In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.

in this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. we present sufficient conditions for the existence of long exact extended d- homology sequence. also we give some illustrative examples.

We present a profile-profile multiple alignment strategy that uses database searching to collect homologues for each sequence in a given set, in order to enrich their available evolutionary information for the alignment. For each of the alignment sequences, the putative homologous sequences that score above a pre-defined threshold are incorporated into a position-specific pre-alignment profile....

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

We give a new construction of cyclic homology of an associative algebra A that does not involve Connes’ differential. Our approach is based on an extended version of the complex Ω q A, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any represe...

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.

We give a new combinatorial construction of the hat version of the link Floer homology over Z/2Z and verify that in many examples, our complex is smaller than Manolescu–Ozsváth–Sarkar one. Introduction Knot Floer homology is a powerful knot invariant constructed by Ozsváth–Szabo [11] and Rasmussen [14]. In its basic form, the knot Floer homology ĤFK(K) of a knot K ∈ S is a finite–dimensional bi...