Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

Biodegradation of soluble redox polymers. Part 2: (0.017ferrocene)amylose at a rotating disk electrode

The behavior of (ferrocene)amylose (FA), in the presence of amylolytic depolymerases (α-amylase from Aspergillus oryzae and human saliva), has been investigated by cyclic voltammetry at a rotating disk electrode (CVA/RDE). Growth of the limiting current with time in the presence of the enzymes is proportional to the amount of enzyme introduced. The quantitative data treatment to assay the endoamylolytic activity of enzymes at CVA/RDE involves plotting (i_dt/i_d0)^4.5 against time; the slope of the linear plot being equal to (rate) M_n0C⁻¹, where i_dt and i_d0 are the limiting currents at time t and 0, respectively, (rate) is the enzymatic activity, M_n0 is the number averaged molecular weight of FA at t = 0, and c is its concentration. The comparison of CVA/RDE with the 3,5-dinitrosalicylic acid and the Somogyi–Nelson reducing saccharides procedures shows advantages of the former, especially in assaying small quantities of enzymes. Also the CVA/RDE approach is simpler and takes place under much milder conditions. The main disadvantage of CVA/RDE is the inhibiting effect of Triton X-100 in the reaction between FA and the amylases which is not observed in the case of native, ferrocene-free amylose. In general, CVA/RDE appears to be an attractive analytical method for monitoring diverse enzymatic depolymerization reactions.     

Coderivative Analysis of Variational Systems

The paper mostly concerns applications of the generalized differentiation theory in variational analysis to Lipschitzian stability and metric regularity of variational systems in infinite-dimensional spaces. The main tools of our analysis involve coderivatives of set-valued mappings that turn out to be proper extensions of the adjoint derivative operator to nonsmooth and set-valued mappings. The involved coderivatives allow us to give complete dual characterizations of certain fundamental properties in variational analysis and optimization related to Lipschitzian stability and metric regularity. Based on these characterizations and extended coderivative calculus, we obtain efficient conditions for Lipschitzian stability of variational systems governed by parametric generalized equations and their specifications.     

Darboux transformation and elementary exact solutions of the Schrödinger equation

Darboux transformation is applied to three classical potentials, namely the harmonic oscillator, effective Coulomb and Morse potentials to generate exactly solvable potentials of elementary form. For every potential, the isospectral families of potentials are constructed. For almost all potentials, a set of normalized discrete spectrum wave functions is given.     

Description of bimolecular fluorescence-quenching processes on the surface of pyrogenic silica

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 6, pp. 966–971, December, 1991.     

Iterative patching and the asymmetric traveling salesman problem

Although Branch-and-Bound (BnB) methods are among the most widely used techniques for solving hard problems, it is still a challenge to make these methods smarter. In this paper, we investigate iterative patching, a technique in which a fixed patching procedure is applied at each node of the BnB search tree for the Asymmetric Traveling Salesman Problem. Computational experiments show that iterative patching results in general in search trees that are smaller than the classical BnB trees, and that solution times are lower for usual random and sparse instances. Furthermore, it turns out that, on average, iterative patching with the Contract-or-Patch procedure of Glover, Gutin, Yeo and Zverovich (2001) and the Karp–Steele procedure are the fastest, and that ‘iterative’ Modified Karp–Steele patching generates the smallest search trees.     

Effects of coupled vibrations on the acoustical performance of underwater cylindrical shell transducers

An experimental investigation of the effects of coupled vibrations on the acoustical performance of underwater transducers made from radially polarized, thin walled, air-backed, piezoelectric cylinders as a function of their height-to-diameter aspect ratio is presented. Characteristics of the frequency response, directivity patterns, and effectiveness of the transducers are considered in comparison with analogous characteristics for the transducers comprised of mechanically separated rings, otherwise having the same geometry. Recommendations are made on the application of cylindrical piezoelectric elements with different aspect ratios for underwater transducer applications.