Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

the synthesis and single-crystal x-ray structure determination of the title compound [(bipy) , pb(0 ,cme) (o clo )] (1) and [(bipy) pb(clo ) ] (2) is described. compound (i) crystallizes in the triclinic space group p1(2), a= 7.384(2), b= 12.824(3), c= 10.622(6) a, ?= 73.41(2), ?= 80.98(2), ?= 73.68(2)', z= 2, and r =0.033 for 3408 independent reflections .compound (2) crystallizes in the ...

Let E/F be a quadratic extension of p-adic fields. We compute the multiplicity of the space of SL2(F )-invariant linear forms on a representation of SL2(E). This multiplicity varies inside an L-packet similar in spirit to the multiplicity formula for automorphic representations due to Labesse and Langlands.

Cop accepted J School of and repri ins Scho mi.edu). uropean S rition and patology, a 00000000 athleen ‘‘Kay’’ J. Motil, MD, PhD, embodies the K spirit of the NASPGHAN Distinguished Service award. She has worked tirelessly to improve the lives of the children and built a distinguished career within the realm of pediatric gastroenterology and nutrition. She completed her undergraduate education ...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions eα : x → xα where x ≥ 0 and 0 < α ≤ 1/2, and in particular the critical parameter α = 1/2, play a distinguished role.

The present report contains recommendations on the nomenclature of the labuntsovite-group (LG) minerals based on a crystal-structural classification. The labuntsovite group includes hydrous titanium and niobium silicates, both orthorhombic and monoclinic, with a structure characterized by a framework consisting of chains of (Ti,Nb)O-octahedra, linked by four-member rings of Si,O-tetrahedra. Thi...

Two possible quantum descriptions of the classical Not gate are investigated in the framework of the Hilbert space C: the unitary and the anti–unitary operator realizations. The two cases are distinguished interpreting the unitary Not as a quantum realization of the classical gate which on a fixed orthogonal pair of unit vectors, realizing once for all the classical bits 0 and 1, produces the r...