Definite Determinantal polynomials play a crucial role in semidefinite programming problems. Helton and Vinnikov proved that real zero (RZ) bivariate are definite determinantals. Indeed, general, it is difficult problem to decide whether given polynomial determinantal, if is, of paramount interest determine determinantal representation polynomial. We provide necessary sufficient condition for t...

We consider systems of Brownian particles in the space positive definite matrices, which evolve independently apart from some simple interactions. give examples such processes have an integrable structure. These are related to $K$-Bessel functions matrix argument and multivariate generalisations these functions. The latter eigenfunctions a particular quantisation non-Abelian Toda chain.

the phrase “hodood that are not mentioned in this code” in article 220 of islamic penal code of 2013 and “shar’i definite tazir” in article 115 of this code are ambiguous from figh and legal viewpoint, then we have to resort to interpretation for recognizing their instances, in this regard, three interpretations are possible, first, restricting “hodood” to six famous types and allocating defini...