No abstract uploaded!

No abstract uploaded!

We present a generalized learning with errors (LWE) problem, which is essentially a simple and direct extension of the original LWE problem to the case of matrices. Then we use this new version of LWE problem, which we call matrix LWE problem to build new cryptographic schemes, which include a new scalable key distribution scheme, a new key exchanges scheme and a new simple identity-based encryption scheme.

The present paper which represents the fourth part of the series devoted to analysis of a simple Lee-type model of two-particle decay deals with three problems. The first one concerns relation of the model to the scattering theory. We prove asymptotic completeness for the elastic scattering of the two light particles and show that for a sufficiently weak coupling this system has just one resonance whose position is the same as that of the pole which yield the main contribution to the decay law. The second problem concerns spectral concentration; we prove its occurrence for families of intervals around<i>E</i> that shrink slower than quadratically in<i>g</i>. Finally, necessary and sufficient conditions for the existence of bound states are discussed.

We shall consider point systems in$R$_{1}which are stationary renewal distributed. We let the points undergo random translations which are assumed to be independent identically distributed random variables with a non-degenerate distribution function. The translations are also independent of the starting positions. It is shown in theorem 3.1 that the only distribution of the points which is conserved after the random translations is the Poisson one. Finally in section 4 we give a characterization of renewal processes on the positive semiaxis in terms of conditional mean values.