Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.

Measurement of gamma + b + X and gamma + c + X Production Cross Sections in pp > Collisions at s=1.96 TeV

First measurements of the differential cross sections d(3)sigma/(dp(T)(gamma)dy(gamma)dy(jet)) for the inclusive production of a photon in association with a heavy quark (b, c) jet are presented, covering photon transverse momenta 30 < p(T)(gamma)< 150 GeV, photon rapidities |y(gamma)|< 1.0, jet rapidities |y(jet)|< 0.8, and jet transverse momenta p(T)(jet)> 15 GeV. The results are based on an integrated luminosity of 1 fb(-1) in pp collisions at s=1.96 TeV recorded with the D0 detector at the Fermilab Tevatron Collider. The results are compared with next-to-leading order perturbative QCD predictions.

Functions and vector fields on C(CPn)-singular manifolds

Let M2n+1 be a C(CPn) -singular manifold. We study functions and vector fields with isolated singularities on M2n+1. A C(CPn) -singular manifold is obtained from a smooth manifold M2n+1 with boundary in the form of a disjoint union of complex projective spaces CPn boolean OR CPn boolean OR ... boolean OR CPn with subsequent capture of a cone over each component of the boundary. Let M2n+1 be a compact C(CPn) -singular manifold with k singular points. The Euler characteristic of M2n+1 is equal to chi(M2n+1) = k(1 - n)/2. Let M2n+1 be a C(CPn)-singular manifold with singular points m(1), ..., m(k). Suppose that, on M2n+1, there exists an almost smooth vector field V (x) with finite number of zeros m(1), ..., m(k), x(1), ..., x(1). Then chi(M2n+1) = Sigma(l)(i=1) ind(x(i)) + Sigma(k)(i=1) ind(m(i)).

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Chiral Templating Activity of Tris(bipyridine)ruthenium(II) Cation in the Design of Three-Dimensional (3D) Optically Active Oxalate-Bridged {[Ru(bpy) 3 ][Cu 2 x Ni 2(1 - x ) (C 2 O 4 ) 3 ]} n (0 ≤ x ≤ 1; bpy = 2,2‘-bipyridine): Structural, Optical, and Magnetic Studies

Three-dimensional oxalate-based {[Ru(bpy)3][Cu2xNi2(1-x)(ox)3]}n (0≤ x ≤ 1, ox = C2O42-, bpy = 2,2‘bipyridine) were synthesized. The structure was determined for x = 1 by X-ray diffraction on single crystal. The compound crystallizes in the cubic space group P4132. It shows a three-dimensional 10-gon 3-connected (10,3) anionic network where copper(II) has an unusual tris(bischelated) environment. X-ray powder diffraction patterns and their Rietveld refinement show that all the compounds along the series are isostructural and single-phased. According to X-ray absorption spectroscopy, copper(II) and nickel(II) have an octahedral environment, respectively elongated and trigonally distorted. As shown by natural circular dichroism, the optically active forms of {[Ru(bpy)3][CuxNi2(1-x)(ox)3]}n are obtained starting from resolved Δ- or Λ-[Ru(bpy)3]2+. The Curie−Weiss temperatures range between −55 (x = 1) and −150 K (x = 0). The antiferromagnetic exchange interaction thus decreases when the copper contents increases in agreement with the crystallographic structure of the compounds and the electronic structure of the metal ions. At low temperature, the compounds exhibit complex long-range ordered magnetic behavior.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

Ionic transport in (PEG)x LiBr systems

Ionic conductivity in (PEG)(x)LiBr systems is measured using the complex impedance method in the temperature range -20 degrees C to 100 degrees C. For x = 6 and 10, above a certain concentration dependent temperature T-c, a power law fit based on mode coupling theory is seen to better explain the data than the Vogel-Tamman-Fulcher (VTF) expression. Li-7 NMR linewidth measurements indicate two regions of motional narrowing, one attributable to segmental motion and the other to translational diffusion.

