An alternating extragradient method with non euclidean projections for saddle point problems

In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed method is based on three successive projection steps, which can be computed also with respect to non Euclidean metrics. The stepsize parameter can be adaptively computed, so that the method can be considered as a black-box algorithm for general smooth saddle point problems. We develop the global convergence analysis in the framework of non Euclidean proximal distance functions, under mild local Lipschitz conditions, proving also the \(\mathcal {O}(\frac{1}{k})\) rate of convergence on the primal–dual gap. Finally, we analyze the practical behavior of the method and its effectiveness on some applications arising from different fields.     

Analysis of the Temperature and Composition Dependence of Viscosimetric Properties of 2-Butanone <Emphasis Type="Bold">+</Emphasis> 2-Butanol Solvent Mixtures

Kinematic viscosities were measured for 2-butanone + 2-butanol binary liquid mixtures with a capillary Ubbelohde routine viscometer in the temperature range from 273.15 to 353.15 K at atmospheric pressure, and covering the whole miscibility field (0x_i1). Experimental data have been correlated by means of different empirical or semiempirical relationships, such as =(T), =(x_i), and =(T, x_i). Viscosity deviations, , from ideal behavior are negative at all experimental conditions, confirming that structure breaking effects prevail in the liquids. Furthermore, the thermodynamics of viscous flow and excess Gibbs energy of activation of viscous flow, G*^E, have been calculated. As an alternative and complementary approach to such investigations, the fluidity () of this binary system has been analyzed by the modified—Batschinski theory. The results are discussed in terms of the specific molecular interactions between the mixture components.     

Analogies between Jahn–Teller and Rashba spin physics

In developing physical theories, analogical reasoning has been found to be very powerful, as attested by a number of important historical examples. An analogy between two apparently different phenomena, once established, allows one to transfer information and bring new concepts from one phenomenon to the other. Here, we discuss an important analogy between two widely different physical problems, namely, the Jahn–Teller distortion in molecular physics and the Rashba spin splitting in condensed matter physics. By exploring their conceptual and mathematical features and by searching for the counterparts between them, we examine the orbital texture in Jahn–Teller systems, as the counterpart of the spin texture of the Rashba physics, and put forward a possible way of experimentally detecting the orbital texture. Finally, we discuss the analogy by comparing the coexistence of linear Rashba + Dresselhaus effects and Jahn–Teller problems for specific symmetries, which allow for nontrivial spin and orbital textures, respectively.     

Synthetic approach for novel bis(α‐aminophosphonic acid) derivatives of chromone containing 1,2,4,3‐triazaphosphole moieties

Terephthalic acid hydrazide ( 1 ) was reacted with phenylphosphonic dichloride to yield bis(1,3,4,2‐oxadiazaphosphole) derivative 3 , which was condensed with α‐aminophosphonic acid derivative 4 to afford bis[(1,2,4,3‐triazaphospholyl)(chromonyl)methylphosphonic acid] derivative 5 . The addition of diethyl phosphite to Schiff bases 9 and 10 derived from the condensation of bis(4‐amino‐1,2,4,3‐triazaphosphole) derivative 6 or bis(4‐phosphorylamino‐1,2,4,3‐triazaphosphole) derivative 7 with 3‐formyl‐6‐methylchromone ( 8 ) yielded bis[(1,2,4,3‐triazaphospholyl)(chromonyl)aminomethylphosphonate] derivative 11 and bis[(1,2,4,3‐triazaphospholyl)(chromonyl)phosphorylamino‐methylphosphonate] derivative 12 , respectively. The structures of all products were established by elemental analysis and spectral data. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:117–122, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20520     

Exceptional kinetic propensity of hydroxymethyl phosphanes toward Rh(III) stabilization in water

The reactions of (HOCH2)2P(C6H4)P(CH2OH)2 (HMPB) and P(CH2OH)3 (THP) with RhCl3.xH2O in aqueous media gave water-soluble complexes cis-[RhCl2{eta2-(HOCH2)2P(C6H4)P(CH2OH)2}2]Cl (3) and fac-[RhCl3(P(CH2OH)3)3] (4) respectively in good yields, X-ray crystal structures of 3 and 4 confirmed their molecular constitution. These reactions provide the first examples demonstrating the kinetic propensity of hydroxymethyl phosphanes to stabilize Rh in +3 oxidation state in water.     

