Big Bang as a Critical Point by Jakub Mielczarek

“…We show that critical behavior may also be associated with a signature change in Loop Quantum Cosmology, which occurs as a result of quantum deformation of the hypersurface deformation algebra. In the considered cases, classical space-time originates at the critical point associated with a second-order phase transition. …”
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Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem by R. J. Moitsheki, M. D. Mhlongo

“…We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. …”
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The Exact Solutions of a Diffusive SIR Model via Symmetry Groups by R. Naz, A. G. Johnpillai, F. M. Mahomed

“…A four-dimensional Lie point symmetry algebra is obtained for this model. We utilize the Lie symmetries to deduce the optimal system of one-dimensional subalgebras. …”
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Extensions of rational modules by J. Cuadra

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On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups by I. Akbarbaglu, S. Maghsoudi

“…‖𝑝,𝜔)𝜔∈Ω. We study various algebraic and topological properties of the locally convex space 𝐿𝑝(𝐺,Ω). …”
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Time-Compact Scheme for the One-Dimensional Dirac Equation by Jun-Jie Cao, Xiang-Gui Li, Jing-Liang Qiu, Jing-Jing Zhang

“…Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. …”
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Functional-Type Caristi–Kirk Theorem on Menger Space and Application by Soumia Chaira, Mohammed Dahmouni, Abderrahim Eladraoui, Mustapha Kabil

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DESCARTES’ MATHEMATICAL IDEAS IN THE EARLIEST LITHUANIAN TEXTBOOKS by Algirdas Ažubalis

“…Descartes was the first to arrange algebraical symbolics and to ground the method of equations, analytic goemetry, the coordinate system, and the concept of function. …”
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A shadow Markov equation by Bonin, Nathan, Ovsienko, Valentin

“…We show that this equation is characterized by invariance by cluster algebra mutations.…”
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Semi-classical Virasoro blocks: proof of exponentiation by Mert Beşken, Shouvik Datta, Per Kraus

“…We prove this by employing the oscillator formulation of the Virasoro algebra and its representations. The techniques developed are then used to provide new derivations of some standard results on conformal blocks.…”
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Putnam-Fuglede theorem and the range-kernel orthogonality of derivations by B. P. Duggal

“…Let ℬ(H) denote the algebra of operators on a Hilbert space H into itself. …”
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Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A by Shirin Tavkoli, Rasoul Abazari, Ali Jabbari

“…Let X be a nonempty set, A be a commutative Banach algebra, and 1≤p<∞. In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓpX,A. …”
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Quantization of Free Scalar Fields in the Presence of Natural Cutoffs by K. Nozari, F. Moafi, F. Rezaee Balef

“…We construct a quantum theory of free scalar fields in (1+1)-dimensions based on the deformed Heisenberg algebra x^,p^=iħ1-βp+2β2p2, that admits the existence of both a minimal measurable length and a maximal momentum, where β is a deformation parameter. …”
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On constraints of the (β-deformed) partition functions with W-representations by Yu-Sen Zhu, Ren Cuo Ji, Min-Li Li, Rui Wang

“…Meanwhile, we obtain a new realization of the Virasoro algebra in terms of the Dunkl operators and the conserved quantities in the rational Calogero model.…”
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The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) by Patrik Wahlberg

“…We prove that if the covariance function belongs to the Feichtinger algebra S0(ℝ2d) then: (i) the Wigner distribution and the ambiguity function of the process exist as finite variance stochastic Riemann integrals, each of which defines a stochastic process on ℝ2d, (ii) these stochastic processes on ℝ2d are Fourier transform pairs in a certain sense, and (iii) Cohen's class, ie convolution of the Wigner process by a deterministic function Φ∈C(ℝ2d), gives a finite variance process, and if Φ∈S0(ℝ2d) then W∗Φ can be expressed multiplicatively in the Fourier domain.…”
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DESCARTES’ MATHEMATICAL IDEAS IN THE EARLIEST LITHUANIAN TEXTBOOKS by Algirdas Ažubalis

“…Descartes was the first to arrange algebraical symbolics and to ground the method of equations, analytic goemetry, the coordinate system, and the concept of function. …”
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Generalized uncertainty principle and the Zeeman effect: Relativistic corrections unveiled by Gaurav Bhandari, S.D. Pathak, Manabendra Sharma

“…We propose a relativistic GUP algebra using the Stetsko and Tkachuk approximation and incorporate these corrections into the Zeeman effect. …”
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Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions by Pavlos Kassotakis, Theodoros Kouloukas, Maciej Nieszporski

“…We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these generic equations. …”
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Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols by Yessica Hernández-Eliseo, Josué Ramírez-Ortega, Francisco G. Hernández-Zamora

“…We describe certain C∗-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D2⊂ℂ2. …”
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Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics by Alessandro Moia

“…In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates. However, spacetime noncommutativity can also be introduced into single-particle covariant quantum mechanics, replacing the commuting operators representing the particle’s spacetime coordinates with noncommuting ones. …”
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