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.

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).

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.

84.5MeV~(12)C~(4+)离子诱发金属靶原子发射的Kβ与Kα-X射线强度比值的研究

本实验是在中国科学院兰州近代物理研究所,国家实验室的重离子加速器上完成的.实验用OR-TEC公司生产的HPGe X射线探测器测量了84.5 MeV的12C4+离子轰击Cu,Mo,Ag,Cd,In,Sn,W和Au金属靶产生的K壳层特征X射线谱,计算了Kβ与Kα-X射线强度的比值,并将结果与Scofield用Hartree-Fock-Slater模型计算出的理论值与用其它方法(如:衰变幅射,用光子,电子,质子等粒子与靶相互作用)得到的实验值进行了比较.比较结果表明用84.5 MeV的12C4+离子轰击Cu,Mo,Ag,Cd,In,Sn,W和Au金属靶产生的Kβ与K-αX射线强度比值比理论值和其它实验值要大许多.

Analytic Renormings of C(K) Spaces

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.

Antiferromagnetism in Fe1+y Te and Superconductivity in K (x) Fe2Se2

Iron-based layered chalcogenides are interesting because of their structural magnetic and superconducting properties. Single crystals of the parent binary chalcogenides, Fe1+y Te, and intercalated ternary chalcogenides, K0.8Fe2Se2, are grown and investigated in detail. Single crystals are grown by modified horizontal Bridgman method. Fe1+y Te demonstrates an antiferromagnetic (AFM) transition at T (N) =67 K which is identified as a magnetostructural transition. By varying the concentration of excess Fe, we have tuned T (N) over a range of temperature from 67 to 57 K. The superconducting properties of K0.8Fe2Se2 crystals are explored by magnetization measurements. A superconducting transition is observed at T (C) =31 K. The lower critical field of K0.8Fe2Se2 is estimated from field variation of magnetization measurements.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

In-depth analysis of the J.A.C.K. model

The Texas Transportation Commission (“the Commission”) is responsible for planning and making policies for the location, construction, and maintenance of a comprehensive system of highways and public roads in Texas. In order for the Commission to carry out its legislative mandate, the Texas Constitution requires that most revenue generated by motor vehicle registration fees and motor fuel taxes be used for constructing and maintaining public roadways and other designated purposes. The Texas Department of Transportation (TxDOT) assists the Commission in executing state transportation policy. It is the responsibility of the legislature to appropriate money for TxDOT’s operation and maintenance expenses. All money authorized to be appropriated for TxDOT’s operations must come from the State Highway Fund (also known as Fund 6, Fund 006, or Fund 0006). The Commission can then use the balance in the fund to fulfill its responsibilities. However, the value of the revenue received in Fund 6 is not keeping pace with growing demand for transportation infrastructure in Texas. Additionally, diversion of revenue to nontransportation uses now exceeds $600 million per year. As shown in Figure 1.1, revenues and expenditures of the State Highway Fund per vehicle mile traveled (VMT) in Texas have remained almost flat since 1993. In the meantime, construction cost inflation has gone up more than 100%, effectively halving the value of expenditure.

Evaluation of TxDOT’s J.A.C.K. model for revenue and expenditure projections

This research report documents work conducted by the Center for Transportation (CTR) at The University of Texas at Austin in analyzing the Joint Analysis using the Combined Knowledge (J.A.C.K.) program. This program was developed by the Texas Department of Transportation (TxDOT) to make projections of revenues and expenditures. This research effort was to span from September 2008 to August 2009, but the bulk of the work was completed and presented by December 2008. J.A.C.K. was subsequently renamed TRENDS, but for consistency with the scope of work, the original name is used throughout this report.

Factors contributing to wear tolerance of Bermudagrass (Cynodon dactylon (L.) Pers., C. dactylon x C. transvaalensis Burtt-Davey) on a sand-based profile under simulated sports field conditions

Wear resistance and recovery of 8 Bermudagrass (Cynodon dactylon (L.) Pers.) and hybrid Bermudagrass (C. Dactylon x C. transvaalensis Burtt-Davey) cultivars grown on a sandbased soil profile near Brisbane, Australia, were assessed in 4 wear trials conducted over a two year period. Wear was applied on a 7-day or a 14-day schedule by a modified Brinkman Traffic Simulator for 6-14 weeks at a time, either during winter-early spring or during summer-early autumn. The more frequent wear under the 7-day treatment was more damaging to the turf than the 14-day wear treatment, particularly during winter when its capacity for recovery from wear was severely restricted. There were substantial differences in wear tolerance among the 8 cultivars investigated, and the wear tolerance rankings of some cultivars changed between years. Wear tolerance was associated with high shoot density, a dense stolon mat strongly rooted to the ground surface, high cell wall strength as indicated by high total cell wall content, and high levels of lignin and neutral detergent fiber. Wear tolerance was also affected by turf age, planting sod quality, and wet weather. Resistance to wear and recovery from wear are both important components of wear tolerance, but the relative importance of their contributions to overall wear tolerance varies seasonally with turf growth rate.

The X-C---Y (X = O/F, Y = O, S, F, Cl, Br, N, P,) Carbon bond and hydrophobic interactions

While the tetrahedral face of methane has an electron rich centre and can act as a hydrogen bond acceptor, substitution of one of its hydrogens with some electron withdrawing group (such as -F/OH) can make the opposite face electron deficient. Electrostatic potential calculations confirm this and high level quantum calculations show interactions between the positive face of methanol/methyl fluoride and electron rich centers of other molecules such as H2O. Analysis of the wave functions of atoms in molecules shows the presence of an unusual C···Y interaction, which could be called 'carbon bonding'. NBO analysis and vibrational frequency shifts confirm the presence of this interaction. Given the properties of alkyl groups bonded to electronegative elements in biological molecules, such interactions could play a significant role, which is yet to be recognized. This and similar interactions could give an enthalpic contribution to what is called the 'hydrophobic interactions'.

X-Ha center dot center dot center dot C hydrogen bonds in n-alkane-HX (X = F, OH) complexes are stronger than C-Ha <-X hydrogen bonds

Computational study of X-Ha <-C and C-Ha <-X hydrogen bonds in n-alkane-HX complexes (X =F,OH, alkane =propane, butane, pentane) has been carried out in this work. Ab initio and density functional theories were used for this study. For n-alkane-H2O complexes both Oa <-H-C and O-Ha <-C hydrogen bonded complex have been found, while for n-alkane-HF complexes, our attempt to optimize Fa <-H-C H-bond was not successful. Like most of the hydrogen bonded systems, strong correlation between binding energy and stretching frequency of H-F and O-H stretching mode was observed. The values of electron density and Laplacian of electron density are within the accepted range for hydrogen bonds. In all these cases, X-Ha <-C hydrogen bonds are found to be stronger than C-Ha <-X hydrogen bonds.

Isotope shift measurements using k x-rays in Sn, Sm, and W

Electronic Kαl x-ray isotope shifts have been measured for Sn 116-124, Sm 148-154, W 182-184, W 184-186, and W 182-186 using a curved crystal Cauchois spectrometer. The analysis of the measurements has included the electrostatic volume effect, screening by the transition electron as well as the non-transition electrons, normal and specific mass shifts, dynamical nuclear qudrupole polarization, and a radiative correction effect of the electron magnetic moment in the nuclear charge radii are obtained. Where other experimental data are available, the agreement with the present measurements is satisfactory. Comparisons with several nuclear model predictions yield only partial agreement.