COURSE CONTENT: Groups, Examples of groups, Some elementary properties of groups, Subgroups, Cyclic groups, Cosets and Langrange’s theorem, Normal subgroups and Quotient groups, Homomorphisms, The Isomorphism Theorems, Group Actions, orbits and stabilizers, Conjugacy, Class equation of a finite group, Cauchy’s Theorem, The structure of p-groups, The Sylow’s theorems, Some applications of Sylow’...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

We discuss the celebrated Blok-Esakia theorem on the isomorphism between the lattices of extensions of intuitionistic propositional logic and the Grzegorczyk modal system. In particular, we present the original algebraic proof of this theorem found by Blok, and give a brief survey of generalisations of the Blok-Esakia theorem to extensions of intuitionistic logic with modal operators and coimpl...

These theorems turned out to be very useful in complex analysis and their applications include the Levi problem with bounds and cohomology with bounds. It is, therefore, natural to seek to generalize these theorems to manifolds. In [5], Theorem 1.1 was so generalized and we generalize Theorem 1.2 in this paper. The term Carleman estimates refers to the estimates in Theorem 1.2 and we use Theore...

Abstract We establish, in the setting of equivariant motivic homotopy theory for a finite group, version tom Dieck’s splitting theorem fixed points suspension spectrum. Along way we establish structural results and constructions independent interest. This includes geometric fixed-point functors Adams isomorphism.

The Ornstein-Zernike (OZ) equations [1] can be used to find probability distributions of atoms in fluid states where the primary unknowns are the radial pair correlation function and the direct correlation function. In order to specify conditions of the state, certain parameters such as density and temperature are chosen. While one can find a single solution to the OZ equations corresponding to...