The Fundamental Principle of Ehrenpreis asserts that any solution (in an appropiate functional space, which we will assume, to simplify, is the space of C∞ functions in R) of a system of homogeneous linear partial differential equations with constant coefficients in R, n ≥ 2, can be can be represented in terms of the exponential polynomials solutions of the system [Ehr, Pal, Bjo]. Another way t...

In this paper, we present an approximate aggregation principle to reduce the state space of an homogeneous Markov process. This method is then used to compute a bound of the asymptotic unavailability of a Markovian system. Finally, we show that calculating this dependability measure is of much interest even in different contexts, since the unavailability at time t of several ageing systems can ...

The name Siegel’s Lemma is usually used to denote results about non-trivial small-height solutions of a system of homogeneous linear equations, or (which is the same) about non-zero points of small height in a given vector space. Such a result in a simple form was first proved by Thue in 1909 using the Dirichlet’s box principle. Siegel in 1929 was the first to formally state this principle in t...

national security and territorial administration, the most basic principle of any political system. in this regard, the divisions of the territorial office of the most excellent strategy for space and maintain the integrity and strengthening internal solidarity and ultimately increase the coefficient of national security. according to the principle of cultural similar in discussing the dramatic...

For a homogeneous space with connected or abelian stabilizer of a connected linear algebraic group defined over a number field, a cohomological obstruction to the Hasse principle is defined in terms of Galois hypercohomology with coefficients in a complex of two abelian algebraic groups. This obstruction is proved to be the only obstruction to the Hasse principle. It is proved that up to sign t...

Abstract: The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle’s trajectory through the modified space-time is thus formally equivalent to a light ray and can be derived from a mechanical equivalent of Fermat’s principle. The similarities between light propagation and mechanics are the...

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...

in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...