In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

We study the relation between zero loci of Bernstein-Sato ideals and roots b-functions obtain a criterion to guarantee that reducible polynomial are determined by locus associated ideal. Applying together with result Maisonobe we prove set b-function free hyperplane arrangement is its intersection lattice. also relative characteristic cycles for arbitrary central arrangements. multivariable n/d...

Let M be a simple 3-manifold such that one component of ∂M , say F , has genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.

A convex subnearlattice of a nearlattice S containing a fixed element n∈S is called an n-ideal. The n-ideal generated by a single element is called a principal n-ideal. The set of finitely generated principal nideals is denoted by Pn(S), which is a nearlattice. A distributive nearlattice S with 0 is called m-normal if its every prime ideal contains at most m number of minimal prime ideals. In t...

Let $R$ be a commutative ring. An $R$-module $M$ is called semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ $\GV$-torsion for any finitely generated ideal $I$. In this article, we show that the class of modules covering class. Moreover, introduce dimensions $R$-modules and $sr$-$w$-weak global ring $R$. Utilizing these notions, give some homological characterizations $\WQ$-rings $Q_0$-\PvMR s.

the hydraulic characteristic of an up-flow anaerobic sludge blanket fixed film (uasb-ff) were studied by changing two important hydraulic factors that can impact significantly on the hydraulic regime of the uasb-ff bioreactor: the up-flow velocity (vup) and biogas production rate (qg). the analysis of the reactor hydraulic performance was performed by studying hydraulic residence time distribut...

The conversion of the reducible divalent cross-links in collagen to non-reducible multivalent cross-links in mature collagen has resulted in the identification of several new amino acids as the putative mature cross-link. None of these compounds has completely satisfied the necessary criteria. We have now isolated an amino acid of high Mr, derived from lysine, that is only present in high-Mr pe...

This article generalizes the well-known notion of generic forms to the algebra R 0 , introduced in 27]. For the total degree, then reverse lexicographic order, we prove that the initial ideal of an ideal generated by nitely many generic forms (in countably innnitely many variables) is nitely generated. This contrasts to the lexicographic order, for which initial ideals of generic ideals in gene...

Circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic and commonsense reasoning but di cult to apply in practice due to the use of second order formulas One proposal for dealing with the computational problems is to identify classes of rst order formulas whose cir cumscription can be shown to be equivalent to a rst order formula In previous work we pr...