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.     

Effects of thioamide substitutions on the conformation and stability of alpha- and 3(10)-helices

Thiopeptides, formed by replacing the amide oxygen atom with a sp(2) sulfur atom, are useful in protein engineering and drug design because they confer resistance to enzymatic degradation and are predicted to be more rigid. This report describes our free molecular dynamics simulations with explicit water and free energy calculations on the effects of thio substitutions on the conformation of alpha-helices, 3(10)-helices, and their relative stability. The most prominent structural effect of thio substitution is the increase in the hydrogen bond distance from 2.1 A for normal peptides to 2.7 A for thiopeptides. To accommodate for the longer C[double bond]S...H-N hydrogen bond, the (phi, psi) dihedral angles of the alpha-helix changed from (-66 degrees, -42 degrees) to (-68 degrees, -38 degrees), and the rise per turn increased from 5.5 to 6.3 A. For 3(10)-helices, the (phi, psi) dihedral angles (-60 degrees, -20 degrees) and rise per turn (6.0 A) changed to (-66 degrees, -12 degrees) and 6.8 A, respectively. In terms of relative stability, the most prominent change upon thio substitution is the decrease in the free energy difference, Delta A(alpha --> 3(10)), from 14 to 3.5 kcal/mol. Therefore, normal peptides are less likely to form 3(10)-helix than are thiopeptides. Component analysis of the Delta A(alpha --> 3(10)) reviews that the entropy advantage of the 3(10)-helix for both Ac-Ala(10)-NHMe and Act-Alat(10)-NHMe is attributed to the 3(10)-helix being more flexible than the alpha-helix. Interestingly, upon thio substitution, this differential flexibility is even more apparent because the alpha-helix conformation of Act-Alat(10)-NHMe becomes more rigid due to the bulkier sulfur atom.     

Capillary gas chromatographic-mass spectrometric study of the effect of solvents on metoprolol and other aryloxypropanolamines

When metoprolol in methanol was analysed by capillary gas chromatography (GC), an additional peak was observed; mass spectrometry (MS) showed this additional peak to have a molecular weight 12 dalton higher than that of the parent compound. A similar phenomenon was observed with other beta-adrenergic blocking aryloxypropanolamines in methanol or dichloromethane. Capillary GC-MS using deuterated solvents as isotopic markers showed that a methylene group from the solvents was incorporated into the parent molecule. The structure of the observed products and the mechanism of their formation are proposed.     

Effect of diffusion on rates and molecular weights in graft polymerization

A theoretical analysis has been made of the graft polymerization process in terms of the quantitative interrelationship between the initiation rate R_i, the k_p/k_t^1/ ratio of the monomer, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, and the diffusivity D of the monomer in the polymer. It is shown how the values of these parameters in any grafting system interact to lead to diffusion-controlled graft polymerization. Whether graft polymerization is diffusion-free or diffusion-controlled depends on the values of K_p, d, k_p/k_p^1/2, and L as gathered in the parameter A = [(K_p/k_t^1/2)R_i, D,/^1/2] L/2. When the values of the various terms are such that A is less than 0.1 (i.e., D is large while R_i, k_p, and L are small), the reaction is diffusion-free. When A is greater than 3 (i.e., D is small while R_i, k_p, and L are large), the reaction is diffusion-controlled. The derived equations showing the relationship between kinetic and diffusional parameters are theoretically applicable to all grafting systems, i.e., for all monomer-polymer combinations under all conditions of reaction temperature, radiation intensity and polymer film thickness. The theoretical analysis has been verified for the rate and degree of polymerization for the radiation-induced graft polymerization of styrene to polyethylene.