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# Algebra - Science topic

For discussion on linear algebra, vector spaces, groups, rings and other algebraic structures.
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We introduce the category of stable compactications of T 0-spaces and obtain a dual description of it in terms of what we call Raney extensions of proximity frames. These are proximity frame embeddings of a regular proximity frame into a Raney lattice , i.e. the lattice of upsets of a poset. This duality generalizes the duality between compacticati...
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The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D(G). A graph is called distance integral if all of its distance eigenvalues are integers. Let n and k be integers with n > 2k, k ≥ 1. The bipartite Kneser graph H(n, k) is the graph with the set of all k and n − k subsets of the set [n] = {1, 2, ..., n} as v...
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We prove that polyhedra P1 and P2 in R^n, n≥3, are homothetic if and only if their orthogonal projections on every 2-dimensional plane of R^n are homothetic (this assertion does not hold for arbitrary closed convex sets). Also, we show that closed convex sets K1 and K2 in R^n are directly homothetic if and only if for any point p1 ∈ R^n \ K1 there...
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In this paper, we address computation of the degree $$\deg {\rm Det} A$$ deg Det A of Dieudonné determinant $${\rm Det} A$$ Det A of \begin{aligned} A = \sum_{k=1}^m A_k x_k t^{c_k}, \end{aligned} A = ∑ k = 1 m A k x k t c k , where $$A_k$$ A k are $$n \times n$$ n × n matrices over a field $$\mathbb{K}$$ K , $$x_k$$ x k are noncommutative vari...
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Background Single-step genomic predictions obtained from a breeding value model require calculating the inverse of the genomic relationship matrix $$({\mathbf{G}}^{-1})$$ ( G - 1 ) . The Algorithm for Proven and Young (APY) creates a sparse representation of $${\mathbf{G}}^{-1}$$ G - 1 with a low computational cost. APY consists of selecting a grou...
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In this paper, Hopf bifurcation and center problem are investigated for a class of more generalized Lorenz systems, which are Z2 symmetric and quadratic three-dimensional systems. Firstly, the singular point quantities of one equilibrium are calculated carefully, and the two symmetric fourth-order weak foci are found. Secondly, the corresponding in...
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We show that any Algebraic Branching Program (ABP) computing the polynomial ∑i=1nxin has at least Ω(n2) vertices. This improves upon the lower bound of Ω(nlogn), which follows from the classical result of Strassen (1973a) and Baur & Strassen (1983), and extends the results in Kumar (2019), which showed a quadratic lower bound for homogeneous ABPs c...
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A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem by the Ritz method. In this process,it may be difficult to solve a large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) is applied to solve this problem. The results show that the variational approa...
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The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by EA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin...
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The existing topological representation of an orthocomplemented lattice via the clopen orthoregular subsets of a Stone space depends upon Alexander’s Subbase Theorem, which asserts that a topological space X is compact if every subbasic open cover of X admits of a finite subcover. This is an easy consequence of the Ultrafilter Theorem—whose proof d...
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In an ac microgrid, reactive power sharing accuracy is affected due to unequal values of interconnecting cable impedances. To resolve this issue, secondary controllers are used to compensate the effect of cable impedances. Various types of secondary controllers are suggested in the literature which includes linear proportional plus integral (PI) co...
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The Riemann-Roch theorem is a classical result which forms a beautiful algebraic connection between complex analysis on a compact Riemann surface and a global topological property of that surface (the genus). We present a survey of the theorem and its many variants and generalisations. We also provide an alternative elementary proof of the Riemann-...
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A well-known result in quasigroup theory says that an associative quasigroup is a group, i.e. in quasigroups, associativity forces the existence of an identity element. The converse is, of course, far from true, as there are many, many non-associative loops. However, a remarkable theorem due to David Mumford and C.P. Ramanujam says that any project...
