Two-dimensional convexities are join-hull commutative

It is shown that two-dimensional convex structures with certain natural properties are join-hull commutative. The main intermediate step is the computation of the so-called exchange number. We also give two examples of three-dimensional convexities which are not join-hull commutative. The second one has certain additional properties showing that the main theorem is sharp in many other respects. These properties are obtained from a study of convex hyperspaces.     

Explicit constructions of graphs without short cycles and low density codes

We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given.     

Padé-type approximants with orthogonal generating polynomials

The interpolation of the function x → 1/(1 ? xt) generating the series f(t) = ∑^∞_{i = 0}c_itⁱ at the zeros of an orthogonal polynomial with respect to a distribution d α satisfying some conditions will give us a process for accelerating the convergence of f_n(t) = ∑ⁿ_{i = 0}c_itⁱ. Then, we shall see that the polynomial of best approximation of x → 1/(1 ? xt) over some interval or its development in Chebyshev polynomials T_n or U_n are only particular cases of the main theorem.At last, we shall show that all these processes accelerate linear combinations with positive coefficients of totally monotonic and oscillating sequences.     

Examples of cell-like decompositions of the infinite-dimensional manifolds σ and Σ

Denote by σ the subspace of Hilbert space {(x_i)?l₂:x_i=0 for all but finitely many i}. Examples of cell-like decompositions of σ are constructed that have decomposition spaces that are not homeomorphic to σ. At one extreme is a cell-like decomposition G of σ produced using ghastly finite dimensional examples such that the decomposition space σ?G contains no embedded 2-cell but (σ?G)×$\text{R}$ is homeomorphic to σ. At the other extreme is a cell-like decomposition G of σ satisfying: (a) the nondegeneracy set N_G={g?G:g≠point} consists of countably many arcs (necessarily tame); (b) the nondegeneracy set N_G is a closed subset of the decomposition space σ?G; (c) each map f:B²→σ?G of a 2-cell into σ?G can be approximated arbitrarily closely by an embedding; (d) σ?G is not homeomorphic to σ but (σ?G)×$\text{R}$ is homeomorphic to σ. The fact that both conditions (a) and (b) can be satisfied (and have (d) hold) is directly attributable to σ’s incompleteness as a topological space.     

Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

This paper is concerned with large-$\text{O}$ error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.     

Interaction between two folded solitary waves for a modified Broer--Kaup system

By means of a Painlevé-Baicklund transformation and a multi-linear separation-of-variable approach, abundant localized coherent excitations of a modified Broer-Kaup system are derived. There appear possible phase shifts for the interactions of the （2＋1）-dimensional novel localized structures, which are discussed in this paper.     

Are the New Physics Contributions from the Left-Right Symmetric Model Important for the Indirect CP Violation in the Neutral B Mesons?

No Heading Several works analyzing the new physics contributions from the Left-Right Symmetric Model to the CP violation phenomena in the neutral B mesons can be found in the literature. These works exhibit interesting and experimentally sensible deviations from the Standard Model predictions but at the expense of considering a low right scale υ_R around 1 TeV. However, when we stick to the more conservative estimates for υ_R, which say that it must be at least 10⁷ GeV, no experimentally sensible deviations from the Standard Model appear for indirect CP violation. This estimate for υ_R arises when the generation of neutrino masses is considered. In spite of the fact that this scenario is much less interesting and says nothing new about both the CP violation phenomenon and the structure of the Left-Right Symmetric Model, this possibility must be taken into account for the sake of completeness and when considering the see-saw mechanism that provides masses to the neutrino sector. ¹ Associate researcher of the Centro Internacional de Física, Ciudad Universitaria, Bogotá D.C., Colombia.     

Using a Hybrid Evolutionary Algorithm to Minimize Variance in Response Time for Multimedia Object Requests

This research addresses the scheduling problem of multimedia object requests, which is an important problem in information systems, in particular, for World Wide Web applications. The performance measure considered is the variance of response time which is crucial as end users expect fair treatment to their service requests. This problem is known to be NP-hard. The literature survey indicates that two heuristics have been proposed to solve the problem. In this paper, we present a new heuristic, a hybrid evolutionary heuristic, which is shown to perform much better than the two existing ones, e.g., the overall average errors of the existing ones are 1.012 and 2.042 while the error of the proposed hybrid evolutionary heuristic is 0.154.     

Localization Operators and Exponential Weights for Modulation Spaces

We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows φ₁, φ₂, we investigate the multilinear mapping from to the localization operator Results are formulated in terms of modulation spaces with weights which may have exponential growth. We give sufficient and necessary conditions for a to be bounded or to belong to a Schatten class. As an application, we study symbols defined by ultra-distributions with compact support, that give trace class localization operators.