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The Case of Equality in Geometric Instances of Barthe’s Reverse Brascamp-Lieb Inequality
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we...
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Ergodic decompositions of geometric measures on Anosov homogeneous spaces
Let G be a connected semisimple real algebraic group and Γ a Zariski dense Anosov subgroup of G with respect to a minimal parabolic subgroup P . Let N ...
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Topology optimization and geometric nonlinear modeling using positional finite elements
Topology optimization is an effective approach for the efficient layout design of structures and their components. This approach is well-established...
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Geometric Optics for Quasilinear Hyperbolic Boundary Value Problems
This paper presents the work in Kilque (2022) which investigate the existence of the leading profile of a WKB expansion for quasilinear initial...
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Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies
Very recently J. Kotrbatý[14] has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge-Riemann...
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Uniform convolution estimates for complex polynomial curves in \({\mathbb {C}}^3\)
We establish optimal ( p , q ) ranges for the weighted convolution operator associated with a complex polynomial curve. Establishing this estimate comes...
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Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric...
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A geometric approach to equivariant factorization homology and nonabelian Poincaré duality
Fix a finite group G and an n -dimensional orthogonal G -representation V . We define the equivariant factorization homology of a V -framed smooth G -manif...
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Velocity-Vorticity Geometric Constraints for the Energy Conservation of 3D Ideal Incompressible Fluids
In this paper we consider the 3D Euler equations and we first prove a criterion for energy conservation for weak solutions, where the velocity...
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A survey of geometric constraints on the blowup of solutions of the Navier–Stokes equation
In this survey article, we will discuss some regularity criteria for the Navier–Stokes equation that provide geometric constraints on any possible...
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Higher-Order Spectral Clustering for Geometric Graphs
The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we...
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Multiple Convolution Formulae of Bernoulli and Euler Numbers
By examining higher derivatives of hyperbolic functions, we derive monomial and binomial representation formulae, that are utilized to establish...
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Traveling Wave Solutions for Two Perturbed Nonlinear Wave Equations with Distributed Delay
Traveling wave solutions are a class of invariant solutions which are critical for shallow water wave equations. In this paper, traveling wave...
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Using a Graph Transformer Network to Predict 3D Coordinates of Proteins via Geometric Algebra Modelling
The state of the art in protein structure prediction (PSP) is currently achieved by complex deep learning pipelines that require several input...
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A Numerical Study of the Convergence of Two Hybrid Convolution Quadrature Schemes for Broadband Wave Problems
In this chapter, we compare the performance of two recently proposed hybrid methods for numerically solving the wave equation in two spatial...
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Convolution conditions for two subclasses of analytic functions defined by Jackson q-difference operator
By using Jackson q -derivative, some characterizations in terms of convolutions for two classes of analytic functions in the open unit disc are given....