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In this paper, we extend Gang Liu’s three circle theorem for Kähler manifolds to almost Hermitian manifolds. As applications of the three circle theorem, we obtain sharp dimension estimates for spaces of holomorphic functions of polynomial growth and rigidity for the estimates, Liouville theorems for pluri-subharmonic functions of sub-logarithmic g...
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By a purely algebraic way, we investigate a necessary and sufficient condition for the existence of differentially algebraic and transcendental solutions to certain difference equations whose form is related to Riccati equations. Our result roughly implies that all the solutions do not satisfy any algebraic differential equations if there is no alg...
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In this paper, we study the Batalin–Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras Aq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{{\... Article Full-text available By appending a constant to the Weierstrass form of the conventional Tresca yield condition, a new yield condition is generated that allows a continuous transition of yield criteria spanning the Tresca to the von Mises and beyond. The Weierstrass form of the Tresca yield condition is defined by a cubic algebraic relationship between the second and t... Article Full-text available Automated melanoma classification remains a challenging task because skin lesion images are prone to low contrast and many kinds of artifacts. To handle these challenges, we introduce a novel and efficient method for skin lesion classification based on the machine learning approach and sparse representation (SR) in the quaternion wavelet (QW) domai... Article Full-text available In this paper we study holomorphic foliations on P2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {P}}^2$$\end{document} with only one singular point. If the... Article Full-text available We revisit the symmetry structure of integrable PDEs, looking at the specific example of the KdV equation. We identify four nonlocal symmetries of KdV depending on a parameter, which we call generating symmetries. We explain that since these are nonlocal symmetries, their commutator algebra is not uniquely determined, and we present three possibili... Preprint Full-text available Although many well-intentioned organizations and institutions emphasize the importance of antiracism and social justice in mathematics education, there remains a lack of practitioner-oriented curricular materials exhibiting how these long-overdue shifts can and do manifest in classrooms. This article describes how modifying a project on absolute va... Article Full-text available Let X and Y be compact subsets of \mathbb{R} with at least two points. For p\geq 1, let \AC^p(X) be the space of all absolutely continuous complex-valued functions f on X such that f'\in L^{p}(X), with the norm \left\|f\right\|_{\Sigma}=\left\|f\right\|_\infty+\|f'\|_p. We describe the topological reflexive closure of the set of l... Article Full-text available The paper concerns nilpotent diassociative algebras (also known as associative dialgebras) and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five-term cohomological sequence under alternative conditions in the nilpotent setting. This main result is then applied to obtain a ne... Article Full-text available In this work, our motivation is to design a new collocation method based on Müntz–Legendre polynomial involving operational matrices to solve variable‐order stochastic fractional integro‐differential equation. We first prove the existence and uniqueness result for the solution of considered problem. The operational matrices are used to convert the... Article Full-text available In this paper, we show that the fiber cones of rational normal scrolls are Cohen–Macaulay. As an application, we compute their Castelnuovo–Mumford regularities and a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen... Article Full-text available Let (X, L) be a polarized variety over a number field K. We suppose that L is an hermitian line bundle. Let M be a non compact Riemann Surface and $$U\subset M$$ be a relatively compact open set. Let $$\varphi :M\rightarrow X(\mathbf{C})$$ be a holomorphic map. For every positive real number T, let $$A_U(T)$$ be the cardinality of the set of $$z\in... Article Full-text available The control-based approach has been proved to be effective for developing robust online learning methods. However, the existing control-based kernel methods are infeasible for large-scale modeling due to their high computational complexity. This paper aims to propose a computationally efficient control-based framework for robust large-scale kernel... Article Full-text available Let f(x,y)=1+∑p=1m+n=p∞am,nxmyn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}f(x,y)=1+\sum \limits _{\begin{array}{c} p=1\\ m+n=p \end{array}}^{\infty }a_{m,n}x^my^n... Article Full-text available G-operators, a class of differential operators containing the differential operators of minimal order annihilating Siegel’s G-functions, satisfy a condition of moderate growth called Galochkin condition, encoded by a p-adic quantity, the size. Previous works of Chudnovsky, André and Dwork have provided inequalities between the size of a G-operator... Article Full-text available We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepacka... Article Full-text available The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological data analysis. Its input is a simplicial filtration defined over the integers Z\documentclass[12pt]{minimal}... Article Full-text available Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are formal; indeed, scalability can be thought of as a metric version of formality. They are also characterized by parti... Article Full-text available We presented an interpolation method