The first total synthesis of (−)-bitungolide E

The first total synthesis of (−)-bitungolide E is described. The key steps include a Myers’ alkylation, modified Evans’ syn aldol-reaction, using Crimmins protocol, Sharpless asymmetric epoxidation and ring-closing metathesis reaction.     

Diameter of P.A. random graphs with edge‐step functions

In this work we prove general bounds for the diameter of random graphs generated by a preferential attachment model whose parameter is a function f:N→[0,1] that drives the asymptotic proportion between the numbers of vertices and edges. These results are sharp when f is a regularly varying function at infinity with strictly negative index of regular variation ?γ. For this particular class, we prove a characterization for the diameter that depends only on ?γ. More specifically, we prove that the diameter of such graphs is of order 1/γ with high probability, although its vertex set order goes to infinity polynomially. Sharp results for the diameter for a wide class of slowly varying functions are also obtained.     

On the feasibility of full pattern-operated all-optical XOR gate with single semiconductor optical amplifier-based ultrafast nonlinear interferometer

The possibility of implementing an ultrafast all-optical XOR gate using a single semiconductor optical amplifier (SOA)-based ultrafast nonlinear interferometer (UNI) is theoretically investigated and demonstrated. For this purpose a comprehensive model that characterizes the performance of a SOA when it is successively driven by two strong pseudorandom binary sequences is applied to simulate the specific module under dual rail switching mode of operation. In this manner an extensive set of curves is obtained allowing to analyze and evaluate the impact of the input data, SOA and interferometer critical parameters on the fully loaded Q-factor. Their thorough study and interpretation reveals that the satisfaction of their requirements in order to render acceptable this metric is feasible from a technological perspective and thus if their selection is made according to the extracted guidelines then pattern-free and error-free modulo-2 arithmetic can be straightforwardly realized at 20 Gb/s. This prediction can be of practical interest in simplifying and assisting the design of more sophisticated interconnections of enhanced combinatorial and sequential functionality in which the XOR gate is the core logical unit.     

Combined regression models

The goal of this paper is two-fold. First, new regression models obtained by combinations of the least squares (LS), minimax (MM), and the least sum of absolute deviations (LSAD) are proposed. Second, measures for assessing the influence of observations on the fitted models are suggested. The paper is interdisciplinary because the theory behind the proposed method draws from results in the operations research area. The methods are illustrated by their application to some examples and graphical illustrations are given.     

Analytical approximation for laminar film condensation of saturated stream on an isothermal vertical plate

In this paper, the laminar film condensation of saturated stream on an isothermal vertical plate is studied. The boundary layer equations of momentum and thermal energy are reduced to two ordinary differential equations by means of a set of similarity transformations. The problem is then solved analytically using the homotopy analysis method (HAM). The dual solutions are obtained for a range of values of the parameter η_δ. However, it should be noted that the second branch solution of the considered problem has only mathematical meanings. The present work shows the validity and the great potentiality of the proposed technique for the nonlinear problems with multiple solutions.     

Uncountable products of determined groups need not be determined

If H is a dense subgroup of G, we say that H determines G if their groups of characters are topologically isomorphic when equipped with the compact open topology. If every dense subgroup of G determines G, then we say that G is determined. The importance of this property is justified by the recent generalizations of Pontryagin-van Kampen duality to wider classes of topological Abelian groups. Among other results, we show (a) _⊕i∈IR determines the product _∏i∈IR if and only if I is countable, (b) a compact group is determined if and only if its weight is countable. These answer questions of Comfort, Raczkowski and the third listed author. Generalizations of the above results are also given.     

Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the kth eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.     

On the structural stability of thermoelastic model of porous media

In the present paper we study the structural stability of the mathematical model of the linear thermoelastic materials with voids. We prove that the solutions of problems depend continuously on the constitutive quantities, which may be subjected to error or perturbations in the mathematical modelling process. Thus, we assume to have changes in the various coupling coefficients of the model and then we establish estimates of continuous dependence of solutions. We have to outline that such estimates play a central role in obtaining approximations to these kinds of problems. To derive a priori estimates for a solution we first establish appropriate bounds for the solutions of certain auxiliary problems. These are achieved by means of so‐called Rellich‐like identities. We also investigate how the solution in the coupled model behaves as some coupling coefficients tend to zero. Copyright © 2007 John Wiley & Sons, Ltd.     

Some generalized hypergeometric d-orthogonal polynomial sets

In this paper, we characterize the d-orthogonal polynomial sets given by their explicit expressions in a specific basis. As application, we consider the generalized hypergeometric case to characterize d-orthogonal polynomial sets of Laguerre type, Meixner type, Meixner-Pollaczek type, Krawtchouk type, continuous dual Hahn type, and dual Hahn type. For d=1, we obtain a unification of some characterization theorems in the orthogonal polynomials theory.