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.

     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

New labdane-type diterpenoids from Leonurus heterophyllus SW

Five new natural labdane-type diterpenoids (5-9), designated leoheteronins A-E, together with four known diterpenoids (1-4), two phytosterols as a mixture of beta-sitosterol and stigmasterol, and the flavone genkwanin (10) were isolated from the aerial parts of Leonurus heterophyllus SW. (Lamiaceae) collected in northern Vietnam. Compound 1 was isolated for the first time from a Leonurus species, and 10 is considered to be a chemotaxonomic marker of the Leonurus genus. Their structures were determined using spectroscopic analyses.     

In situ preparation of protein-"smart" polymer conjugates with retention of bioactivity

Protein-polymer conjugates are widely used in biotechnology and medicine, and new methods to prepare the bioconjugates would be advantageous for these applications. In this report, we demonstrate that bioactive "smart" polymer conjugates can be synthesized by polymerizing from defined initiation sites on proteins, thus preparing the polymer conjugates in situ. In particular, free cysteines, Cys-34 of bovine serum albumin (BSA) and Cys-131 of T4 lysozyme V131C, were modified with initiators for atom transfer radical polymerization (ATRP) either through a reversible disulfide linkage or irreversible bond by reaction with pyridyl disulfide- and maleimide-functionalized initiators, respectively. Initiator conjugation was verified by electrospray-ionization mass spectroscopy (ESI-MS), and the location of the modification was confirmed by muLC-MSMS (tandem mass spectrometry) analysis of the trypsin-digested protein macroinitiators. Polymerization of N-isopropylacrylamide (NIPAAm) from the protein macroinitiators resulted in thermosensitive BSA-polyNIPAAm and lysozyme-polyNIPAAm in greater than 65% yield. The resultant conjugates were characterized by gel electrophoresis and size exclusion chromatography (SEC) and easily purified by preparative SEC. The identity of polymer isolated from the BSA conjugate was confirmed by (1)H NMR, and the polydispersity index was determined by gel permeation chromatography (GPC) to be as low as 1.34. Lytic activities of the lysozyme conjugates were determined by two standard assays and compared to that of the unmodified enzyme prior to polymerization; no statistical differences in bioactivity were observed.     

Theoretical and experimental reevaluation of the basicity of lambda3-phosphinine

We have investigated the basicity of phosphinine (C5H5P, phosphabenzene) in reevaluating its proton affinity (PA) and gas-phase basicity (GB) and the pK(a) value of its protonated form. As a necessary step, we have first determined its gas-phase proton affinity. Using both mass spectrometric and quantum chemical methods, we have obtained the values PA(C5H5P) = 195.8 +/- 1.0 kcal mol(-1) and GB(298)(C5H5P) = 188.1 +/- 1.0 kcal mol(-1), in good agreement with previous results. We then derived a value of pK(a)(C5H6P+) = -16.1 +/- 1.0 in aqueous solution using three different approaches: the latter markedly differs from the currently available value of -10. The reason for such a discrepancy in the pK(a) of protonated phosphinine in solution is discussed. In the theoretical determination of PAs, evaluation of the basis set superposition error (BSSE) showed that this effect is quite small, being 0.1-0.2 kcal mol(-1) for phosphinine, when a density functional theory (DFT) method in conjunction with a large basis set were used.     

Reactivity of DNA guanyl radicals with phenolate anions

Guanine bases are the most easily oxidized sites in DNA. Electron-deficient guanine species are major intermediates produced in DNA by the direct effect of ionizing radiation (ionization of the DNA itself) because of preferential hole migration within DNA to guanine bases. By using thiocyanate ions to modify the indirect effect (ionization of the solvent), we are able to produce these single-electron-oxidized guanine radical species in dilute aqueous solutions of plasmid DNA where the direct effect is negligible. The guanyl radical species produce stable modified guanine products. They can be detected in the plasmid by converting them to strand breaks after incubation with a DNA repair enzyme. If a phenol is present during irradiation, the yield of modified guanines is decreased. The mechanism is reduction of the guanine radical species by the phenol. It is possible to derive a rate constant for the reaction of the phenol with the guanyl radical. The pH dependence shows that phenolate anions are more reactive than their conjugate acids, although the difference for guanyl radicals is smaller than with other single-electron-oxidizing agents. At physiological pH values, the reduction of a guanyl radical entails the transfer of a proton in addition to the electron. The relatively small dependence of the rate constant on the driving force implies that the electron cannot be transferred before the proton. These results emphasize the potential importance of acidic tyrosine residues and the intimate involvement of protons in DNA repair.     

Cell-permeable GPNA with appropriate backbone stereochemistry and spacing binds sequence-specifically to RNA

Guanidine-based peptide nucleic acid (GPNA) with a d-backbone configuration and alternate spacing binds sequence-specifically to RNA and is readily taken up by both human somatic and embryonic stem (ES) cells.     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.