for solving weakly singular Volterra integral equations of the second kind (SVK2). The method based on the barycentric Lagrange interpolation.. For the chosen nodes of the two singular kernel variables, we created two rules that confirm that the denominator of the kernel will never become zero or have an imagina... Article Full-text available Suppose that N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}{\mathfrak {N}}\end{document} is a von Neumann algebra and that φ\documentclass[12pt]{minimal} \usepacka... Article Full-text available A class of boundary value problems for fractional linear/non-linear two- dimensional partial differential equations is studied. A new algorithm based on the approximation technique is proposed to solve them. To this end, the terms of the considered problems are approximated through a series expansion of triple-shifted Legendre polynomials. Then col... Article Full-text available For a given field F of characteristic different from 2 and a,b,d∈F∗ we construct an invariant inv for an element D∈2Br(F(a,b,d)/F). This invariant takes value in the quotient group H3(F,μ2)/D∪NFd,ab/FFd,ab∗.Let k be a field, let k(a,b,d)/k be a triquadratic field extension. We apply the invariant inv and a few deep results from algebraic geometry a... Article Full-text available The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum special linear group Oq2(SL2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a... Article Full-text available Let G be a locally compact abelian group with a Haar measure, and Y be a measure space. Suppose that H is a reproducing kernel Hilbert space of functions on G×Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\... Article Full-text available A vector sublattice of the order bounded operators on a Dedekind complete vector lattice can be supplied with the convergence structures of order convergence, strong order convergence, unbounded order convergence, strong unbounded order convergence, and, when applicable, convergence with respect to a Hausdorff uo-Lebesgue topology and strong conver... Article Full-text available The concept of topological IL-algebra is introduced in this paper. It generalizes the idea of topological FLew\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}_{\text{ e... Article Full-text available A phase-fitting, first and second derivatives phase-fitting method is produced. The new algorithm is singularly P-Stable and belongs to the economic algorithms. The new method is symbolized as PF2DPFN2SPS. It can be used to any problem with periodical and/or oscillating solutions. We chosen to be applied to a well known problem of Quantum Chemistry... Article Full-text available Let \pi _{\alpha } π α be a holomorphic discrete series representation of a connected semi-simple Lie group G with finite center, acting on a weighted Bergman space A^2_{\alpha } (\Omega ) A α 2 ( Ω ) on a bounded symmetric domain \Omega Ω , of formal dimension d_{\pi _{\alpha }} > 0 d π α > 0 . It is shown that if the Bergman kern... Article Full-text available We study the partial ordering on isomorphism classes of central simple algebras over a given field F, defined by setting \(A_1 \le A_2$$ if $$\deg A_1 = \deg A_2$$ and every étale subalgebra of $$A_1$$ is isomorphic to a subalgebra of $$A_2$$, and generalizations of this notion to algebras with involution. In particular, we show that this partial o... Article Full-text available We give a complete classification of twists of supersymmetric Yang–Mills theories in dimensions 2≤n≤10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\le n \le 10$$\en... Article Full-text available We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general unstructured grids. Within such an algebraic framework, the multidimensional summation-by-parts (SBP) property is used to establish the discrete equivalence of strong and... Article Full-text available We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary represe... Article Full-text available In this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemarg... Article Full-text available In this paper, we construct various simple vertex superalgebras which are extensions of affine vertex algebras, by using abelian cocycle twists of representation categories of quantum groups. This solves the Creutzig and Gaiotto conjectures (Creutzig and Gaiotto in Comm Math Phys 379:785–845, 2020, Conjecture 1.1 and 1.4) in the case of type ABC. I... Article Full-text available We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians of curves over an algebraically closed non-Archimedean field. Let J be the Jacobian of a curve X, and let W_d \subset J be the locus of effective divisor classes of degree d. We show that the pair (J^{an},W_d^{an}) is d-connected, and thus in par... Article Full-text available In this article, we study homogeneous spaces Uq(2)/ϕT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_q(2)/_\phi \mathbb {T}$$\end{document} and Uq(2)/ψT\documentclass... Article Full-text available This article deals with constructing an operational matrix method based on fractional-order Lagrange polynomials to solve the non-local boundary value problems (BVPs) of fractional order arising in chemical reactor theory. In the proposed numerical technique, first, we determine the operational matrix of integer and fractional derivatives. Using th... Article Full-text available Recently, the concept of overlap functions on complete lattices has been introduced by extending the truth values set from the unit closed interval to complete lattices. On the other hand, the residual implications induced from commonly used aggregation functions (see, e.g., t-norms, pseudo-t-norms, uninorms, semi-uninorms and pseudo-uninorms), as... Article Full-text available We describe the holonomy algebras of all canonical connections and their action on complex hyperbolic spaces CH(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathb...
