H. Weyl has defined a semi-simple algebra (of finite rank) to be an algebra which admits a faithful semi-simple linear representation. Now, algebras are rings with a field of operators; Artin and others have shown that the theory of semi-simple algebras can be generalized to a theory of semi-simple rings (without the field of operators) provided we replace the condition of finite rank by suitab...

This paper presents modeling of an Alternating Current (AC) Photovoltaic (PV) module using Matlab/Simulink. The proposed AC-PV module model is simple, realistic, and application oriented. The model is derived on module level as compared to cell level directly from the information provided by the manufacturer data sheet. DC-PV module, MPPT control, BC, VSI and LC filter, all were treated as a si...

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra ĝ 6= A(2k, 2l). We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.

We give a simple proof of an isomorphism between two C[t]-modules corresponding to bivariate polynomial H with nondegenerate highest homogeneous part: the module of relative cohomologies Λ 2 /dH ∧ Λ 1 and the module of Abelian integrals. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

A concept of quantum triad and its solution is introduced. It represents a common framework for several situations where we have a quantale with a right module and a left module, provided with a bilinear inner product. Examples include Van den Bossche quantaloids, quantum frames, simple and Galois quantales, operator algebras, or orthomodular lattices.

We make a first step towards a classification of simple generalized Harish-Chandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras (g, k), we construct, via cohomological induction, the fundamental series F ·(p, E) of generalized Harish-Chandra modules. We then use F ·(p, E) to characterize any simp...