The possibility is discussed to improve the ray approximation up to an exact representation of a wave field by the Feynman–Kac probabilistic formula (this formula gives an exact solution of the Helmholtz equation in the form of the expectation of a certain functional on the space of Brownian random walks). Some examples illustrate an application of the solutions obtained to diffraction problems...

We show that the Lei et al.’s scheme [Information Sciences, 280 (2014), 205-217] fails, because the verifying equation does not hold over the infinite field R. For the field R, the computational errors should be considered seriously. We also remark that the incurred communication cost in the scheme could be overtake the computational gain, which makes it somewhat artificial.

We remark that the Lei et al.’s scheme [IEEE Transactions on Cloud Computing, 1 (1), 78-87, 2013] fails, because the verifying equation does not hold over the infinite field R. For the field R, the computational errors should be considered seriously.

An axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the bivector field F. In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either elec...

in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck's functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current ~j = ρ∇S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may...

Gauge equivalence between the two-dimensional continuous classical Heisenberg ferromagnets(CCHF) of spin 1 2 -the M-I equation with singleside anisotropy and the Zakharov equation(ZE) is established for the easy axis case. The anisotropic CCHF is shown to be gauge equivalent to the isotropic CCHF. Preprint CNLP-1994-05. Alma-Ata.1994 In the study of 1+1 dimensional ferromagnets, a well known La...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...