Abstract We compute the asymptotic for eigenvalues of a particular class compact operators deeply linked with second variation optimal control problems. characterize this family in terms set finite dimensional data and we apply results to singular extremal get nice description spectrum variation.

Let WQ = Proj(Q[g2' g3' X, Y, ZJI(homogeneous ideal generated by y 2Z + 4X3 g2XZ2 g3Z3». This is said to be the Weierstrass Family over the field Q. Then the first homology with compact supports of the Weierstrass Family is computed explicitly, i.e., it is generated by {C-kdX 1\ dYh .. , and {XC-kdX 1\ dYh .. 1 over the ring Q[g2' g3]' where C is a polynomial y 2 4X3 + g2 X + g3' When one tenso...

We investigate the relative opers over complex analytic family of compact manifolds dimension one. introduce notion arising from second fundamental form associated with a holomorphic connection. also differential operators whose symbol is identity automorphism. show that set equivalent in bijective correspondence

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

In this paper, we establish the relationships between spaces with a compact-countable weak-base and spaces with various compact-countable networks, and give two mapping theorems on spaces with compact-countable weakbases. Weak-bases and g-first countable spaces were introduced by A.V.Arhangel’skii [1]. Spaces with a point-countable weak-base were discussed in [5,6], and spaces with a locally co...

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

It is well known that the space of invariant probability measures for transitive sub-shifts finite type a Poulsen simplex. In this article we prove in non-compact setting, large family countable Markov shifts, sub-probability simplex and its extreme points are ergodic together with zero measure. particular, obtain minus vertex corresponding convex combinations. Our results apply to entropy non-...

background: vitrification has proven to be more effective than slow freezing methods to cryopreserve mammalian oocytes. the objectives of this study were to evaluate the effects of vitrification on immature and in vitro matured, denuded and cumulus compact goat oocytes and their subsequent fertilization. methods: oocytes were either cryopreserved as immature cumulus compact (imcc) (n=98 exp 1; ...