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.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

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)).

{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

Fabrication, thermal stability and mechanical properties of novel (W0.5Al0.5)C-0.8-Co composite prepared by mechanical alloying and hot-pressing sintering

A novel cemented carbides (W0.5Al0.5)C-0.8-Co with different cobalt contents were prepared by mechanical alloying and hot-pressing technique. Hot-pressing technique as a common technique was performed to fabricate the bulk bodies of the hard alloys. The novel cemented carbides have superior mechanical properties compared to WC-Co. The density, operating cost of the novel material were much lower than WC-Co. There is almost no eta-phase in the (W0.5Al0.5)C-0.8-Co cemented carbides system although the carbon deficient get the value of 20%, and successfully got the nanostructured rounded (W0.5Al0.5)C-0.8 particles.

High-pressure sintering study of a novel hard material (W0.5Al0.5)C-0.5 without binder metal

A novel hard material of (W0.5Al0.5)C-0.5 has been successfully sintered under high-pressure (4.5 GPa). The influence of sintering time and temperature on the microstructure, Vickers microhardness and density of the as-prepared specimens are well described. Interestingly, sintering temperature has an amazing influence on the hardness, density and microstructure of the specimen while the sintering time does not. It is found that the most suitable sintering condition from our work is 1600 degrees C and 10 min under pressure of 4.5 GPa. The hardness and relative density of the as-prepared sample can reach 2340 kg mm(-2) and 98.62%, respectively. The cell parameters of the sintered specimen is found to be little smaller than that of the powder, which we propose is related to the high pressure.

Crystallization and characterization of substoichiometric compound (W0.5Al0.5)C-0..5 obtained by solid-state reaction

(W0.5Al0.5)C-0.5 substoichiometric compound is synthesized by a combination of mechanical milling and high-pressure reactive sintering. X-ray diffraction is used to monitor the phase changes and crystallization of (W0.5Al0.5) C-0.5 during the whole reaction process. As a result, (W0.5Al0.5) C-0.5 is identified as the hexagonal WC-type belonging to the P-6m2 space group (No. 187), and the lattice parameters of (W0.5Al0.5)C-0.5 are calculated to be a = 2.907 (1) angstrom, c = 2.838 (1) angstrom, which are very similar to those of WC even if there are approximately 50 pct carbon vacancies in the cell of (W0.5Al0.5)C-0.5 as compared with WC. The substoichiometric (W0.5Al0.5)C-0.5 compound has a Vickers microhardness of 2385 +/- 70 kg mm(-2), which is as high as that of WC, while its density is far lower than that of WC.

Aplicación de los Diagramas de Gantt a la programación del B.U.P. y C.0.U.

Las fases necesarias para elaborar un diagrama de Gant son: determinación de las actividades principales; estimación de la duración efectiva de las mismas; enunciación en el diagrama de las actividades principales y de su relación entre si; representación gráfica de su duración; su utilización sus limitaciones, las actividades que se presentan tienen que ser limitadas perfectamente sin excederse en detalles. Tienen a su favor que son fácilmente realizables por personas no especializadas y que su representación sinóptica e intuitiva es muy útil. En definitiva, podemos decir que es un método útil para las programaciones de los docentes y puede contribuir a la mejora de la enseñanza, ya que proporciona un método sencillo de resumir las progresiones efectuadas y anotar la marcha de las actividades es de fácil seguimiento y una clara visión de conjunto lo que contribuirá a una clara coordinación.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

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.