The non-existence of some NMDS codes and the extremal sizes of complete (n,3)-arcs in PG(2,16)

The non-existence of $[29+h,3+h,26]_{16}$ and $[29+h,4+h,25]_{16}$ -codes, $h\ge 0$ , is proven. These results are obtained using geometrical methods, exploiting the equivalence between NMDS codes of dimension $3$ and $(n,3)$ -arcs in $PG(2,q)$ . Along the way the packing problem for complete $(n,3)$ -arcs in $PG(2,16)$ is solved, proving that $m_{3}(2,16)=28$ and $t_{3}(2,16)=15$ and that the complete $(28,3)$ -arc and the complete $(15,3)$ -arc are unique up to collineations.     

Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming

In this paper, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming (MINLP). The proposed hybrid algorithm is an improved version of the classical nonlinear branch-and-bound (BB) procedure, where the enhancements are obtained with the application of the outer approximation algorithm on some nodes of the enumeration tree. The two methods are combined in such a way that each one collaborates to the convergence of the other. Computational experiments with benchmark instances of the MINLP problem show the good performance of the proposed algorithm, which is compared to the outer approximation algorithm, the nonlinear BB algorithm and the hybrid algorithm implemented in the solver Bonmin.     

Testing optimality for quadratic 0-1 problems

Received June 4, 1996 / Revised version received November 19, 1997 Published online November 24, 1998     

On complete graphs with negative r-mean curvature

We generalize Efimov's Theorem for graphs in Euclidean space using the scalar curvature, with an additional hypothesis on the second fundamental form.     

Generalized Hopf Bifurcation for Planar Vector Fields via the Inverse Integrating Factor

In this paper we study the maximum number of limit cycles that can bifurcate from a focus singular point p ₀ of an analytic, autonomous differential system in the real plane under an analytic perturbation. We consider p ₀ being a focus singular point of the following three types: non-degenerate, degenerate without characteristic directions and nilpotent. In a neighborhood of p ₀ the differential system can always be brought, by means of a change to (generalized) polar coordinates (r, θ), to an equation over a cylinder in which the singular point p ₀ corresponds to a limit cycle γ ₀. This equation over the cylinder always has an inverse integrating factor which is smooth and non-flat in r in a neighborhood of γ ₀. We define the notion of vanishing multiplicity of the inverse integrating factor over γ ₀. This vanishing multiplicity determines the maximum number of limit cycles that bifurcate from the singular point p ₀ in the non-degenerate case and a lower bound for the cyclicity otherwise. Moreover, we prove the existence of an inverse integrating factor in a neighborhood of many types of singular points, namely for the three types of focus considered in the previous paragraph and for any isolated singular point with at least one non-zero eigenvalue.     

Pattern’s reliability importance under dependence condition and different information levels

Using martingale methods in reliability theory we developed the Barlow and Proschan reliability importance of a pattern to the system reliability under dependence conditions. We allowed several levels of information to calculate the importance measure.     

Numerical Properties of Shifted Tridiagonal LU Factorizations

In this paper, we consider shifted tridiagonal matrices. We prove that the standard algorithm to compute the LU factorization in this situation is mixed forward-backward stable and, therefore, componentwise forward stable. Moreover, we give a formula to compute the corresponding condition number in O(n) flops. This research has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain through grants BFM2003-06335-C03-02 and MTM2006-06671 as well as by the Postdoctoral Fellowship EX2004-0658 provided by Ministerio de Educación y Ciencia of Spain.     

On the Michelson-Morley experiment

A rigorous wave-theoretic approach to the Michelson-Morley (M-M) experiment is presented, with special emphasis on the Huygens' principle derivation of the laws of reflection by a moving mirror. A detailed discussion of the Lorentz-Fitzgerald contraction hypothesis (CH) is included. Several mistakes appearing in the standard textbook treatments of these issues are pointed out, and a number of related historical questions are considered.     

Practical synthesis of aromatic ethers by SNAr of fluorobenzenes with alkoxides

Aromatic fluorines have been substituted by alkoxides in a variety of activated and unactivated aromatic systems.