A note on one-parameter groups of automorphisms by A. B. Thaheem, Noor Mohammad

“…Let {αt:t∈R} and {βt:t∈R} be two commuting one-parameter groups of ∗-automorphisms of a von Neumann algebra M such that αt+α−t=βt+β−t for all t∈R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=β−t on M(1−p) for a central projection p∈M, without using the theory of spectral subspaces.…”
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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications by Mawardi Bahri, Ryuichi Ashino, Rémi Vaillancourt

“…We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.…”
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Limit Cycles in a Cubic Kolmogorov System with Harvest and Two Positive Equilibrium Points by Qi-Ming Zhang, Feng Li, Yulin Zhao

“…With the help of computer algebra system MATHEMATICA, we prove that five limit cycles can be bifurcated simultaneously from the two critical points (1, 1) and (2, 2), respectively, in the first quadrant. …”
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Primary decomposition of torsion R[X]-modules by William A. Adkins

“…This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. …”
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Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations by Shou-Ting Chen, Wen-Xiu Ma

“…We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. …”
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Thermodynamic matrix exponentials and thermodynamic parallelism by Samuel Duffield, Maxwell Aifer, Gavin Crooks, Thomas Ahle, Patrick J. Coles

“…It was recently shown that certain linear algebra problems can be solved thermodynamically, leading to a speedup scaling with the matrix dimension. …”
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Dirac Equation on the Torus and Rationally Extended Trigonometric Potentials within Supersymmetric QM by Özlem Yeşiltaş

“…In addition, using the aspects of the Lie algebraic approaches, the iso(2,1) algebra is also applied to the system where we have arrived at the spectrum solutions of the extended potentials using the Casimir operator that matches with the results of the exact solutions.…”
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Normal characterizations of lattices by Carmen D. Vlad

“…Let 𝒜(ℒ) denote the algebra generated by ℒ and I(ℒ) denote those nontrivial, zero-one valued, finitely additive measures on 𝒜(ℒ). …”
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Poisson structures on cotangent bundles by Gabriel Mitric

“…We make a study of Poisson structures of T∗M which are graded structures when restricted to the fiberwise polynomial algebra and we give examples. A class of more general graded bivector fields which induce a given Poisson structure w on the base manifold M is constructed. …”
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Factorization Method in Oscillator with the Aharonov-Casher System by J. Sadeghi, Jalil Naji, Behnam Pourhassan

“…The corresponding operators give us the generators of the algebra.…”
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r-neutrosophic subset of G-submodules by BINU R

“…This article explains a particular category of neutrosophic subsets of G-submodules, specifically r-neutrosophic subsets, where r ∈ [0, 1]. The algebra of r-neutrosophic subsets of G-submodules is dis-cussed, along with some fundamental characteristics of their sum. …”
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The Strong Disjoint Blow-Up/Collapse Property by Héctor N. Salas

“…Let be a topological vector space, and let be the algebra of continuous linear operators on . The operators are disjoint hypercyclic if there is such that the orbit is dense in . …”
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Algebro-Geometric Solutions for a Discrete Integrable Equation by Mengshuang Tao, Huanhe Dong

“…With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. …”
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The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures by Juhui Zhang, Yuqin Yao

“…Furthermore, based on the semidirect sums of matrix Lie algebras consisting of 3×3 block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.…”
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Statistical Entropy of Quantum Black Holes in the Presence of Quantum Gravity Effects by A. D. Kamali, H. Shababi

“…We investigate the effects of deformed algebra, admitted from minimal length, on canonical description of quantum black holes. …”
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Bi-Integrable Couplings of a New Soliton Hierarchy Associated with SO(4) by Yan Cao, Liangyun Chen, Baiying He

“…Based on the six-dimensional real special orthogonal Lie algebra SO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. …”
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Some Intersections of the Weighted -Spaces by F. Abtahi, H. G. Amini, H. A. Lotfi, A. Rejali

“…Furthermore, for an arbitrary subset of and a positive submultiplicative weight function on , Banach subspace of is introduced. Then some algebraic properties of , as a Banach algebra under convolution product, are investigated.…”
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Multiplicative polynomials and Fermat's little theorem for non-primes by Paul Milnes, C. Stanley-Albarda

“…Also presented are characterizations of the gn's and an indication of the ideas from topological dynamics and algebra that brought these matters to our attention.…”
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Random trilinear forms and the Schur multiplication of tensors by Ibrahim Almasri, Jinlu Li, Andrew Tonge

“…As an application, we make progress on the problem when ℓr⊗⌣ℓp⊗⌣ℓq is a Banach algebra under the Schur multiplication.…”
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Smoothness conditions on measures using Wallman spaces by Charles Traina

“…In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ-regular. …”
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