Regularity of a boundary point for quasilinear elliptic systems of the second order

There is considered a quasilinear elliptic system of the divergence type. There are obtained continuity conditions for a general solution and its gradient at a boundary point. These conditions depend on the geometry of the domain and also on the sparseness of eigenvalues of the coefficient matrix of the system.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 590–596, May, 1991.     

Application of radioisotope XRF for the determination of noble metals in aqueous solutions

Radiometric methods of determination of platium and palladium (0.1 to 5% of Pt and 0.1 to 2% of Pd), gold and indium (0.01 to 1% of Au and 1 to 4 g In/l) and of platinum and rhodium (0.1 to 9% of Pt and 0.05 to 1% of Rh) in aqueous solution has been worked out. A suitable measuring device has been designed and constructed. The methods are based on the measurement of characteristic radiation of the L_α line for gold and platinum and of the K-series for indium, palladium and rhodium, as well as on the measurement of scattered radiation from a²³⁸Pu source. The r.m.s. error of the determination varies from 0.01 to 0.10% of Pt, 0.002 to 0.01% of Au and 0.01 to 0.15% of Pd depending on the concentration. In the case of Rh and In the errors are 0.008% and 0.04 g In/l, respectively.     

A Class of Subdifferential Inclusions for Elastic Unilateral Contact Problems

We consider a class of stationary subdifferential inclusions in a reflexive Banach space. We reformulate the problem in terms of a variational inequality with multivalued term and prove an existence result using the Kakutani-Fan-Glicksberg fixed point theorem. This approach allows to consider, in a natural way, a dual variational formulation of the problem. Next, we study the link between the primal and dual formulations and provide an equivalence result. Then, we consider a new mathematical model which describes the contact of an elastic body with a foundation. We apply the abstract formalism to derive the primal and the dual variational formulations of the problem, in terms of displacement and stress, respectively. Finally, we present existence and equivalence results in the study of this contact model.     

Hydrous zinc halide-catalyzed aminosulfonation of hydrocarbons

Benzylic and allylic hydrocarbons are selectively converted to the corresponding sulfonamides by a ZnBr(2)-H(2)O-catalyzed reaction with PhI[double bond, length as m-dash]NTs; saturated adamantane is aminosulfonated at the tertiary C-H bond.     

Thermal dependency of RAG1 self-association properties

Background  

Functional immunoglobulin and T cell receptor genes are produced in developing lymphocytes by V(D)J recombination. The initial site-specific DNA cleavage steps in this process are catalyzed by the V(D)J recombinase, consisting of RAG1 and RAG2, which is directed to appropriate DNA cleavage sites by recognition of the conserved recombination signal sequence (RSS). RAG1 contains both the active site and the RSS binding domains, although RAG2 is also required for DNA cleavage activity. An understanding of the physicochemical properties of the RAG proteins, their association, and their interaction with the RSS is not yet well developed.     

A new,convenient and expeditious synthesis of 4-alkyl-5-methyl-1H-pyrazol-3-ols in water through a multicomponent reaction

A new, simple and efficient synthesis of 4-alkyl-5-methyl-1H-pyrazol-3-ols in water by a two-pot four component reaction of ethyl acetoacetate, hydrazine hydrate, aldehyde and ketone in presence K₂CO₃ as the catalyst is described. Use of water as the reaction medium, operational simplicity, mild reaction conditions, application of a cost-effective, nontoxic and easily available catalyst with auto-tandem catalysis, wide substrate scope, easy workup and purification process make the protocol highly attractive.     

A Solvent Switch for the Stabilization of Multiple Hemiacetals on an Inorganic Platform: Role of Supramolecular Interactions

Reaction of Zn(OAc)₂ ? 2 H₂O with 2,6‐diisopropylphenyl phosphate (dippH₂) in the presence of pyridine‐4‐carboxaldehyde (Py‐4‐CHO) in methanol resulted in the isolation of a tetrameric zinc phosphate cluster [Zn(dipp)(Py‐4‐CH(OH)(OMe))]₄ ? 4 MeOH ( 1 ) with four hemiacetal moieties stabilized on the double‐4‐ring inorganic cubane cluster. The change of solvent from methanol to acetonitrile leads to the formation of [Zn(dipp)(Py‐4‐CHO)]₄ ( 2 ), in which the coordinated Py‐4‐CHO retains its aldehydic form. Dissolution of 1 in CD₃CN readily converts it to the aldehydic form and yields 2 . Similarly 2 , which exists in the aldehyde form in CD₃CN, readily converts to the hemiacetal form in CD₃OD/CH₃OH. Compound 1 is an unprecedented example in which four hemiacetals have been stabilized on a single molecule in the solid state retaining its stability in solution as revealed by its ¹H NMR spectrum in CD₃OD. The solution stability of 1 and 2 has further been confirmed by ESI‐MS studies. To generalize the stabilization of multiple hemiacetals on a single double‐four‐ring platform, pyridine‐2‐carboxaldehyde (Py‐2‐CHO) was used as the auxiliary ligand in the reaction between zinc acetate and dippH₂, leading to isolation of [Zn(dipp)(Py‐2‐CH(OH)(OMe))]₄ ( 3 ). Understandably, recrystallization of 3 from acetonitrile yields the parent aldehydic form, [Zn(dipp)(Py‐2‐CHO)]₄ ( 4 ). Single‐crystal X‐ray diffraction studies reveal that supramolecular bonding, aided by hydrogen‐bonding interactions involving the hemiacetal functionalities (C?OH, C?OMe, and C?H), are responsible for the observed stabilization. The hemiacetal/aldehyde groups in 1 and 2 readily react with p‐toluidine, 2,6‐dimethylaniline, and 4‐bromoaniline to yield the corresponding tetra‐Schiff base ligands, [Zn(dipp)(L)]₄ (L=4‐methyl‐N‐(pyridin‐4‐ylmethylidene)aniline ( 5 ), 2,6‐dimethyl‐N‐(pyridin‐4‐ylmethylene)‐aniline ( 6 ), and 4‐bromo‐N‐(pyridin‐4‐ylmethylene)aniline ( 7 )). Isolation of 5 – 7 opens up further possibilities of using 1 and 2 as new supramolecular synthons and ligands.     

On local weak solutions to Nernst–Planck–Poisson system

We study the one-dimensional nonlinear Nernst–Planck–Poisson system of partial differential equations with the class of nonlinear boundary conditions which cover the Chang–Jaffé conditions. The system describes certain physical and biological processes, for example ionic diffusion in porous media, electrochemical and biological membranes, as well as electrons and holes transport in semiconductors. The considered boundary conditions allow the physical system to be not only closed but also open. Theorems on existence, uniqueness, and nonnegativity of local weak solutions are proved. The main tool used in the proof of the existence result is the Schauder–Tychonoff fixed point theorem.