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Tightening the Penrose inequality
The Penrose inequality estimates the lower bound of the mass of a black hole in terms of the area of its horizon. This bound is relatively loose for...
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Weighted p-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory
We study the p -Rényi entropy power inequality with a weight factor t on two independent continuous random variables X and Y . The extension...
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Estimation of the size of the solar system and its spatial dynamics using Sundman inequality
The essential development of a new mathematical ansatz for estimating the size of the solar system with help of Sundman inequality via...
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On one interpolation inequality and its application to the Bürgers equation
AbstractWe consider the Cauchy problem for the nonlinear Bürgers equation and prove a new interpolation inequality. The method of energy...
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A holographic inequality for N = 7 regions
In holographic duality, boundary states that have semiclassical bulk duals must obey inequalities, which bound their subsystems’ von Neumann...
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Optimal Hardy Inequality for Fractional Laplacians on the Integers
We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight and hence affirmatively answer the question of...
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Solution Stability of Delay Differential Equations in Banach Spaces
AbstractThe Lyapunov stability of steady-state solutions to nonlinear differential equations with time-dependent operators and time-dependent delay...
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Exploring Gender Inequality and Practical Solutions for an Equitable Environment for Women in Scientific Vocations
Despite progress towards gender equality in science and educationEducation, womenWomen remain underrepresented in decision-makingDecision-making...
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Discrete Differential Geometry. Integrability as Consistency
We discuss a new geometric approach to discrete integrability coming from discrete differential geometry. A d–dimensional equation is called...
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Limited and Smooth Controls of Oscillations in Systems Given by Differential and Integro-Differential Equations
AbstractThe paper considers the problem of dam** vibrations of a membrane and a plate with the help of forces distributed over their entire area....
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Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition
AbstractWe consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion...
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A quantum complexity lower bound from differential geometry
Differential geometry has long found applications in physics in general relativity and related areas. More recently, it was proposed by Nielsen that...
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Differential and Difference Equations as Dynamical Systems
We introduce the concept of a dynamical system and review the basic results and the terminology of the qualitative theory of differential and...
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Bohm’s Hidden Variables and Bell’s Inequality
David Bohm was a Ph.D. student of Robert Oppenheimer at the University of California at Berkeley. In 1943, after Oppenheimer was appointed as the...
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Partial Differential Equations of Mathematical Physics
If an unknown function of several variables and its partial derivatives are combined in an equation, the latter is called a partial differential...
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Revisiting the Differential Geometry of Surfaces in 3D-Spaces
We intend to present some basic facts related to the Differential Geometry of a surface in a 3D-space in the simplest form we imagined. All readers...
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Loop-by-loop differential equations for dual (elliptic) Feynman integrals
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We...
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Modeling and analysis of an implicit fractional order differential equation with multiple first-order fractional derivatives and non-local boundary conditions
In recent years, researchers have investigated boundary value problems of single terms and, in rare circumstances, multi-term fractional differential...
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On the spectrum of the differential operators of even order with periodic matrix coefficients
In this paper, we consider the band functions, Bloch functions and spectrum of the self-adjoint differential operator L with periodic matrix...