We define two (n + 1) graded Lie brackets on spaces of multilinear mappings. The first one is able to recognize n-graded as-sociative algebras and their modules and gives immediately the correct differential for Hochschild cohomology. The second one recognizes n-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.

there has been a recent development and explosion of interest among academicians across a wide range of disciplines in the use of virtual class room. utilization of the virtual class room as a laboratory experimentation for teaching and learning has increased significantly in recent years as development tools for web based applications have become easier to use and computers have become more ca...

the aim of this paper is to report on an attempt to design and implement an intelligent system capable of generating the correct part of speech for a given sentence while the sentence is totally new to the system and not stored in any database available to the system. it follows the same steps a normal individual does to provide the correct parts of speech using a natural language processor. it...

background: integrons are mobile genetic elements able to obtain the antibiotic resistance gene cassettes. the prevalence of integrons in the enterobacteriaceae family has been varied and played an important role in the development of the drug resistant bacteria. the present study aimed to investigate the contribution of class 2 and 3 integrons in drug resistant diarrheagenic escherichia coli s...

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

We give an elementary description of the maps in the linear strand of the minimal free resolution of a square-free monomial ideal, that is, the Stanley-Reisner ideal associated to a simplicial complex. The description is in terms of the homology of the canonical Alexander dual complex. As applications we are able to prove for monomial ideals and j = 1 a conjecture of J. Herzog giving lower boun...

The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category Db(OX -mod). To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a cohere...