Tate local cohomology and Gorenstein theory, which are important generalizations of the classical cohomology, has been investigated. It found that they have such vanishing properties long exact sequences. However, for homology, what about duality? In this paper we concerned with homology homology. first part generalize as study properties, artinianness some sequence modules. We find an artiania...

We consider the following question: If a simplicial complex $$\Gamma $$ has d-homology, then does corresponding d-cycle always induce cycles of smaller dimension that are not boundaries? provide an answer to this question in fixed dimension. use breaking homology show subadditivity property for maximal degrees syzygies monomial ideals homological degree.

The gene encoding a major 28-kilodalton antigen of Mycobacterium leprae has now been sequenced and identified as the enzyme superoxide dismutase (SOD) on the basis of the high degree of homology with known SOD sequences. The deduced amino acid sequence shows 67% homology with a human manganese-utilizing SOD and 55% homology with the Escherichia coli manganese-utilizing enzyme. The gene is not e...

Design of high-quality primers for multiple target sequences is essential for qPCR experiments, but is challenging due to the need to consider both homology tests on off-target sequences and the same stringent filtering constraints on the primers. Existing web servers for primer design have major drawbacks, including requiring the use of BLAST-like tools for homology tests, lack of support for ...

Topology is the subfield of mathematics that is concerned with the study of shape. Mathematicians have studied topological questions for the past 250 years. However, in just the past 15 years topology has been found to have many different applications to real world problems. One of these is to use a topological tool called persistence homology to understand and analyze high dimensional and comp...

There are different notions of homology and cohomology that can be defined for a group with an action another by automorphisms. In this paper we address three natural questions arise in context. Namely, the relation these usual (co)homology semidirect product, interpretation first as some kind abelianization classification (invariant) extensions.