Superlinear convergence of symmetric Huang's class of methods

Summary In this paper the problem of minimizing the functionalf:DR ⁿ R is considered. Typical assumptions onf are assumed. A class of Quasi-Newton methods, namely Huang's class of methods is used for finding an optimal solution of this problem. A new theorem connected with this class is presented. By means of this theorem some convergence results known up till now only for the methods which satisfy Quasi-Newton condition are extended, that is the results of superlinear convergence of variable metric methods in the cases of exact and asymptotically exact minimization and the so-called direct-prediction case. This theorem allows to interpretate one of the parameters as the scaling parameter.     

Space-times with spherically symmetric hypersurfaces

When discussing spherically symmetric gravitational fields one usually assumes that the whole space-time is invariant under theO(3) group of transformations. In this paper, the Einstein field equations are investigated under the weaker assumption that only the 3-spacest=const areO(3) symmetric. The following further assumptions are made: (1) Thet lines are orthogonal to the spacest=const. (2) The source in the field equations in a perfect fluid, or dust, or the term, or the empty space. (3) With respect to the center of symmetry the fluid source may move only radially if at all. Under these assumptions one solution with a perfect fluid source, found previously by Stephani, is recovered and interpreted geometrically, and it is shown that it is the sole solution which is not spherically symmetric in the traditional sense. The paper ends with a general discussion of cosmological models whose 3-spacest=const are the same as in the Robertson-Walker models. No new solutions were explicitly found, but it is shown that such models exist in which the sign of curvature is not fixed in time.     

COMPARISON OF THE SPECTROSCOPIC PROPERTIES OF 4'-AMINO PHENYLALANINE AS AN UNPROTECTED AMINO ACID AND AS A RESIDUE IN PEPTIDES

Abstract— Ultraviolet absorption and fluorescence spectra of 4'-amino phenylalanine (Aphe) and of some peptides and esters containing Aphe, are characterized. Based on these results, the applicability of Aphe for fluorescence structural investigations of peptides is evaluated. The use of Aphe as an acceptor in fluorescence energy transfer measurements offers the possibility of facilitating the determination of donor fluorescence quantum yield (φ_D) in the absence of energy transfer which usually turns out to be difficult in systems containing donor and acceptor moities. The Aphe residue in peptides also allows a better insight into intramolecular interactions.     

New imide 5-HT1A receptor ligands - modification of terminal fragment geometry

Two sets of new o-methoxyphenylpiperazine (MPP; series a) and 1,2,3,4-tetrahydroisoquinoline (THIQ; series b) derivatives, containing various imide moieties derived from NAN190, were synthesized and evaluated in vitro for their ability to bind to the serotonin 5-HT(1A) and 5-HT(2A) receptors. All new derivatives from series a demonstrated high 5-HT(1A) affinities, whereas THIQ analogues were much less active. With respect to 5-HT(2A) receptors, three MPP derivatives presented moderate activity but the rest of the investigated compounds were practically inactive. The influence of changes in terminus geometry on 5-HT(1A) receptor affinity was analyzed in regard to model compounds NAN190and MM199.     

Functional tetrahydroquinoxalines from perfluoroaromatic precursors

A short series of bromo- and nitro-polyfluorobenzene derivatives gave the corresponding tetrahydroquinoxaline systems upon reaction with N,N′-dimethylethylene diamine. This annelation strategy gives useful quantities of functionalised tetrahydroquinoxaline systems which may be interesting scaffolds for the drug discovery arena.     

The potential dependence and kinetics of HCOOH adsorption on rhodium electrodes

The formic acid adsorption on an electrochemically prepared rhodium electrode has been studied by the radiochemical method. Electrochemical properties of the rhodium electrode surface in 0.5 M H₂SO₄ have been investigated by cyclic voltammetry. It has been shown that starting from E=0.20 V the rate of HCOOH adsorption is markedly potential dependent being practically independent of the electrode potential up to E=0.20 V. It seems that the HCOOH adsorption process may be explained on the basis of the two-sites kinetics model. The data obtained for HCOOH adsorption on a rhodium electrode have been compared with those for a platinum electrode reported previously.     

