相关论文: Euclidean Maxwell-Einstein Theory
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…
We show that the Gersten derivation of Maxwell equations can be generalized. It actually leads to additional solutions of `S=1 equations'. They follow directly from previous considerations by Majorana, Oppenheimer, Weinberg and Ogievetskii…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal…
Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems…
We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion…
We consider light propagation through a twisted nematic liquid crystal. At first, an expression for light transmission is obtained using a rather intuitive approach. Secondly, an accurate solution for light transmission based on Maxwell's…
We discuss a categorical version of the celebrated belief propagation algorithm. This provides a way to prove that some algorithms which are known or suspected to be analogous, are actually identical when formulated generically. It also…
Motivated by a number of recent experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which ``feels''…
We present a reformulation of Mawxell's equation and examine the consequence of this new formulation. We argue that studies of such diverse topics as magnetic monopole, magnetic recombination and magneto-genesis could benefit from the new…
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…
We consider in detail how the quantum-mechanical tunneling phenomenon occurs in a well-behaved octic potential. Our main tool will be the euclidean propagator just evaluated between two minima of the potential at issue. For such a purpose…
In Fick's time-honored theory of diffusion, the system responds instantaneously to external perturbations, resulting in acausal behavior. Maxwell-Cattaneo theory addresses this issue by introducing a relaxation time, rendering the diffusion…
An extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
A procedure to teach Electrodynamics independently of unit systems is presented and compared with some of those given in physics literature.
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.