Let g be a reductive Lie algebra over C. We say that a g-module M is a generalized Harish-Chandra module if, for some subalgebra k ⊂ g, M is locally k-finite and has finite k-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when k is a Cartan subalgebra. We ...

In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalge...

z Sir, we are truly six special and interesting characters. Believe us. However we have gone lost. Abstract We consider the following six hypotheses: P = NP. SAT is truth-table reducible to a P-selective set. SAT is truth-table reducible to a k-approximable set for some k.

We show that any p-selective and self-reducible set is in P. As the converse is also true, we obtain a new characterization of the class P. A generalization and several consequences of this theorem are discussed. Among other consequences, we show that under reasonable assumptions auto-reducibility and self-reducibility diier on NP, and that there are non-p-T-mitotic sets in NP.

We investigate the complexity of Boolean clone membership problem (CMP): given a set functions $F$ and function $f$, determine if $f$ is in generated by $F$, i.e., it can be expressed circuit with $F$-gates. Here, elements are as circuits or formulas over usual De Morgan basis. B\"ohler Schnoor (2007) proved that for any fixed coNP-complete, few exceptions where P. Vollmer (2009) incorrectly cl...