Lanthanide assisted cross-coupling of aryl bromides with triethylaluminum

Cerium trichloride, as well as some other lanthanide salts, promote the palladium-catalyzed cross-coupling of triethylaluminum with bromoarenes. The lanthanide compounds also increase the selectivity by diminishing the undesired hydrodebromination process.     

Esters derived from 7-decanoyloxychromone-3-carboxylic acid: synthesis and mesomorphic properties

The synthesis and liquid crystalline properties of a new series of calamitic liquid crystals containing 4-H-benzopyran-4-one (chromone) within the central core is reported. The first homologue in the series display SmA phase (8a), the homologues (8b-e) exhibit SmA and SmC mesophases and the homologues (8f-h) exhibit only a SmC mesophase.     

Symmetric esters derived from 1,3,4-oxadiazole: synthesis, mesomorphic properties and structural study by semi-empirical calculations

Three homologous series of symmetric esters derived from 2-alkylthio-5-( p -hydroxy)phenyl-1,3,4-oxadiazole (series 3 , 4 and 5 ) were synthesized and their liquid crystalline properties investigated by optical microscopy and differential scanning calorimetry. Depending on the chain length, nematic and smectic C phases were observed in the series 3 ; smectic A and smectic C phases in series 4 . None of the homologues of series 5 shows mesomorphic properties. These three series are compared with other previously reported oxadiazoles. A structural study of AM1 semi-empirical calculations is also described.     

Synthesis and molecular structure of the 1-phenyl-2-(2-pyridyl)ethanol intermediate obtained from the condensation reaction of 2-picoline and benzaldehyde

Research on Chemical Intermediates - The 1-phenyl-2-(α-pyridyl)ethanol [or 1-phenyl-2-(2-pyridyl)ethanol] compound was obtained from the Knoevenagel condensation reaction between...     

Analysis of the comparison of in situ measurements made on biological shielding of the BR3 nuclear reactor

Journal of Radioanalytical and Nuclear Chemistry - INSIDER (Improved Nuclear SIte characterization for waste minimization in D&D operations under constrained EnviRonment) was a European...     

A new type of orthogonality for normed planes

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d ⩾ 3.     

Eigenvalues of the Dirac Operator on Fibrations over S1

We consider the Dirac operator on fibrations overS ¹ which have up to holonomy a warped product metric. Wegive lower bounds for the eigenvalues on M and if the Diracoperator on the typical fibre F has a kernel, we calculatethe corresponding part of the spectrum on M explicitly.Moreover, we discuss the dependence of the spectrum of theholonomy and obtain bounds for the multiplicity of the eigenvalues.     

On the Continuity of the Optimal Value in Parametric Linear Optimization: Stable Discretization of the Lagrangian Dual of Nonlinear Problems

This paper is focused on the stability of the optimal value, and its immediate repercussion on the stability of the optimal set, for a general parametric family of linear optimization problems in ⁿ. In our approach, the parameter ranges over an arbitrary metric space, and each parameter determines directly a set of coefficient vectors describing the linear system of constraints. Thus, systems associated with different parameters are not required to have the same number (cardinality) of inequalities. In this way, discretization techniques for solving a nominal linear semi-infinite optimization problem may be modeled in terms of suitable parametrized problems. The stability results given in the paper are applied to the stability analysis of the Lagrangian dual associated with a parametric family of nonlinear programming problems. This dual problem is translated into a linear (semi-infinite) programming problem and, then, we prove that the lower semicontinuity of the corresponding feasible set mapping, the continuity of the optimal value function, and the upper semicontinuity of the optimal set mapping are satisfied. Then, the paper shows how these stability properties for the dual problem entail a nice behavior of parametric approximation and discretization strategies (in which an ordinary linear programming problem may be considered in each step). This approximation–discretization process is formalized by means of considering a double parameter: the original one and the finite subset of indices (grid) itself. Finally, the convex case is analyzed, showing that the referred process also allows us to approach the primal problem.Mathematics Subject Classifications (2000) Primary 90C34, 90C31; secondary 90C25, 90C05.