Variational analysis of fully coupled electro‐elastic frictional contact problems

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a foundation. The material behavior is described with a nonlinear electro‐elastic constitutive law. The novelty of the model consists in the fact that the foundation is assumed to be electrically conductive and both the frictional contact and the conductivity on the contact surface are described with subdifferential boundary conditions which involve a fully coupling between the mechanical and electrical variables. We derive a variational formulation of the problem which is in the form of a system coupling two hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on recent results for inclusions of subdifferential type in Sobolev spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polymer Nano- and Microparticle Based Systems for Medical Diagnostics

Summary: Synthesis, properties and medical diagnostic applications of hydrophilic nano- and microspheres with carboxyl, aldehyde and hydroxyl groups on their surface are described. The particles were obtained by emulsion copolymerization of styrene, acrolein, methyl methacrylate, methacrylic acid, and 2-hydroxyethyl methacrylate carried on in water media and initiated with potassium persulfate. Stabilization of particles' suspensions was provided by addition of sodium dodecyl sulfate to polymerizing mixture or by formation of surfactants in situ in copolymerization involving acrolein or α-tert-butoxy-ω-vinylbenzyl-polyglycidol macromonomer (PGL). Relations between interfacial properties of these particles and their ability for covalent immobilization of proteins, with eliminated or at least reduced nonspecific adsorption of these species were investigated. The particles with covalently attached proteins (antigens or antibodies) were used for preparation of diagnostic tests based on visual or turbidimetric observation of particles' aggregation or by monitoring changes in their electrophoretic mobility accompanying specific antigen (or antibody) binding. The later test was directed toward determination of antibodies against Helicobacter pylori. Principle of a new type of diagnostic test based on photonic crystals of microspheres are described.     

A Nonsymmetric Correlation Inequality for Gaussian Measure

Letμbe a Gaussian measure (say, onRⁿ) and letK,LRⁿbe such thatKis convex,Lis a “layer” (i.e.,L={x: ax, ub} for somea, bRanduRⁿ), and the centers of mass (with respect toμ) ofKandLcoincide. Thenμ(K∩L)μ(K)·μ(L). This is motivated by the well-known “positive correlation conjecture” for symmetric sets and a related inequality of Sidak concerning confidence regions for means of multivariate normal distributions. The proof uses the estimateΦ(x)> 1−((8/π)^1/2/(3x+(x²+8)^1/2))e^−x2/2,x>−1, for the (standard) Gaussian cumulative distribution function, which is sharper than the classical inequality of Komatsu.     

An application of the Lefschetz fixed-point theorem to non-convex differential inclusions on manifolds

A selector theorem for non-convex orientor fields on closed manifolds is given and the Lefschetz fixed point theorem is used to establish an existence result for these ones.

     

The influence of side branches on the structure of crystalline phase in ethylene-1-alkene copolymers

The influence of side branches on the unit cell dimensions in ethylene-1-alkene copolymers was investigated both at room temperature as well as during heating of the samples up to melting. Time resolved X-ray diffraction investigations revealed that in the case of ethylene-1-octene copolymers with low and moderate comonomer content, the transversal expansion of the unit cell occurs due to the limited thickness of lamellae, however the samples with higher comonomer content (above 5 mol %) exhibit distinctly larger expansion resulting from the stresses imparted on the basal surfaces of crystals by the excluded branches. At high temperatures, independently on the thermal expansion, an additional increase of the unit cell volume occurs, caused probably by a penetration of the end-parts of side branches, residing near the crystals surface, into the surface cells. Similar phenomenon is observed for ethylene-1-butene copolymer. On contrary, the ratio of the average unit cell volume in ethylene-1-propene copolymer to the unit cell volume in linear polyethylene at the same temperature, decreases starting from about 50 °C. Such a behavior is a new confirmation of a partial inclusion of methyl branches into the crystalline phase. Most probably, when the temperature increases, the volume of included branch becomes a decreasing fraction of the thermally expanding unit cell volume.     

