Invariant Solutions for Nonhomogeneous Discrete Diffusion Equation by M. N. Qureshi, A. Q. Khan, M. Ayub, Q. Din

“…Also generating solutions are calculated, using the elements of the symmetry algebra.…”
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More on (𝜶,𝜷)-Normal Operators in Hilbert Spaces by Rasoul Eskandari, Farzollah Mirzapour, Ali Morassaei

“…We study some properties of (𝛼,𝛽)-normal operators and we present various inequalities between the operator norm and the numerical radius of (𝛼,𝛽)-normal operators on Banach algebra ℬ(ℋ) of all bounded linear operators 𝑇∶ℋ→ℋ, where ℋ is Hilbert space.…”
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Lindblad superoperators from Wigner’s phase space continuity equation by Ole Steuernagel, Ray-Kuang Lee

“…For a simple quantum system weakly interacting with the environment, Wigner’s 1932 formulation of quantum physics can be used to derive coupling to the environment using simple algebra. We show that the correct expressions, using coupling terms of “Lindblad form,” are forced upon us. …”
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Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions by Marian Nowak

“…Let Σ be a σ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. …”
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Multilocal invariants for the classical groups by Paul F. Dhooghe

“…The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.…”
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Gradual Sets: An Approach to Fuzzy Sets by Josefa M. García, Pascual Jara

“…., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers.…”
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Extension of Spectral Scales to Unbounded Operators by M. D. Wills

“…We extend the notion of a spectral scale to n-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. …”
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On the geometry of Riemannian manifolds with a Lie structure at infinity by Bernd Ammann, Robert Lauter, Victor Nistor

“…We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.…”
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An Extension of the Spectral Mapping Theorem by A. R. Medghalchi, S. M. Tabatabaie

“…We give an extension of the spectral mapping theorem on hypergroups and prove that if 𝐾 is a commutative strong hypergroup with 0𝑥0005𝑒𝐾=𝑋𝑏(𝐾) and 𝜅 is a weakly continuous representation of 𝑀(𝐾) on a 𝑊∗-algebra such that for every 𝑡∈𝐾, 𝜅𝑡 is an ∗-automorphism, 𝑠𝑝𝜅 is a synthesis set for 𝐿1(𝐾) and 𝜅(𝐿1(𝐾)) is without order, then for any 𝜇 in a closed regular subalgebra of 𝑀(𝐾) containing 𝐿1(𝐾), 𝜎(𝜅(𝜇))=0𝑥0005𝑒𝜇(𝑠𝑝𝜅), where 𝑠𝑝𝜅 is the Arveson spectrum of 𝜅.…”
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A Geometric Property of the Laplacian matrix of a Connected Nonsingular Mixed Graph by Zheng-Da Zhou, Shi-Cai Gong

“…Fiedler, Geometry of the Laplacian, Linear Algebra Appl., 2005, 403: 409–413). In addition, the relations of geometric properties between a connected (singular or nonsingular) mixed graph, and all its resigned graphs will be characterized.…”
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Best Proximity Point Theorems for Cyclic Relatively ρ-Nonexpansive Mappings in Modular Spaces by Karim Chaira, Samih Lazaiz

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Proofs without words by Edmundas Mazėtis, Grigorijus Melničenko

“… Usually, proofs of mathematical statements involve both algebraic rearrangements and logical reasoning. But there are mathematical statements whose truth is obvious at first glance when there is a diagram illustrating that proof. …”
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Some topologies on the set of lattice regular measures by Panagiotis D. Stratigos

“…Alexandroff, namely, an arbitrary set X and an arbitrary lattice of subsets of X, ℒ. 𝒜(ℒ) denotes the algebra of subsets of X generated by ℒ and MR(ℒ) the set of all lattice regular, (finitely additive) measures on 𝒜(ℒ).…”
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Double Hodge Theory for a Particle on Torus by Vipul Kumar Pandey, Bhabani Prasad Mandal

“…We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. …”
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Robust Fault Diagnosis Algorithm for a Class of Nonlinear Systems by Hai-gang Xu, Yue-feng Liao, Xiao Han

“…The novel disturbances constraint condition of the nonlinear system is derived by group algebra method, and the novel constraint condition can meet the system stability performance. …”
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Structures and Low Dimensional Classifications of Hom-Poisson Superalgebras by Qingcheng Zhang, Chunyue Wang, Zhu Wei

“…Moreover, we show that Hom-Poisson superalgebras can be described using only the twisting map and one binary operation. Finally, all algebra endomorphisms on 2-dimensional complex Poisson superalgebras are computed, and their associated Hom-Poisson superalgebras are described explicitly.…”
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Weaving Frames in Hilbert C∗-Modules by Xin Zhao, Pengtong Li

“…By using the analysis operators of frames and frame operators of canonical duals, we obtain several perturbation results for given weaving frames and different weaving frame pairs. When the C∗-algebra is nonunital, we derive a correspondence of adjointable operators which is bounded below woven families. …”
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Mechanical analogy for the wave-particle: helix on a vortex filament by Valery P. Dmitriyev

“…The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of differential geometry of the space curve. …”
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L-Fuzzy Prime Spectrums of ADLs by Natnael Teshale Amare, Srikanya Gonnabhaktula, Ch. Santhi Sundar Raj

“…The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean rings. In this paper, the set of all L-fuzzy prime ideals of an ADL with truth values in a complete lattice L satisfying the infinite meet distributive law is topologized and the resulting space is discussed.…”
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On lattice-topological properties of general Wallman spaces by Carmen Vlad

“…Let X be an arbitrary set and ℒ a lattice of subsets of X such that ϕ,X∈ℒ.𝒜(ℒ) is the algebra generated by ℒ and I(ℒ) consists of all zero-one valued finitely additive measures on 𝒜(ℒ). …”
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