Let $S$ be a finite subset of compact connected Riemann surface $X$ genus $g \geq 2$. $\cat{M}_{lc}(n,d)$ denote the moduli space pairs $(E,D)$, where $E$ is holomorphic vector bundle over and $D$ logarithmic connection on singular $S$, with fixed residues in centre $\mathfrak{gl}(n,\C)$, $n$ $d$ are mutually corpime. $L$ line $D_L$ $S$. $\cat{M}'_{lc}(n,d)$ $\cat{M}_{lc}(n,L)$ spaces parametri...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

The main purpose of this note is to observe that the celebrated theorem of Malliavin on the failure of spectral synthesis for the group algebra L{G) of a non compact locally compact abelian group G can be strengthened to get the failure of weak spectral synthesis (in the sense of Warner [7]) for £(G) and also for the "generalised group algebra" L{G, A). Let A be a commutative, semisimple, regul...

(1) For all subsets A, B of E2 T such that A meets B holds proj1 ◦A meets proj1◦B. (2) Let A, B be subsets of E2 T and s be a real number. If A misses B and A⊆HorizontalLine(s) and B⊆ HorizontalLine(s), then proj1◦A misses proj1◦B. (3) For every closed subset S of E2 T such that S is Bounded holds proj1 ◦ S is closed. (4) For every compact subset S of E2 T holds proj1 ◦ S is compact. (5) Let p,...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Let $$D\subset {\mathbb {C}}^n$$ be a bounded domain. A pair of distinct boundary points $$\{p,q\}$$ D has the visibility property provided there exist compact subset $$K_{p,q}\subset D$$ and open neighborhoods $$U_p$$ p $$U_q$$ q, such that real geodesics for Kobayashi metric which join in intersect $$K_{p,q}$$ . Every Gromov hyperbolic convex domain enjoys any couple points. The Goldilocks do...

Let (Q.,l,ß) be a probability space, X a Banach space, and L (fi, X) the Banach space of Bochner integrable functions f: Í2 —> X . Let W = {/ € Ll(p, X) : for a.e. w in Í2, ||/(w)|| < 1} . In this paper we characterize the rwc (relatively weakly compact) subsets of L (ß, X). The main results are as follows: Theorem A. A subset H of W is rwc iff given any sequence (/„) in H there exists a sequen...

The main objective of this work was to design a novel device for compaction of metal powders so that the green parts could be ejected with applying a negligible force and without the need for any lubricant in either an admixed form or applied to the die wall. For this purpose a 40 mm diameter one-piece die was envisaged which would elastically contracted 0.076 mm before compaction and after com...

1. Introduction. Let A be a topological space, F be a metrizable space, and C be the collection of continuous functions on X into Y. We shall be interested in two topologies on C. The compact-open or k-topology. Given compact subset K of X and open subset W of F, denote by (K, W) the collection of functions fEC such that fiK)E W. The assembly of finite intersections of sets iK, W) forms a base ...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...