We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations...

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schrödinger equation. In this part we study the diffraction managed discrete nonlinear Schrödinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing averag...

‎We mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+P(z)f(z+c)^n=Q(z)$‎, ‎which is a supplement of previous‎ ‎results in [K‎. ‎Liu‎, ‎L. Z‎. ‎Yang and X‎. ‎L‎. ‎Liu‎, ‎Existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎Czechoslovak Math. J. 61 (2011)‎, no. 2, ‎565--576‎, and X‎. ‎G‎. ‎Qi‎...

in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.

This paper gives a proof of existence of price equilibria under certain parameters for a model of product differentiation commonly used in the empirical geographic differentiation literature. This proof is needed because the assumptions of Caplin and Nalebuff (1991) are not generally satisfied once data is introduced to geographic models. The theorem also has implications for existence in mixed...

in his recognition of being and achievement of truth, man has two instruments in his constitution and two ways before him: intellect and heart; reasoning and intuition. some have opted the way of reasoning and underestimated intuition because of its lack of reasoning, and some have preferred intuition over reasoning because of its being presential (intuitive). with their research on philosophy ...