Dual-mode recognition of oxalate by protonated azacryptate hosts; conformational response of the guest maximizes pi-stacking interactions

Exceptionally large complexation constants for oxalate encapsulated within azacryptand hosts are partly explained by pi-stacking interactions between C=O and aromatic rings.     

Properties of the liquid crystals formed by certain 4'-n-alkylbiphenyl-4-yl 5-n-alkylthiophene-2-carboxylates

Thirty compounds, ten members of each of three homologous series of esters derived from 4-hydroxy-4'-n-octyl-, -nonyl-, and -decyl-biphenyl and the 5-n-alkylthiophene-2-carboxylic acids (methyl through to decyl homologues) have been prepared. The liquid crystal properties of these esters, which show extensive smectic polymorphism, have been investigated by thermal optical microscopy, differential scanning calorimetry, and miscibility studies. Four members of the corresponding 4-n-alkylbenzoates have also been prepared in order to compare their liquid crystal behaviour with the 5-n-alkylthiophene-2-carboxylate counterparts: both smectic and nematic thermal stability are higher for the 4-n-alkylbenzoates, by 30.6° and 36.8° C, respectively.     

An explicit procedure for discretizing continuous,optimal control problems

An explicit procedure for obtaining discrete approximations to general, nonlinear, fixed-time, continuous, optimal control problems with no intermediate trajectory constraints is presented. It is proved that, if the associated system of differential equations is linear in the control variable, then the optimal solutions of these approximationsconverge to extremals of the original continuous problem.     

Some remarks on the symmetric rank-one update

We consider the symmetric rank-one, quasi-Newton formula. The hereditary properties of this formula do not require quasi-Newton directions of search. Therefore, this formula is easy to use in constrained optimization algorithms; no explicit projections of either the Hessian approximations or the parameter changes are required. Moreover, the entire Hessian approximation is available at each iteration for determining the direction of search, which need not be a quasi-Newton direction. Theoretical difficulties, however, exist. Even for a positive-definite, quadratic function with no constraints, it is possible that the symmetric rank-one update may not be defined at some iteration. In this paper, we first demonstrate that such failures of definition correspond to either losses of independence in the directions of search being generated or to near-singularity of the Hessian approximation being generated. We then describe a procedure that guarantees that these updates are well-defined for any nonsingular quadratic function. This procedure has been incorporated into an algorithm for minimizing a function subject to box constraints. Box constraints arise naturally in the minimization of a function with many minima or a function that is defined only in some subregion of the space.     

Carbaporphyrinoid chemistry has a silver lining! silver(III) oxybenzi-, oxynaphthi-, tropi-, and benzocarbaporphyrins

[structure: see text] Carbaporphyrinoid systems with semiquinone, cycloheptatriene, or indene subunits react under mild conditions with silver(I) acetate to give stable silver(III) organometallic derivatives.     

Chromium(0)-promoted multicomponent cycloaddition of tethered diynes with cyclic trienes: application to the total synthesis of 9-epi-pentalenic acid

An efficient protecting group controlled regioselective chromium(0)-mediated three-component higher order cycloaddition of tethered diynes with cyclic trienes that generates five rings and six stereogenic centers in one step is described. Following a sequence of reactions featuring a chemoselective Baeyer-Villiger rearrangement and a regioselective cyclopropane hydrogenolysis, the total synthesis of 9-epi-pentalenic acid was achieved.     

Studies on pyridazine azide cyclisation reactions

Reaction of sodium azide with 4-methyl-3,5,6-tribromopyridazine results in the formation of 3,5,6-triazide intermediate which could cyclise to give two possible bicyclic products while ab initio calculations show that the formation of a tricyclic compound is extremely energetically unfavourable. However, experimentally, only one major product is isolated. The structure of this unstable product has been conclusively established by X-ray crystallography as 3,5-diazido-4-methyl[1,5-b]tetrazolopyridazine confirming theoretical predictions.