High-Pressure Metal-Free Catalyzed One-Pot Two-Component Synthetic Approach for New 5-Arylazopyrazolo[3,4-b]Pyridine Derivatives

An appropriate and efficient Q-tube-assisted ammonium acetate-mediated protocol for the assembly of the hitherto unreported 5-arylazopyrazolo[3,4-b]pyridines was demonstrated. This methodology comprises the cyclocondensation reaction of 5-amino-2-phenyl-4H-pyrazol-3-one with an assortment of arylhydrazonals in an NH₄OAc/AcOH buffer solution operating a Q-tube reactor. This versatile protocol exhibited several outstanding merits: easy work-up, mild conditions, scalability, broad substrate scope, safety (the Q-tube kit is simply for pressing and sealing), and a high atom economy. Consequently, performing such reactions under elevated pressures and utilizing the Q-tube reactor seemed preferable for achieving the required products in comparison to the conventional conditions. Diverse spectroscopic methods and X-ray single-crystal techniques were applied to confirm the proposed structure of the targeted compounds.     

The node-edge weighted 2-edge connected subgraph problem: Linear relaxation, facets and separation

Let G=(V,E) be a undirected k-edge connected graph with weights c_e on edges and w_v on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable.     

About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half‐space, of which the cross‐section is a local perturbation of a homogeneous half‐plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S‐waves. Thanks to the boundary of the deformed half‐plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright © 2002 John Wiley & Sons, Ltd.     

Molybdenum(V) chloride-catalyzed amidation of secondary benzyl alcohols with sulfonamides and carbamates

A general and selective method for the direct amidation of secondary benzyl alcohols with both sulfonamides and carbamates is described. This method has been applied to a variety of substrates and the reaction proceeded smoothly at room temperature in the presence of 5 mol % molybdenum(V) chloride to give the desired products in good yields.     

Hermitean Matrix Ensembles and Orthogonal Polynomials

In this article, we investigate orthogonal polynomials associated with complex Hermitean matrix ensembles using the combination of the methods of Coulomb fluid (or potential theory), chain sequences, and Birkhoff–Trjitzinsky theory. We give a general formula for the largest eigenvalue of the N×N Jacobi matrices (which is equivalent to estimating the largest zero of a sequence of orthogonal polynomials) and the two-level correlation function for the α ensembles (α>0) introduced previously for α>1. In the case of 0<α<1, we give a natural representation for the weight function that is a special case of the general Nevanlinna parametrization. We also discuss Hermitean matrix ensembles associated with general indeterminate moment problems.     

Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations

In this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.     

Ramanujan continued fractions via orthogonal polynomials

Some Ramanujan continued fractions are evaluated using asymptotics of polynomials orthogonal with respect to measures with absolutely continuous components.     

Condensations aryniques d'enolates de cetones—VI: Synthese de phenyl-2 cyclohexanones tricyclo[6,n,0,02,7]trienes-2,4,6 ols-1 diversement substitues

The condensation of benzyne in aprotic medium with the enolates of the 2,2,6-trimethyl, 3,3,5,5-tetramethyl, 4-4-dimethyl, 4-methyl, 4-t-butyl cyclohexanones as well as with those of α-tetralone and α-benzosuberone leads to the corresponding α-phenyl ketones and several tri and tetracyclic benzocyclobutenols.     

The Milne problem for partially plane-polarized light

An accurate numerical method has been devised to solve half-range problems for the scattering of azimuth-independent polarized radiation in stellar atmospheres. The use of the method is illustrated by solving the Milne problem for the radiation intensity at any optical depth, for the extrapolation distance, and for the law of darkening.