Extremal properties of strong quadrature weights and maximal mass results for truncated strong moment problems

A bisequence of complex numbers {μ_n}_−∞^∞ determines a strong moment functional satisfying L[xⁿ] = μ_n. If is positive-definite on a bounded interval (a,b) R{0}, then has an integral representation , n=0, ±1, ±2,…, and quadrature rules {w_ni,x_ni} exist such that μ_k = ∑_i=i^n_ns_ni^kw_ni. This paper is concerned with establishing certain extremal properties of the weights w_ni and using these properties to obtain maximal mass results satisfied by distributions ψ(x) representing when only a finite bisequence of moments {μ_k}_k=−nⁿ⁻¹ is given.     

Asymptotics of orthogonal L-polynomials for log-normal distributions

Asymptotic properties of orthogonal Laurent (L-) polynomialsV _n (z), associated with log-normal distributions, are derived by constructive methods. It is shown that the sequences {V _2n (z)} and {V _2n+1 (z)} converge separately (asn→∞) to functionsV ⁽⁰⁾ (z) andV ⁽¹⁾ (z), respectively, both holomorphic in 0<|z|<∞. Explicit Laurent series expansions are obtained, from which it follows that each limit function has essential, isolated singularities atz=0 andz=∞.     

A point mass in a Einstein Universe

An exact solution of Einstein's equations is presented for a perfect fluid representing a point mass in a Einstein Universe.     

Non-energy-weighted sum rule analysis of one nucleon transfer data on 41Ca, 43Ca, 45Se, 49Ti and 51V and the validity of the shell model

Spin-dependent sum rules for spectroscopic factors have been fitted to experimental data for the transfer of f_{$\text{7}\text{2}$} nucleons. The fits give the error in absolute normalizations in terms of the percentage error, σ, in relative spectroscopic factors, and evidence is presented that standard distorted wave Born approximation analyses of light-ion induced reactions give σ < 10%. The sum rule analyses then imply f_{$\text{7}\text{2}$} occupancies m agreement with simple shell-model expectations to an accuracy of about 10%. The f_{$\text{7}\text{2}$} occupancy deduced for ⁵¹V is completely inconsistent with the results of a Hartree-Fock-Bogolyubov calculation.     

Positive energy bound states in resonating group calculations

Spurious resonances occuring in numerical resonating group calculations off the oscillator limit are explained as being due to positive energy bound states. A generalization of Swan's version of the Levinson theorem is given which takes into account these states.     

Transitions dans une serie de clathrates de thiourée et d'urée avec encages cycliques

Crystallographic and thermal studies have been made on the adducts of thiourea with cyclohexane, cycloheptane, cyclooctane, and tetrahydropyran over the temperature range ?170 to 25°C. All the samples exhibit several transitions, which have been classified. Results from previous work are recalled in order to discuss the possible nature of the transitions.     

Optical Properties of Lanthanide Doped Hybrid Organic-Inorganic Materials

Sol-gel matrices have been investigated for some years as potential matrices for rare earth luminescence. Sm³⁺, Eu³⁺, Dy³⁺, Er³⁺ and Tm³⁺ optical properties in siloxane-zirconium hybrid matrices prepared at room temperature have been investigated. Even if luminescence efficiency is governed by non-radiative relaxation linked to hydroxyl groups, in these matrices, rare earth fluorescence is always observed but lifetimes and quantum yields are dependent on the elaboration procedure. Eu³⁺ is used as a probe of the local surrounding around the dopant and the emission and decay profiles measurements in rare earth doped and undoped matrices are presented.     

Categorical axiomatics of dynamic programming

In systems theory, we need some general framework to take into account various concepts from different fields (automata theory, dynamical systems, optimization theory, etc.). This work is a proposal for such a framework. A decision process model is given with the help of category theory. Sufficient conditions for the validity of the equation of optimality of Bellman are established in this model. This model also generalizes the concept of finite automaton. Thus we unify the concepts of automaton and decision system. Especially, we propose the new concept of “opt-automaton” (automaton which optimizes).