On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Structure and catalytic activity of some soluble polyethylene glycol-peptide conjugates

Soluble catalysts for the Juliá-Colonna asymmetric epoxidation reaction have been constructed in three different ways, using NH₂-PEG-OMe as the support system: suitable solvents have been identified and it is shown that the degree of helicity of the conjugates correlates with the extent of conversion and (to a lesser extent) the enantioselectivity of epoxidation.     

Some New Results on Key Distribution Patterns and Broadcast Encryption

This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption).In a recent paper st95a, Stinson described a method of constructing key predistribution schemes by combining Mitchell-Piper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines Fiat-Naor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combinatorial structures such as orthogonal arrays, perpendicular arrays, Steiner systems and universal hash families.     

On non-stationary Navier-Stokes flows with vanishing viscosity associated with a variational inequality

Let g is a positive increasing function with 1?g(0). The existence of a unique solution of the Navier-Stokes flow associated with K_ε,γ and the convergence of the solution to that of the Euler equations as the viscosity goes to zero are established.     

Graph bisection algorithms with good average case behavior

In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixedd≧3, all sufficiently largen and allb=o(n ^{1?1/[(d+1)/2]}), the algorithm finds the minimum bisection for almost alld-regular labelled simple graphs with 2n nodes and bisection widthb. For example, the algorithm succeeds for almost all 5-regular graphs with 2n nodes and bisection widtho(n ^2/3). The algorithm differs from other graph bisection heuristics (as well as from many heuristics for other NP-complete problems) in several respects. Most notably:

1. the algorithm provides exactly the minimum bisection for almost all input graphs with the specified form, instead of only an approximation of the minimum bisection,
2. whenever the algorithm produces a bisection, it is guaranteed to be optimal (i.e., the algorithm also produces a proof that the bisection it outputs is an optimal bisection),
3. the algorithm works well both theoretically and experimentally,
4. the algorithm employs global methods such as network flow instead of local operations such as 2-changes, and
5. the algorithm works well for graphs with small bisections (as opposed to graphs with large bisections, for which arbitrary bisections are nearly optimal).

     

1,4-Addition of benzene to a dihydrocyclopent[a]indene diradical: synthesis and DFT study

Photochemical cyclization of compound 1, a homoenediyne (-CCC=CCH2CC-) bearing two ethynylanthracene chromophores, yields two isomeric dihydrocyclopent[a]indene ring systems, spiro-fused to the 9-position of a 9,10-dihydroanthracene moiety. Evidence of a photochemically initiated diradical cyclization pathway is proposed on the basis of (i) hydrogen abstraction from reaction with 1,4-cyclohexadiene (1,4-CHD) and (ii) the observation of 1,4-addition of benzene (solvent). The reaction was further analyzed by a complete density functional theory (DFT) study, using an unrestricted approach (UBLYP) with a 6-31G* basis set for the open-shell triplet states of the reactants, products, and diradical intermediates to model the photochemical nature of observed transformation. A mechanism detailing the observed cyclization/addition reaction is proposed.     

Motion of foam films in diverging-converging channels

Existing theories of the motion of foam films in capillaries often assimilate the pressure drop over the foam films to the static capillary pressure obtained from the Young-Laplace equation. Hence, they ignore the contribution of dynamic effects associated with the rapid stretching and contraction of the foam films to the overall viscous dissipation. This paper reports an investigation of the motion of foam films in axisymmetric diverging-converging channels, taking into account surface viscosity and elasticity. First, a phenomenological theory for the motion of the foam films is developed using simple physical arguments. We show that the displacement of the film obeys a nonlinear second-order differential equation, which can be solved numerically for the (dimensionless) distance from the inlet and the pressure drop as a function of time. Experiments with foam film motion, conducted using glass diverging-converging channels (minimum radius = 3.00 +/- 0,01 mm, maximum diameter = 7,98 +/- 0,01 mm) and nitrogen foam stabilized with sodium dodecyl sulfate (SDS) in brine, are discussed. For a single film motion in the diverging channel, we find that (a) the static pressure drop is a concave-upward function of distance and decreases from 1.0 to about 0.3, whereas (b) the dynamic pressure drop is concave downward and increases from 1 to a maximum of 1.3 and then decreases to 0.7. In the converging channel both the static and dynamic pressure drops are concave-downward functions, but the dynamic pressure drop values are always higher than the static ones. For two films the motions were found to be rather sensitive to the initial arrangement in the channel. The experiments are found to be in excellent agreement with the theoretical predictions. These observations imply that the large flow resistance obtained during foam flow in granular porous media, where converging-diverging channels are abundant, is largely due to the surface elasticity and viscosity of the films.     

Selective reduction of aldehydes by a formic acid- trialkylamine- RuCl2(PPh3)3 system

In the presence of trialkylamine and formic acid RuCl₂(PPh₃)₃ selectively reduces aldehydes to the corresponding alcohols at room temperature. Other reducible groups are unaffected.