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In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] are projections in different settings, such as ∗-rings, ∗-reducing rings and [Formula: see text]-algebras. Moreover, severa...
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An approach to phase-fitting is devised, which includes methods for fitting the phase-lag and for fitting its first, second, and third derivatives. Singularly P-Stable, the novel system belongs to the family of economic algorithms [(i.e. algorithms which use the minimum number of function evaluations (FEvs) per integration step in order to achieve...
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For a semisimple Lie algebra defined over a discrete valuation ring with field of fractions K, we prove that any primitive ideal with rational central character in the affinoid enveloping algebra, U(g)K^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
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The k -cardinality assignment ( k -assignment, for short) problem asks for finding a minimal (maximal) weight of a matching of cardinality k in a weighted bipartite graph $$K_{n,n}$$ K n , n , $$k \le n$$ k ≤ n . Here we are interested in computing the sequence of all k -assignments, $$k=1,\ldots ,n$$ k = 1 , … , n . By applying the algorithm of Ga...
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We show how our p -adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is the use of “moduli-friendly” Eisenstein series introduced by Makdisi, which allow us to evaluate modular forms at p -adic points of modular curves and dispenses us of the...
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Koornwinder polynomials are q-orthogonal polynomials equipped with extra five parameters and the BCn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B C_n$$\end{document...
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Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum...
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In this work, a new basic framework of robotic mechanism topology is proposed, which includes: ① two important concepts (i.e., topological structure and kinematic characteristics), ② three basic formulas (i.e., POC equation of serial mechanisms, POC equation of parallel mechanisms (PMs), and DOF formula) and ③ topological structure synthesis method...
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Let X be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products SymnX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...
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Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the...
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In this paper we consider some important non Kubo–Ando means on positive definite cones of C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebra...
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Recently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its origins go back to the harmonic analysis on ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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We introduce a general class of combinatorial objects, which we call multi-complexes, which simultaneously generalizes graphs, multigraphs, hypergraphs and simplicial and delta complexes. We introduce a natural algebra of multi-complexes which is defined as the algebra which has a formal basis C of all isomorphism types of multi-complexes, and mult...
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Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary c...
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For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between prop...
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Tsao, Hung-ping (2022). Evolutionary mathematics and science for Combinatorial Algebra III. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 8C, August 2022; 100 pages. Lenox Institute Press, MA, USA. No. STEAM-VOL4-NUM8C-AUG2022; ISBN 9...
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During the last decades, the structure of mod-2 cohomology of the Steenrod ring $\mathscr A$ became a major subject in Algebraic Topology. One of the most direct attempt in studying this cohomology by means of modular representations of the general linear groups was the surprising work [Math. Z. \textbf{202} (1989), 493-523] by W.M. Singer, which i...
