How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

COPIES OF c(0)(Gamma) IN C(K, X) SPACES

We extend some results of Rosenthal, Cembranos, Freniche, E. Saab-P. Saab and Ryan to study the geometry of copies and complemented copies of c(0)(Gamma) in the classical Banach spaces C(K, X) in terms of the carclinality of the set Gamma, of the density and caliber of K and of the geometry of X and its dual space X*. Here are two sample consequences of our results: (1) If C([0, 1], X) contains a copy of c(0)(N-1), then X contains a copy of c(0)(N-1). (2) C(beta N, X) contains a complemented copy of c(0)(N-1) if and only if X contains a copy of c(0)(N-1). Some of our results depend on set-theoretic assumptions. For example, we prove that it is relatively consistent with ZFC that if C(K) contains a copy of c(0)(N-1) and X has dimension NI, then C(K, X) contains a complemented copy of cc(0)(N-1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Final results from the KTeV experiment on the decay KL ->pi(0)gamma gamma

We report on a new measurement of the branching ratio B(K(L) -> pi(0)gamma gamma) using the KTeV detector. We reconstruct 1982 events with an estimated background of 608, that results in B(K(L) -> pi(0)gamma gamma)=(1.29 +/- 0.03(stat) +/- 0.05(syst)) x 10(-6). We also measure the parameter, a(V), which characterizes the strength of vector meson exchange terms in this decay. We find a(V) = -0.31 +/- 0.05(stat) +/- 0.07(syst). These results utilize the full KTeV data set collected from 1997 to 2000 and supersede earlier KTeV measurements of the branching ratio and a(V).

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Measurement of the Forward-Backward Charge Asymmetry and Extraction of sin(2)theta(eff)(W) in pp -> Z/gamma(*)+X -> e(+)e(-)+X Events Produced at s=1.96 TeV

We present a measurement of the forward-backward charge asymmetry (A(FB)) in pp -> Z/gamma(*)+X -> e(+)e(-)+X events at a center-of-mass energy of 1.96 TeV using 1.1 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. A(FB) is measured as a function of the invariant mass of the electron-positron pair, and found to be consistent with the standard model prediction. We use the A(FB) measurement to extract the effective weak mixing angle sin(2)theta(eff)(W)=0.2326 +/- 0.0018(stat)+/- 0.0006(syst).

Search for the rare decay K(L)->pi(0)pi(0)gamma

The KTeV E799 experiment has conducted a search for the rare decay K(L)->pi(0)pi(0)gamma via the topology K(L)->pi(0)pi(0)(D)gamma (where pi(0)(D)->gamma e(+)e(-)). Because of Bose statistics of the pi(0) pair and the real nature of the photon, the K(L)->pi(0)pi(0)gamma decay is restricted to proceed at lowest order by the CP conserving direct emission (DE) of an E2 electric quadrupole photon. The rate of this decay is interesting theoretically since chiral perturbation theory predicts that this process vanishes at level O(p(4)). Therefore, this mode probes chiral perturbation theory at O(p(6)). In this paper we report a determination of an upper limit of 2.43x10(-7) (90% CL) for K(L)->pi(0)pi(0)gamma. This is approximately a factor of 20 lower than previous results.

Metal location and thickness in a multilayered sheet by measuring K alpha/K beta, L alpha/L beta and L alpha/L gamma X-ray ratios

When a multilayered material is analyzed by means of energy-dispersive X-ray fluorescence analysis, then the X-ray ratios of K alpha/K beta, or L alpha/L beta and L alpha/L gamma, for an element in the multilayered material, depend on the composition and thickness of the layer in which the element is situated, and on the composition and thickness of the superimposed layer (or layers). Multilayered samples are common in archaeometry, for example, in the case of pigment layers in paintings, or in the case of gilded or silvered alloys. The latter situation is examined in detail in the present paper, with a specific reference to pre-Columbian alloys from various museums in the north of Peru. (C) 2009 Elsevier B.V. All rights reserved.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

Structural characterization of 0.5PbMg(1/3)Nb(2/3)O(3)-0.5Ba(x)Pb((1-x))TiO(3) powders

