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.

     

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).

     

Nonlinear spectral-spatial control and localization of supercontinuum radiation

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.     

Target Design of Novel Histone Deacetylase 6 Selective Inhibitors with 2-Mercaptoquinazolinone as the Cap Moiety

Epigenetic alterations found in all human cancers are promising targets for anticancer therapy. In this sense, histone deacetylase inhibitors (HDACIs) are interesting anticancer agents that play an important role in the epigenetic regulation of cancer cells. Here, we report 15 novel hydroxamic acid-based histone deacetylase inhibitors with quinazolinone core structures. Five compounds exhibited antiproliferative activity with IC₅₀ values of 3.4–37.8 µM. Compound 8 with a 2-mercaptoquinazolinone cap moiety displayed the highest antiproliferative efficacy against MCF-7 cells. For the HDAC6 target selectivity study, compound 8 displayed an IC₅₀ value of 2.3 µM, which is 29.3 times higher than those of HDAC3, HDAC4, HDAC8, and HDAC11. Western blot assay proved that compound 8 strongly inhibited tubulin acetylation, a substrate of HDAC6. Compound 8 also displayed stronger inhibition activity against HDAC11 than the control drug Belinostat. The inhibitory mechanism of action of compound 8 on HDAC enzymes was then explored using molecular docking study. The data revealed a high binding affinity (−7.92 kcal/mol) of compound 8 toward HDAC6. In addition, dock pose analysis also proved that compound 8 might serve as a potent inhibitor of HDAC11.     

Synthesis of Polyanionic Cellulose Carbamates by Homogeneous Aminolysis in an Ionic Liquid/DMF Medium

Polyanionic cellulose carbamates were synthesized by rapid and efficient homogeneous aminolysis of cellulose carbonate half-esters in an ionic liquid/DMF medium. Cellulose bis-2,3-O-(3,5-dimethylphenyl carbamate), as a model compound, reacted with different chloroformates to cellulose carbonates. These intermediates were subjected to aminolysis, for which both the reactivity of different chloroformates towards C6-OH and the reactivity/suitability of the respective carbonate half-ester in the aminolysis were comprehensively studied. Phenyl chloroformate and 4-chlorophenyl chloroformate readily reacted with C6-OH of the model cellulose derivative, while 4-nitrophenyl chloroformate did not. The intermediate 4-chlorophenyl carbonate derivative with the highest DS (1.05) was then used to evaluate different aminolysis pathways, applying three different amines (propargyl amine, β-alanine, and taurine) as reactants. The latter two zwitterionic compounds are only sparingly soluble in pure DMF as the typical reaction medium for aminolysis; therefore, several alternative procedures were suggested, carefully evaluated, and critically compared. Solubility problems with β-alanine and taurine were overcome by the binary solvent system DMF/[EMIM]OAc (1:1, v/v), which was shown to be a promising medium for rapid and efficient homogeneous aminolysis and for the preparation of the corresponding cellulose carbamate derivatives or other compounds that are not accessible by conventional isocyanate chemistry. The zwitterionic cellulose carbamate derivatives presented in this work could be promising chiral cation exchangers for HPLC enantiomer separations.     

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

Use of a simple surface-active initiator in controlled/living free-radical miniemulsion polymerization under AGET and ARGET ATRP conditions

This communication describes the first example of the efficient use of a simple amphiphilic molecule as both a surfactant and an initiator in the miniemulsion polymerization of methyl methacrylate under AGET and ARGET ATRP conditions.     

Controlled pinewood fractionation with supercritical ethanol: A prerequisite toward pinewood conversion into chemicals and biofuels

The objective of this work was to investigate the ability of supercritical (SC) ethanol conditions to attack preferentially the lignin fraction against the carbohydrate fraction and their effects on the product distribution among gases, light products, bio-oils, and chars. In this study, the conversion of each pinewood component was determined by the analysis of solid residues to quantify cellulose, hemicellulose, lignin, and char contents. It is shown that, by tuning the temperature, hemicellulose and lignin are already transformed in subcritical ethanol conditions, lignin being more reactive than hemicellulose. In contrast, native wood cellulose is recalcitrant to liquefaction in SC ethanol near the critical point (T_c = 241 °C and P_c = 61 bar), but 20% of native wood cellulose is converted in SC ethanol at 280 °C. Besides, the severity of the conditions, in terms of temperature and treatment time, does not significantly influence the yields of gases, light products, and bio-oils but strongly enhances char formation. Interestingly, the increase in SC ethanol density does not change the conversion of biomass components but has a marked effect on bio-oil yield and prevents char formation. The optimum fractionation conditions to convert the lignin component, while keeping unattacked the cellulose fraction with a minimum formation of char, are dense SC ethanol, at 250 °C for 1 h, in batch conditions. However, although lignin is more reactive than hemicellulose under these conditions, these fractions are converted, in a parallel way, to around 50% and 60%, respectively.