相关论文: Euclidean Maxwell-Einstein Theory
A particular problem about special kind of two light pulses propagation has been considered in cases of inertial motion, constant homogeneous gravitation field and progressive non-inertial motion with constant acceleration. A contradiction…
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…
Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.
The paper concerns front propagation for the following mono-stable reaction-diffusion-advection equation \[f(u)u_x + g(u)u_\tau = [d(u)|u_x|^{p-2} u_x]_x+ \rho(u), \quad (x,\tau)\in \R\times [0,+\infty).\] Besides existence and…
We mainly consider the general Caffarelli-Kohn-Nirenberg inequality in the Euclidean and Riemannian setting. In both cases, our proof relies mostly on a new parameter s conveniently introduced, see (2.7).
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity…
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
Various numerical methods exist for obtaining the radiances inside a canopy of leaves above a partly reflecting ground. In view of testing the accuracy of these diverse methods, it is desirable to have at one's disposal non-trivial models…
We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples. The cases are distinguished whether the underlying laws are the same or different. Results are based on the (quadratic)…
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…
It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional…
We study the half advanced and half retarded Wheeler Green function and its relation to Feynman propagators. First for massless equation. Then, for Klein-Gordon equations with arbitrary mass parameters; real, imaginary or complex. In all…
Schoenberg transformations, mapping Euclidean configurations into Euclidean configurations, define in turn a transformed inertia, whose minimization produces robust location estimates. The procedure only depends upon Euclidean distances…
This survey article gives an account of quasiconformal extensions of univalent functions with its motivational background from Teichm\"uller theory and classical and modern approaches based on Loewner theory.
We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method.…