The present work reports the effects caused by barium on phase formation, morphology and sintering of lead magnesium niobate-lead titanate (PMN-50PT). Ab initio study of 0.5PbMg(1/3)Nb(2/3)O(3)-0.5Ba(x)Pb((1-x))TiO(3) ceramic powders, with x = 0, 0.20, and 0.40 was proposed, considering that the partial substitution of lead by barium can reestablish the equilibrium of monoclinic-tetragonal phases in the system. It was verified that even for 40 mol% of barium, it was possible to obtain pyrochlore-free PMN-PT powders. The increase of the lattice parameters of PMN-PT doped-powders confirmed dopant incorporation into the perovskite phase. The presence of barium improved the reactivity of the powders, with an average particle size of 120 nm for 40 mol% of barium against 167 mn for the pure sample. Although high barium content (40 mol%) was deleterious for a dense ceramic, contents up to 20 mol% allowed 95% density when sintered at 1100 degrees C for 4 h. (c) 2007 Elsevier Ltd. All rights reserved.

Novel sol–gel preparation of (P2O5)0.4–(CaO)0.25–(Na2O)X–(TiO2)(0.35−X) bioresorbable glasses (X = 0.05, 0.1, and 0.15)

Quaternary phosphate-based glasses in the P2O5–CaO–Na2O–TiO2 system with a fixed P2O5 and CaO content of 40 and 25 mol% respectively have been successfully synthesised via sol–gel method and bulk, transparent samples were obtained. The structure, elemental proportion, and thermal properties of stabilised sol–gel glasses have been characterised using X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), 31P nuclear magnetic resonance (31P NMR), titanium K-edge X-ray absorption near-edge structure (XANES), fourier transform infrared (FTIR) spectroscopy, and differential thermal analysis (DTA). The XRD results confirmed the amorphous nature for all stabilized sol–gel derived glasses. The EDX result shows the relatively low loss of phosphorus during the sol–gel process and Ti K-edge XANES confirmed titanium in the glass structure is in mainly six-fold coordination environment. The 31P NMR and FTIR results revealed that the glass structure consist of mainly Q1 and Q2 phosphate units and the Ti4+ cation was acting as a cross-linking between phosphate units. In addition DTA results confirmed a decrease in the glass transition and crystallisation temperature with increasing Na2O content. Ion release studies also demonstrated a decrease in degradation rates with increasing TiO2 content therefore supporting the use of these glasses for biomedical applications that require a degree of control over glass degradation. These sol–gel glasses also offer the potential to incorporate proactive molecules for drug delivery application due to the low synthesis temperature employed.

Structural models for yttrium aluminium borate laser glasses: NMR and EPR studies of the system (Y(2)O(3))(0.2)-(Al(2)O(3))(x)-(B(2)O(3))(0.8-x)

The structure of laser glasses in the system (Y(2)O(3))(0.2){(Al(2)O(3))(x))(B(2)O(3))(0.8-x)} (0.15 <= x <= 0.40) has been investigated by means of (11)B, (27)Al, and (89)Y solid state NMR as well as electron spin echo envelope modulation (ESEEM) of Yb-doped samples. The latter technique has been applied for the first time to an aluminoborate glass system. (11)B magic-angle spinning (MAS)-NMR spectra reveal that, while the majority of the boron atoms are three-coordinated over the entire composition region, the fraction of three-coordinated boron atoms increases significantly with increasing x. Charge balance considerations as well as (11)B NMR lineshape analyses suggest that the dominant borate species are predominantly singly charged metaborate (BO(2/2)O(-)), doubly charged pyroborate (BO(1/2)(O(-))(2)), and (at x = 0.40) triply charged orthoborate groups. As x increases along this series, the average anionic charge per trigonal borate group increases from 1.38 to 2.91. (27)Al MAS-NMR spectra show that the alumina species are present in the coordination states four, five and six, and the fraction of four-coordinated Al increases markedly with increasing x. All of the Al coordination states are in intimate contact with both the three-and the four-coordinate boron species and vice versa, as indicated by (11)B/(27)Al rotational echo double resonance (REDOR) data. These results are consistent with the formation of a homogeneous, non-segregated glass structure. (89)Y solid state NMR spectra show a significant chemical shift trend, reflecting that the second coordination sphere becomes increasingly ""aluminate-like'' with increasing x. This conclusion is supported by electron spin echo envelope modulation (ESEEM) data of Yb-doped glasses, which indicate that both borate and aluminate species participate in the medium range structure of the rare-earth ions, consistent with a random spatial distribution of the glass components.