation. Solutions, significant facilitation suggestions, and possibilities for deep mathematical extensions are discussed; extensive illustrations are included.

Algebraic Graph-Assisted Bidirectional Transformers For Molecular Property Prediction, 2021 Peking University, China

#### Algebraic Graph-Assisted Bidirectional Transformers For Molecular Property Prediction, Dong Chen, Kaifu Gao, Duc Duy Nguyen, Xin Chen, Yi Jiang, Guo-Wei Wei, Feng Pan

*Mathematics Faculty Publications*

The ability of molecular property prediction is of great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative prediction of various molecular properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled molecular data into molecular representations via a self-supervised learning strategy, it neglects three-dimensional (3D) stereochemical information. Algebraic graph, specifically, element-specific multiscale weighted colored algebraic graph, embeds complementary 3D molecular information into graph invariants. We propose an algebraic graph-assisted bidirectional transformer (AGBT) framework by fusing representations generated by algebraic graph and bidirectional transformer, as well as ...

On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, 2021 Politecnico di Milano, Milan, 20133, Italy

#### On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, Franco Fagnola, Zheng Li

*Journal of Stochastic Analysis*

No abstract provided.

Noncommutative Tensor Triangular Geometry And Its Applications To Representation Theory, 2021 Louisiana State University and Agricultural and Mechanical College

#### Noncommutative Tensor Triangular Geometry And Its Applications To Representation Theory, Kent Barton Vashaw

*LSU Doctoral Dissertations*

One of the cornerstones of the representation theory of Hopf algebras and finite tensor categories is the theory of support varieties. Balmer introduced tensor triangular geometry for symmetric monoidal triangulated categories, which united various support variety theories coming from disparate areas such as homotopy theory, algebraic geometry, and representation theory. In this thesis a noncommutative version will be introduced and developed. We show that this noncommutative analogue of Balmer's theory can be determined in many concrete situations via the theory of abstract support data, and can be used to classify thick tensor ideals. We prove an analogue of prime ...

Energy On Spheres And Discreteness Of Minimizing Measures, 2021 The University of Texas Rio Grande Valley

#### Energy On Spheres And Discreteness Of Minimizing Measures, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the *p*-frame energy has empty interior whenever *p* is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials.

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, 2021 CUNY La Guardia Community College

#### The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

*Open Educational Resources*

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in ...

On Digital Metric Space Satisfying Certain Rational Inequalities, 2021 Institute for Excellence in Higher Education

#### On Digital Metric Space Satisfying Certain Rational Inequalities, Krati Shukla

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we have established some new results by extending some existing theorems in the setting of Digital Metric Space. We also proved some results in Digital Metric Space which were established earlier in the context of Complete Metric Space by different authors.

Hamacher Operations Of Fermatean Fuzzy Matrices, 2021 Annamalai University

#### Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan

*Applications and Applied Mathematics: An International Journal (AAM)*

The purpose of this study is to extend the Fermatean fuzzy matrices to the theory of Hamacher operations. In this paper, the concept of Hamacher operations of Fermatean fuzzy matrices are introduced and some desirable properties of these operations, such as commutativity, idempotency, and monotonicity are discussed. Further, we prove DeMorgan’s laws over complement for these operations. Furthermore, the scalar multiplication and exponentiation operations of Fermatean fuzzy matrices are constructed and their algebraic properties are investigated. Finally, some properties of necessity and possibility operators of Fermatean fuzzy matrices are proved.

Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, 2021 Urmia University

#### Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we prove the Hyers-Ulam stability of the 2-dimensional Pexider quadratic functional equation in fuzzy normed spaces. Moreover, we prove the Hyers-Ulam stability of this functional equation, where *f*, *g* are functions defined on an abelian group with values in a topological vector space.

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, 2021 King Fahd University of Petroleum and Minerals

#### On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulate two types of higher-order dual models for such optimization problem. Weak, strong and strict converse duality theorems are derived under higher- order generalized invexity.

An Optimal Control Problem Solution For Chemical Reactor, 2021 Prairie View A&M University

#### An Optimal Control Problem Solution For Chemical Reactor, Dias Nurmagambetov

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we describe one of the solutions of a nonlinear optimal control problem for a chemical reactor. A solution on finding a chemical reactor’s optimal temperature regime for having a maximum concentration of final product is presented. The optimal control has been found by immersion method for boundary value problem with a phase and control restrictions. This method is reducing the original boundary value problem to a special optimal control problem, using the general solution of the Fredholm integral equation of the first kind. With this method's solution had been created a software for the problem ...

Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, 2021 Annamalai University

#### Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, Veerappan Chinnadurai, Albert Bobin

*Applications and Applied Mathematics: An International Journal (AAM)*

The primary focus of this manuscript comprises three sections. Initially, we introduce the concept of a simplified intuitionistic neutrosophic soft set. We impose an intuitionistic condition between the membership values of truth and falsity such that their sum does not exceed unity. Similarly, for indeterminacy, the membership value is a real number from the closed interval [0, 1]. Hence, the sum of membership values of truth, indeterminacy, and falsity does not exceed two. We present the notion of necessity, possibility, concentration, and dilation operators and establish some of its properties. Second, we define the similarity measure between two simplified intuitionistic ...

Orthogonality In Terms Of 2-Hh Norm And Bounded Linear Operators In Banach Spaces, 2021 Tribhuvan University

#### Orthogonality In Terms Of 2-Hh Norm And Bounded Linear Operators In Banach Spaces, Bhuwan P. Ojha, Prakash M. Bajracharya

*Applications and Applied Mathematics: An International Journal (AAM)*

In the present paper, the generalization of the Carlson orthogonality for functionals to operators in Banach spaces has been studied. We will also investigate various properties related to the Carlsson, Birkhoff-James, and Pythagorean orthogonality for operators. Kikianty and Dragomir (2010) mentioned in their paper by stating that Pythagorean and isosceles orthogonality through the medium of 2 − HH norm satisfies the non-degeneracy, symmetry and continuity properties without mentioning detailed proof. This paper provides the complete proof of these properties as well as the equivalency of additivity and homogeneity of the isosceles orthogonality with the help of 2 − HH norm. In the ...

Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, 2021 Vasyl Stefanyk Precarpathian National University

#### Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, Taras Goy, Mark Shattuck

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we evaluate determinants of several families of Hessenberg matrices having various subsequences of the Jacobsthal sequence as their nonzero entries. These identities may be written equivalently as formulas for certain linearly recurrent sequences expressed in terms of sums of products of Jacobsthal numbers with multinomial coefficients. Among the sequences that arise in this way include the Mersenne, Lucas and Jacobsthal-Lucas numbers as well as the squares of the Jacobsthal and Mersenne sequences. These results are extended to Hessenberg determinants involving sequences that are derived from two general families of linear second-order recurrences. Finally, combinatorial proofs are provided ...