Preparation, Characterization And Properties Of C-60 And C-70 - Spectroscopy, Structure, Anions, Interaction With Electron-Donors And Superconductivity

Preparation and characterization of the fullerenes, C60 and C70, are described in detail, including the design of the generators fabricated locally. The characterization techniques employed are UV-visible, IR, Raman and C-13 NMR spectroscopies, scanning as well as transmission electron microscopy and mass spectrometry. The electron energy level diagram of C60 as well as the one-electron reductions of C60 and C70 leading to various anions are discussed. Electronic absorption spectra of C60- and C60(2-) are reported. Phase transitions from the plastic to the crystalline states of C60 and C70 are examined. Based on a C-13 NMR study in a mixture of nematic liquid crystals, it has been demonstrated that C60 retains its extraordinary symmetry in solution phase as well. Interaction of C60 and C70 with strong electron-donor molecules has been investigated employing cyclic voltammetry. Superconductivity of K(x)C60 has been studied by non-resonant microwave absorption; Na(x)C60 as well as K(c)C70 are shown to be non-superconducting. Doping C60 with iodine does not make it superconducting. Interaction of C60 with SbCl5 and liquid Br2 gives rise to halogenated products.

Influence of Si-C bond density on the properties of a-Si(1-x)C(x) thin films

Amorphous silicon carbide (a-Si(1-x)C(x)) films were deposited on silicon (100) and quartz substrates by pulsed DC reactive magnetron sputtering of silicon in methane (CH(4))-Argon (Ar) atmosphere. The influence of substrate temperature and target power on the composition, carbon bonding configuration, band gap, refractive index and hardness of a-SiC films has been investigated. Increase in substrate temperature results in slightly decreasing the carbon concentration in the films but favors silicon-carbon (Si-C) bonding. Also lower target powers were favorable towards Si-C bonding. X-ray photoelectron spectroscopy (XPS) results agree with the Fourier Transform Infrared (FTIR), UV-vis spectroscopy results. Increase in substrate temperature resulted in increased hardness of the thin films from 13 to 17 GPa and the corresponding bandgap varied from 2.1 to 1.8 eV. (C) 2011 Elsevier B.V. All rights reserved.

室温铁磁性半导体Mn_xGa_(1-x)Sb

采用离子注入、离子沉积及后期退火方法制备了稀磁半导体单晶Mn_xGa_(1-x)Sb，在室温下（300 K）获得了单晶的磁滞回线。用X射线衍射方法分析了铁磁性半导体单晶Mn_xGa_(1-x)Sb的结构，用电化学C-V法分析了单晶的载流子浓度分布。由X射线衍射得知，Mn_xGa_(1-x)Sb中Mn含量逐渐由近表面处的x = 0.09下降到晶片内部的x = 0。电化学C-V测得单晶的空穴浓度高达1 * 10~(21)cm~(-3)，表明Mn_xGa_(1-x)Sb单晶中大部分Mn原子占据Ga位，起受主作用。

Uniaxial Strain Effects on Optical Properties of c-plane Wurtzite GaN

We investigate the uniaxial strain effect in the c-plane on optical properties of wurtzite GaN based on k center dot p theory, the spin-orbit interactions are also taken into account. The energy dispersions show that the uniaxial strain in the c-plane gives an anisotropic energy splitting in the k(x) - k(y) plane, which can reduce the density of states. The uniaxial strain also results in giant in-plane optical polarization anisotropy, hence causes the threshold carrier density reduced. We clarify the relations between the uniaxial strain and the optical polarization properties. As a result, it is suggested that the compressive uniaxial strain perpendicular to the laser cavity direction in the c-plane is one of the preferable approaches for the effcient improvement of GaN-based laser performance.

室温铁磁性半导体Mn_xGa_(1-x)Sb

采用离子注入、离子沉积及后期退火方法制备了稀磁半导体单晶Mn_xGa_(1-x)Sb，在室温下（300 K）获得了单晶的磁滞回线。用X射线衍射方法分析了铁磁性半导体单晶Mn_xGa_(1-x)Sb的结构，用电化学C-V法分析了单晶的载流子浓度分布。由X射线衍射得知，Mn_xGa_(1-x)Sb中Mn含量逐渐由近表面处的x = 0.09下降到晶片内部的x = 0。电化学C-V测得单晶的空穴浓度高达1 * 10~(21)cm~(-3)，表明Mn_xGa_(1-x)Sb单晶中大部分Mn原子占据Ga位，起受主作用。