Hydrogen Peroxide/Boric Acid: An Efficient System for Oxidation of Aromatic Aldehydes and Ketones to Phenols

Hydrogen peroxide activated by boric acid in the presence of sulfuric acid has been shown to be an efficient oxidizing system for direct conversion of aromatic aldehydes and ketones to phenols.     

Orbit closures in the enhanced nilpotent cone

We study the orbits of G=GL(V) in the enhanced nilpotent cone , where is the variety of nilpotent endomorphisms of V. These orbits are parametrized by bipartitions of n=dimV, and we prove that the closure ordering corresponds to a natural partial order on bipartitions. Moreover, we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of Kostka polynomials, defined by Shoji. Finally, we make a connection with Kato's exotic nilpotent cone in type C, proving that the closure ordering is the same, and conjecturing that the intersection cohomology is the same but with degrees doubled.     

On the convergence of a class of algorithms using linearly independent search directions

Powell has shown that the cyclic coordinate method with exact searches may not converge to a stationary point. In this note we consider a more general class of algorithms for unconstrained minimization, and establish their convergence under the assumption that the objective function has a unique minimum along any line.     

Nonlinear programming without differentiability in banach spaces: necessary and sufficient constraint qualification

The problem under consideration is a maximization problem over a constraint set defined by a finite number of inequality and equality constraints over an arbitrary set in a reflexive Banach space. A generalization of the Kuhn-Tucker necessary conditions is developed where neither the objective function nor the constraint functions are required to be differentiable. A new constraint qualification is imposed in order to validate the optimality criteria. It is shown that this qualification is the weakest possible in the sense that it is necessary for the optimality criteria to hold at the point under investigation for all families of objective functions having a constrained local maximum at this point     

On the Transfer of Energy between Widely Spaced Modes in Structures

An experimental and theoretical study of the response of aflexible cantilever beam to an external harmonic excitation nearthe beam's third natural frequency is presented. For a certain range ofthe excitation frequency, we observed experimentally that the responseincludes a large contribution due to the first mode of the beamaccompanied by a slow modulation of the amplitude and phase of the thirdmode. In addition, we noted that the energy transfer between the thirdand first modes is very much dependent upon the closeness of themodulation (or Hopf bifurcation) frequency to the first-mode naturalfrequency. In earlier studies by Nayfeh and coworkers, the modulationfrequency was close to the first-mode natural frequency, and thereforelarge first-mode swaying was observed. But for higher forcingamplitudes, the present experiments show that the modulation frequencytends to shift away from the first-mode natural frequency, andsubsequently very little swaying is observed. We also developed areduced-order analytical model by discretizing the integralpartial-differential equation of motion, derived by Crespo daSilva and Glenn, using the Galerkin procedure with a four-modeapproximation. The reduced-order model demonstrates the energy transferfrom the third mode to the first mode.     

Fixed-width confidence intervals for contrasts in the means

The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147–152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of additional observations after stopping is derived, which ensures the mxact probability of coverage. Moreover, two-stage, three-stage and modified sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.     

A dipyrromethane based receptor as a dual colorimetric sensor for F− and Cu2+ ions

A novel dipyrromethane based receptor has been synthesized. It works as a highly selective colorimetric sensor for F^? and Cu²⁺ ions, which can be used for their necked eye detection with evident colour change of its solution.     

Trace level determination of manganese in liver tissues employing substoichiometric thermal neutron activation analysis

Liver tissues from rat have been analyzed for determining trace amounts of manganese present by employing thermal neutron activation analysis and substoichiometric solvent extraction of Mn/II/ with 1,2,3-benzotriazole into 1-octanol. Three samples and a standard can be processed and counted within three hours.     

Cyclopentane construction by Rh-catalyzed intramolecular C-h insertion: relative reactivity of a range of catalysts

The preparation and Rh-mediated cyclization of the alpha-diazoester 1 are outlined, and its utility in determining the elements that contribute to the reactivity of the intermediate Rh-carbenoid is presented. The rate of disappearance of diazo ester 1 catalyzed by several representative Rh(II) complexes was determined. The observed relative rate constants for the reaction of the Rh(II) complexes with 1 varied over a range of >10(7). The reactivity of the Rh-carbenoid intermediate was explored using the ratio of the sum of (3 + 4 + 5) to 2 (cyclization vs elimination), the ratio of 3 to the sum of (4 + 5) (chemoselectivity), and the ratio of 4 to 5 (diastereoselectivity). It is striking that these four measures of reactivity were found to be independent of each other.