Infrared spectra and structure of substituted unsaturated carbonyl compounds: XVII. Enamino ketone and aldehyde quaternary ammonium salts

The β-trialkylammonium chloride derivatives of several α,β-unsaturated carbonyl compounds have been shown by infrared spectra to exist in the s-cis and s-trans rotational forms. The equilibrium between these two forms shifts towards the s-cis with the increasing steric requirements of the alkyl substituent linked to carbonyl. The CO and CC stretching frequencies are shifted to higher values as compared with other types of α,β-unsaturated ketones.     

HREELS, STM, and STS study of CH(3)-terminated Si(111)-(1x1) surface

An ideally (1x1)-CH(3)(methyl)-terminated Si(111) surface was composed by Grignard reaction of photochlorinated Si(111) and the surface structure was for the first time confirmed by Auger electron spectroscopy, low energy electron diffraction, high-resolution electron energy loss spectroscopy (HREELS), scanning tunneling microscopy (STM), and scanning tunneling spectroscopy (STS). HREELS revealed the vibration modes associated to the CH(3)-group as well as the C-Si bond. STM discerned an adlattice with (1x1) periodicity on Si(111) composed of protrusions with internal features, covering all surface terraces. The surface structure was confirmed to be stable at temperatures below 600 K. STS showed that an occupied-state band exists at gap voltage of -1.57 eV, generated by the surface CH(3) adlattice. This CH(3):Si(111)-(1x1) adlayer with high stability and unique electronic property is prospective for applications such as nanoscale lithography and advanced electrochemistry.     

Star-branched polymers in an adsorbing slit: a Monte Carlo study

A coarse-grained model of star-branched polymer chains confined in a slit was studied. The slit was formed by two parallel impenetrable surfaces, which were attractive for polymer beads. The polymer chains were flexible homopolymers built of identical united atoms whose positions in space were restricted to the vertices of a simple cubic lattice. The chains were regular star polymers consisted of f = 3 branches of equal length. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between the polymer beads-only the excluded volume was present. Monte Carlo simulations were carried out using the algorithm based on a chain's local changes of conformation. The influence of the chain length, the distances between the confining surfaces, and the strength of the adsorption on the properties of the star-branched polymers was studied. It was shown that the universal behavior found previously for the dimension of chains was not valid for some dynamic properties. The strongly adsorbed chains can change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the temperature only.     

Molecular modeling of matrix chain deformation in nanofiber filled composites

The effects of the oriented fiber filler particles on the microscopic properties of the matrix network chains were investigated by using nanofiber filler particles as reinforcing material. Monte Carlo Rotational Isomeric State simulations were carried out for filled poly(ethylene) (PE) networks to study the dependence of the conformational distribution functions of polymer chains and their elastomeric properties on filler loadings. We were especially interested how the excluded volume effect of the nanofiber particles and their orientation (specifically orientational anisotropy) in the matrix influence elastomeric properties of the network. Distribution functions of the end-to-end distances of polymer chains for both unfilled and filled networks were calculated. Effects of nanofiber reinforcements with varying fiber radii and fiber volume fractions were investigated. We have found that the presence of nanofibers significantly increase the non-Gaussian behavior of polymer chains in the composite. The anisotropic effects of the nanofibers on mechanical properties of polymeric composites were studied as a function of their relative orientation to the direction of deformation. The modulus (reduced nominal stress per unit strain) was calculated from the distribution of end-to-end distances of polymer chains using the Mark–Curro method. Relatively small amount of nanofibers was found to increase the normalized moduli of the composite. Our results are quite in satisfactory qualitative agreement with experimental data reported in the literature. This shows that computer simulations provide a powerful tool in predicting physical properties of composite materials.