Book
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This book includes fully-solved examples with detailed explanations for 139 standard physics problems. There are also 66 math examples, including algebra and calculus, which are essential toward mastering physics. That makes a total of 205 problems. Each example breaks the solution down into terms that make it easy to understand. The written explan...
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Modules are one of fundamental and rich algebraic structure with respect to some binary operation in the study of algebra. The objective of this paper is to introduce the concept of Neutro 𝑅 − 𝑚𝑜𝑑𝑢𝑙𝑒 and NeutroOrdered 𝑅 − 𝑚𝑜𝑑𝑢𝑙𝑒 . Several interesting results and examples on Neutro 𝑅 − 𝑚𝑜𝑑𝑢𝑙𝑒 , NeutroOrdered 𝑅 − 𝑚𝑜𝑑𝑢𝑙𝑒,NeutroOrdered Sub 𝑅 − 𝑚𝑜𝑑𝑢𝑙𝑒,...
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The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations of a flag Bott manifold. We apply our results to give a presentation for the topological K-ring and hence the Grothendieck ring of algebraic vector bundles over flag Bott Samelson varieties.
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Tsao, Hung-ping (2022). Evolutionary mathematics and science for combinatorial algebra II. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 4, Number 8B, August 2022; 100 pages. Lenox Institute Press, MA, USA. No. STEAM-VOL4-NUM8B-AUG2022; ISBN 97...
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In 2010, Muthuswamy and Chua presented an autonomous chaotic circuit using only three elements in series: an inductor, a capacitor and a memristor. This circuit is known as the simplest chaotic circuit and it is determined by a three-dimensional differential system, which depends on the real parameters C, L, α and β. Although the Muthuswamy-Chua sy...
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For the vanishing deformation parameter $\lambda$, the full structure of the (anti)commutator relations in the ${\cal N}=4$ supersymmetric linear $W_{\infty}[\lambda=0]$ algebra is obtained for arbitrary weights $h_1$ and $h_2$ of the currents appearing on the left hand sides in these (anti)commutators. The $w_{1+\infty}$ algebra can be seen from t...
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The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. We undertake a comprehensive study of congruence families for $d_k(n)$ modulo powers of 5, with $n$ and $k$ in respective linear progressions. In particular, we give an infinite congruence family for...
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We discuss an approach to transforming and solving algebraic equations via the so-called bar model, based on the strategy of transposing. After developing a learning environment, we conducted design experiments to get insights into how students work with it. First, this paper aims to present the core idea of our learning environment. Second, we hig...
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Geometric algebras of dimension n<6$$n<6$$ are becoming increasingly popular for the modeling of 3D and 3 + 1D geometry. With this increased popularity comes the need for efficient algorithms for common operations such as normalization, square roots, and exponential and logarithmic maps. The current work presents a signature‐agnostic analysis of...
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We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on the space of characters of the amenable radical, and in particular we establish stiffness: any stationary probab...
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In this article, the numerical solution of the mixed Volterra–Fredholm integro-differential equations of multi-fractional order less than or equal to one in the Caputo sense (V-FIFDEs) under the initial conditions is presented with powerful algorithms. The method is based upon the quadrature rule with the aid of finite difference approximation to C...
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A simple model for the localization of the category $$\mathbf {CLoc}_2$$ CLoc 2 of oriented and time-oriented globally hyperbolic conformal Lorentzian 2-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of 2-dimensional conformal algebraic quantum field theories (AQFTs) satisfying the time-slice axiom in term...
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Since Ref.  shows the emergence of non-Abelian fusion rules in some examples of a class of Abelian models, but does not prove whether these rules also exist in other cases, the purpose of this paper is to present such proof emphasizing the importance of the existence of these rules. By the way, as the ground state of these models can be degenera...
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Cryptographic algorithms are used to ensure confidentiality, integrity and authenticity of data in information systems. One of the important areas of modern cryptography is that of symmetric key ciphers. They convert the input plaintext into ciphertext, representing it as a random sequence of characters. S-boxes are designed to complicate the input...