We prove that the obstacle problem for a non-uniformly parabolic operator of Kolmogorov type, with Cauchy (or Cauchy-Dirichlet) boundary conditions, has a unique strong solution u. We also show that u is a solution in the viscosity sense.

We introduce a quantization map and study the quantization of Schubert and Grothendieck polynomials, monomials, elementary and complete polynomials. Our construction is based on the quantum Cauchy identity. As a corollary, we prove the Lascoux–Schützenberger type formula for quantum Schubert polynomials of the flag manifold. Our formula gives a simple method for computation of quantum Schubert ...

In this paper, we prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov-Petrovsky-Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability propert...

Ateya and Madhagi (2011) introduced a multivariate form of truncated generalized Cauchy distribution (TGCD), which introduced by Ateya and Al-Hussaini (2007). The multivariate version of (TGCD) is denoted by (MVTGCD). Among the features of this form are that subvectors and conditional subvectors of random vectors, distributed according to this distribution, have the same form of distribution ...

In this paper, we study the concepts of Wijsman statistical convergence, Hausdorff statistical convergence and  Wijsman statistical Cauchy double sequences of sets and investigate the relationship between them.

Within the categoryW of archimedean lattice-ordered groups with weak order unit, we show that the objects of the form C (L), the set of continuous real-valued functions on a locale L, are precisely those which are divisible and complete with respect to a variant of uniform convergence, here termed indicated uniform convergence. We construct the corresponding completion of aW-object A purely alg...

This paper proposes a new, large diffusion layer for the AES block cipher. This new layer replaces the ShiftRows and MixColumns operations by a new involutory matrix in every round. The objective is to provide complete diffusion in a single round, thus sharply improving the overall cipher security. Moreover, the new matrix elements have low Hamming-weight in order to provide equally good perfor...

Relative to the current Master/Slave computing model cloud storage file systems, including GFS, HDFS, Sector, we proposed a general model of Peer-to-Peer based Cloud Storage file system, and constructed a prototype system named MingCloud based on Kademlia algorithm. Focused on redundant strategy selection and design of the storage system, our experiment used the Cauchy Codes as coding algorithm...