Enhancement of Europium Luminescence in Tetracycline–Europium Complexes in the Presence of Urea Hydrogen Peroxide

An increase in the europium emission band was observed, for the first time, with addition of urea hydrogen peroxide to the tetracycline–europium (Tc–Eu)solution. We have observed that the wavelength, the band width and the area of ⁵D₀→⁷F₂ europium transition change with the urea hydrogen peroxide concentration. We claim that the tetracycline–europium complexes can be used as probes of urea hydrogen peroxide concentration.     

The solutions of a variational inequality as critical points of a real valued smooth function

Let H be a real Hilbert space, A : H → H a self-adjoint continuous linear operator. Given a variational inequality related to A, we construct a Lipschitz continuously differentiable function F:H→$\text{R}$ so that the critical points of F are the solutions of the variational inequality.     

Quarkonia with a variational method

A variational method, based in independent minimization of energy levels, is applied to quantum mechanical quarkonium systems. A discussion is presented of the method, with emphasis on quark mass dependence of energy levels (Feynman-Hellman theorem), on the behaviour of wave functions at the origin (Martin's theorem) and on the ordering of energy levels. The potential used in the applications is the Coulomb (4-vector) + Linear (4-scalar) potentials, the fine and hyperfine splittings being included by means of the Fermi-Breit hamiltonian. An attempt is made for an overall treatment of the known splittings (radials-wave, hyperfine and fine splittings) for all quarkonium systems, using an approximately flavour independent potential. Thep-wave splittings, as well as the hyperfine splittings, are shown to be particularly sensitive to the nature and mass dependence of the potential. In particular, asymptotic freedom can be more easily tested there. On the other hand, radial excitations provide the place where the set up of short range potential effects should be first detected. Some results concerning the ordinary mesons are presented, and it is specifically pointed out that strong restrictions exist for the masses of the ρ′ and theA ₁. Predictions for the toponium family are also presented.     

On the approach to the final aperiodic regime in maps of the interval

We present a global approach to the final aperiodic regime in maps of the interval displaying a simple pattern with similarities to the Feigenbaum scheme.     

Periodic orbits in magnetic billiards

We propose a simple method to calculate periodic orbits in two-dimensional systems with no symbolic dynamics. The method is based on a line by line scan of the Poincaré surface of section and is particularly useful for billiards. We have applied it to the Square and Sinai's billiards subjected to a uniform orthogonal magnetic field and we obtained about 2000 orbits for both systems using absolutely no information about their symbolic dynamics. Received 21 September 1999 and Received in final form 13 April 2000     

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED. PACS  11.10.Gh; 11.15.Bt; 11.15.-q     

Synthesis and Diels-Alder reactions of 4-vinylimidazoles

[structure in text] The synthesis of several 4-vinylimidazoles via Stille cross-coupling reactions of the corresponding protected 4-iodoimidazoles with tributylvinylstannane is described. These heterocyclic dienes are shown to be effective partners in the Diels-Alder reaction, providing adducts in good yield and exhibiting useful levels of isomer selectivity and stereoselectivity (endo/exo).     

MPOC: an agglomerative algorithm for multicriteria partially ordered clustering

In the field of multicriteria decision aid, considerable attention has been paid to supervised classification problems where the purpose is to assign alternatives into predefined ordered classes. In these approaches, often referred to as sorting methods, it is usually assumed that classes are either known a priori or can be identified by the decision maker. On the other hand, when the objective is to identify groups (clusters) of alternatives sharing similar characteristics, the problem is known as a clustering problem, also called an unsupervised learning problem. This paper proposes an agglomerative clustering method based on a crisp outranking relation. The method regroups alternatives into partially ordered classes, based on a quality of partition measure which reflects the percentage of pairs of alternatives that are compatible with a decision-maker’s multicriteria preference model.     

Counting spectral radii of matrices with positive entries

The sum–product conjecture of Erd?s and Szemerédi states that, given a finite set A$A$ of positive numbers, one can find asymptotic lower bounds for max{|A+A|,|A⋅A|}$max\{|A+A|,|A\cdot A|\}$ of the order of |A|^1+δ${\left|A\right|}^{1+\delta }$ for every δ<1$\delta <1$. In this paper we consider the set of all spectral radii of n×n$n\times n$ matrices with entries in A$A$, and find lower bounds for the cardinality of this set. In the case n=2$n=2$, this cardinality is necessarily larger than max{|A+A|,|A⋅A|}$max\{|A+A|,|A\cdot A|\}$.     

Simple dynamic location problem with uncertainty: a primal-dual heuristic approach

Abstract

In this paper, the simple dynamic facility location problem is extended to uncertain realizations of the potential locations for facilities and the existence of customers as well as fixed and variable costs. With limited knowledge about the future, a finite and discrete set of scenarios is considered. The decisions to be made are where and when to locate the facilities, and how to assign the existing customers over the whole planning horizon and under each scenario, in order to minimize the expected total costs. Whilst assignment decisions can be scenario dependent, location decisions have to take into account all possible scenarios and cannot be changed according to each scenario in particular. We first propose a mixed linear programming formulation for this problem and then we present a primal-dual heuristic approach to solve it. The heuristic was tested over a set of randomly generated test problems. The computational results are provided.