In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...

there are many techniques to knock out directed genes in bacteria, some of which have been described in salmonella species. in this study, a combination of soeing pcr method and the λ red disruption system were used to disrupt phop gene in wild type and standard strains of salmonella typhimurium. three standards pcr and one fusion pcr reactions were performed to construct a linear dna including...

We introduce several geometric notions, including the width of a homology class, to theory persistent homology. These ideas provide interpretations persistence diagrams. Indeed, we give quantitative and descriptions “life span” or “persistence” class. As case study, analyze power filtration on unweighted graphs explicit bounds for life spans classes in diagrams all dimensions.

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.

Two new techniques for remote protein homology detection particulary suited for sparse data are introduced. These methods are based on position specific scoring matrices or profiles and use a support vector machine (SVM) for discrimination. The performance on standard benchmarks outperforms previous non-discriminative techniques and is comparable to that of other SVM-based methods while giving ...

In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on four-manifolds. We will show here that this is not the case for the Hopf surface, all integer homology Hopf surfaces we obtain are diffeomorphic to the standard Hopf surface.

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...