Structure of the nitrogen-centered radical formed during inactivation of E. coli ribonucleotide reductase by 2'-azido-2'-deoxyuridine-5'-diphosphate: trapping of the 3'-ketonucleotide

Ribonucleotide reductases (RNRs) catalyze the conversion of nucleotides to deoxynucleotides providing the monomeric precursors required for DNA replication and repair. The class I RNRs are composed of two homodimeric subunits: R1 and R2. R1 has the active site where nucleotide reduction occurs, and R2 contains the diiron tyrosyl radical (Y*) cofactor essential for radical initiation on R1. Mechanism-based inhibitors, such as 2'-azido-2'-deoxyuridine-5'-diphosphate (N(3)UDP), have provided much insight into the reduction mechanism. N(3)UDP is a stoichiometric inactivator that, upon interaction with RNR, results in loss of the Y* in R2 and formation of a nitrogen-centered radical (N*) covalently attached to C225 (R-S-N*-X) in the active site of R1. N(2) is lost prior to N* formation, and after its formation, stoichiometric amounts of 2-methylene-3-furanone, pyrophosphate, and uracil are also generated. On the basis of the hyperfine interactions associated with N*, it was proposed that N* is also covalently attached to the nucleotide through either the oxygen of the 3'-OH (R-S-N*-O-R') or the 3'-C (R-S-N*-C-OH). To distinguish between the proposed structures, the inactivation was carried out with 3'-[(17)O]-N(3)UDP and N* was examined by 9 and 140 GHz EPR spectroscopy. Broadening of the N* signal was detected and the spectrum simulated to obtain the [(17)O] hyperfine tensor. DFT calculations were employed to determine which structures are in best agreement with the simulated hyperfine tensor and our previous ESEEM data. The results are most consistent with the R-S-N*-C-OH structure and provide evidence for the trapping of a 3'-ketonucleotide in the reduction process.     

Coulometric titrations in microscale study of ionic equilibria

Summary Coulometric titration, a well established technique in research and in routine analysis, can successfully be applied to the study of ionic equilibria in solution. Processes, where either lyate or lyonium ions serve as titrants, for determination of acids and bases, respectively, were investigated. Among the systems studied are: autoprotolytic equilibria of various amphiprotic solvents, acid-base equilibria in water, organic and mixed solvents and complexation reactions. In all these examples the titration was followed by a potentiometric pH-indicator electrode. In nonaqueous solvents coulometry overcame the limited solubility of electrolytes, the difficulty of standardization on solutions and the necessity of working in isolated systems to avoid contamination of the sample with water vapour or with carbon dioxide.Because volumes below 1 ml and concentrations in the order of 0.001 mol/l can be used, this technique can be successfully applied to the investigation of micromole amounts of compounds, when protolytic properties of substances available in minute quantities should be evaluated. Furthermore this technique was applied to the evaluation of protonation constants of biologically important buffers and the stability constants of their calcium complexes.     

Carbon-mineral adsorbents prepared by pyrolysis of waste materials in the presence of tetrachloromethane

Natural bentonite spent in the process of plant oil bleaching was used as an initial material for preparation of carbon-mineral adsorbents. The spent bleaching earth was treated using four procedures: T (thermal treatment); H (hydrothermal treatment); C (thermal treatment with addition of CCl4 vapor); M (modification of porous structure). Raw bentonite, RB (raw bleaching earth), and carbon materials prepared using plant oil were compared. The physicochemical characteristics of the adsorbents were determined using different methods: nitrogen adsorption/desorption, XRD, TEM, and MS-TPD. Carbon-mineral adsorbents contain from 5.23 to 19.92% C (w/w) and carbon adsorbents include from 84.2 to 91.18% C (w/w). Parallel processes of organic substance carbonization, porous structure modification, sublimation or evaporation of metal chlorides, and removal of hydrogen chloride take place during pyrolysis of waste mineral materials in the CCl4 atmosphere.     

Controlled polymerization of cyclic esters. structure of initiators and of active species related to the selectivity of initiation and propagation

This paper reviews mostly the already published work of our own, complemented with some new data and related to the control (i.e. selectivity) in the anionic and covalent (pseudoanionic) polymerization of cyclic esters. Ionic and covalent growing species are briefly compared in terms of their susceptibility to undergo side reactions. Then, structures of covalent initiators (mostly multivalent metal alkoxides) are discussed from the view point of their behavior in initiation and formation of active species. R₂AlOR', (RO)₃Al, and other metal alkoxides are discussed.