NMR and structural investigations of a nonplanar iron corrolate: modified patterns of spin delocalization and coupling in a slightly saddled chloroiron(III) corrolate radical

An undecasubstituted chloroiron corrolate, octamethyltriphenylcorrolatoiron chloride, (OMTPCorr)FeCl, has been synthesized and studied by X-ray crystallography and (1)H and (13)C NMR spectroscopy. It is found that, although the structure is slightly saddled, the average methyl out-of-plane distance is only 0.63 Angstroms, while it is much greater for the dodecasubstituted porphyrinate analogue (OMTPP)FeCl (1.19 Angstroms) (Cheng, R.-J.; Chen, P.-Y.; Gau, P.-R.; Chen, C.-C.; Peng, S.-M. J. Am. Chem. Soc. 1997, 119, 2563-2569). In addition, the distance of iron from the mean plane of the four macrocycle nitrogens is also smaller for (OMTPCorr)FeCl (0.387 Angstroms) than for (OMTPP)FeCl (0.46 Angstroms). The (1)H and (13)C NMR spectra of (OMTPCorr)FeCl, as well as the chloroiron complexes of triphenylcorrolate, (TPCorr)FeCl; 7,13-dimethyl-2,3,8,12,17,18-hexaethylcorrolate, (DMHECorr)FeCl; 7,8,12,13-tetramethyl-2,3,17,18-tetraethylcorrolate, (TMTECorr)FeCl; and the phenyliron complex of 7,13-dimethyl-2,3,8,12,17,18-hexaethylcorrolate, (DMHECorr)FePh, have been assigned, and the spin densities at the carbons that are part of the aromatic ring of the corrole macrocycle have been divided into the part due to spin delocalization by corrole --> Fe pi donation and the part due to the unpaired electron present on the corrole ring. It is found that although the spin density at the beta-pyrrole positions is fairly similar to that of (TPCorr)FeCl, the meso-phenyl-carbon shift differences delta(m) - delta(p) are opposite in sign of those of (TPCorr)FeCl. This finding suggests that the radical electron is ferromagnetically coupled to the unpaired electrons on iron, rather than antiferromagnetically coupled, as in all of the other chloroiron corrolates. The solution magnetic moment was measured for (OMTPCorr)FeCl and found to be mu(eff) = 4.7 +/- 0.5 micro(B), consistent with S = 2 and ferromagnetic coupling. From this study, two conclusions may be reached about iron corrolates: (1) the spin states of chloroiron corrolates are extremely sensitive to the out-of-plane distance of iron, and (2) pyrrole-H or -C shifts are not useful in delineating the spin state and electron configuration of (anion)iron corrolates.     

Influence of Cyclodextrin Complexation on the in vitro Human Skin Penetration and Retention of the Sunscreen Agent, Oxybenzone

The objective of this study was to investigate the influence of cyclodextrins on the cutaneous availability of the sunscreen oxybenzone. The interaction between oxybenzone and hydrophilic α-, β- and γ-cyclodextrin derivatives was studied in water by phase-solubility analysis. Among the available cyclodextrins, hydroxypropyl-β-cyclodextrin (HP-β-CD) and especially sulfobutylether-β-cyclodextrin (SBE-β-CD) had the greatest solubilizing activity. Ethanol–water solutions containing oxybenzone free or complexed with HP-β-CD or SBE-β-CD were applied to human skin in Franz diffusion cells and the amount of sunscreen permeated into the different cutaneous compartments was determined by HPLC. As much as 20.5% of the oxybenzone applied dose diffused within the skin tissue after 6 h application. Between 39.4% and 54.9% of the penetrated UV filter was localized in the stratum corneum, with no significant difference between uncomplexed oxybenzone or its complex with HP-β-CD. Conversely, the amount retained in the stratum corneum was markedly decreased (ca. 50%) by complexation with SBE-β-CD. Considerable quantities of oxybenzone accumulated into the viable epidermis (5.7% of the applied dose) and dermis (6.2% of the applied dose) from the preparation containing the free UV filter. The sunscreen penetration to the deeper living layers of the skin was remarkably lower (1.0% and 2.0% of applied dose for epidermis and dermis, respectively) upon application of the sunscreen complexed with SBE-β-CD, whereas HP-β-CD had no effect. In addition, photostability experiments demonstrated that SBE-β-CD complexation did not alter the sunscreen photochemical properties.     

Electron impact mass spectrometric investigation of pyrrole mono-, di- and tri-carboxylic acids

The electron impact-induced fragmentation processes of pyrrole-2-, -3-, -2,3-, -3,4-, -2,5- and -2,3,4-carboxylic acids were investigated with the aid of metastable ion, collisional and deuterium labelling experiments. The general behaviour of these compounds is discussed in detail, together with the reasonable structures of the more relevant fragment ions.     

Symmetric incidence groupoids

In [7] point-reflection geometries were studied which can be derived from commutative kinematic spaces without involutory elements. But the class of point-reflection geometries is larger. For example, elliptic planes with their reflections cannot be derived from commutative kinematic spaces. Here we investigate a larger class of reflection geometries.This paper was sponsored by Vigoni Program 1999.