Symmetries induced by conserved vector currents in the theory of a scalar field

Let us consider a quantum theory of one scalar, real, local, Poincaré covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsA _{in out} (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the charge of every real, hermitean, locally conserved, Poincaré covariant quantum (pseudo) vector fieldj (x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincaré invariant generators.Our arguments can be easily extended to a theory of one complex scalar field, in this case the only symmetry transformation induced by a current can be the gauge transformation.We prove also that under very weak assumptions two fields related to each other by a unitary (or similarity) transformation are equal barring some patological cases.     

On the multi‐colored Ramsey numbers of cycles

For a graph L and an integer k≥2, R_k(L) denotes the smallest integer N for which for any edge‐coloring of the complete graph K_N by k colors there exists a color i for which the corresponding color class contains L as a subgraph. Bondy and Erdos conjectured that, for an odd cycle C_n on n vertices, They proved the case when k = 2 and also provided an upper bound R_k(C_n)≤(k+ 2)!n. Recently, this conjecture has been verified for k = 3 if n is large. In this note, we prove that for every integer k≥4, When n is even, Sun Yongqi, Yang Yuansheng, Xu Feng, and Li Bingxi gave a construction, showing that R_k(C_n)≥(k?1)n?2k+ 4. Here we prove that if n is even, then © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 169‐175, 2012     

Serre Problem for Unbounded Pseudoconvex Reinhardt Domains in ℂ<Superscript>2</Superscript>

We give a characterization of non-hyperbolic pseudoconvex Reinhardt domains in ℂ² for which the answer to the Serre problem is positive. Moreover, all non-hyperbolic pseudoconvex Reinhardt domains in ℂ² with non-compact automorphism group are explicitly described.     

Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.     

Spectral Studies on Cyclic Chromotropic Acid Tetramers and Their Interaction with Metal Ions

Abstract

With comparable molar quantities, chromotropic acid reacts with compounds containing aldehyde groups -CHO e.g. with formadehyde or glyoxylic acid to form cyclic compounds with rings containing four chromotropic acid fragments — cyclotetrachromotropylene derivatives. The cyclic compounds, due to the presence of a cavity in the molecule, can play the part of host and complex smaller molecules, which has been confirmed on the basis of triethylamine by the ¹H-NMR measurements. Using spectrophotometric method the stability constant of 1:1 complex formed between Ti(IV) and cyclic compound chromotropic acid with formaldehyde has been determined - K = (9,0 ± 0,1) 10⁴.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Gold Surface Functionalization with S‐containing Organic Compounds and Gold Nanoparticles for Ethylene Glycol Electrooxidation

In this work a gold electrode modified with self‐assembled layers (SAMs) composed with organic S‐containing compound and gold nanoparticles was prepared. The electrode with SAMs endowed with gold nanoparticles gave the high catalytic effect for ethylene glycol (EG) electrooxidation in solution at pH 7. For this novel sensor a linear relationship between the current response of EG at the potential of peak maximum (j_p) and the concentration of this compound in solution (c_EG) was found over the range 0.1 µM to 0.7 M with the detection sensitivity j_p/c_EG equal to about 5 A cm^?2 mol^?1 dm³ (at v=0.1 V s^?1) and the detection limit of 0.046 µM.     

Stability of Ibuprofen in its Inclusion Complex with β-Cyclodextrin

The ibuprofen--cyclodextrin inclusion complex was prepared by theco-precipitation method. The identity of the obtained product was verified by X-ray and thermogravimetric techniques. The effect of -cyclodextrin on the stability of ibuprofen was analysed.     

pH gradient reversed-phase liquid chromatography as a fractionation tool for the separation of peptides

Recent reports from our laboratory presented a comprehensive theory and demonstrated feasibility of reversed-phase liquid chromatography (RP-LC) employing the programmed gradient of pH of the mobile phase. The aim of that work was to explore the usefulness of the pH gradient-based approach in fractionation of peptides. The experiments were performed on a series of peptides separated at various LC conditions. Retention parameters of peptides in the pH gradient and in the simultaneous pH/organic modifier gradient RP-LC were compared. The best results were obtained with eluents comprising low but constant concentrations of organic modifier while gradient of pH in the mobile phase was developed several times during each chromatographic run. The elaborated LC conditions allowed controlling the elution of peptides not only according to their hydrophobic properties, but also taking into account their electronic properties, represented by isoelectric point (pI) values. The combination of isocratic (regarding organic modifier) LC mode with recurring eluent pH gradient is proposed as an effective fractionation method of peptide mixtures. Moreover, information on hydrophobicity and pI of the peptides, obtained by that approach, might be an additional peptides database matching constraint. Hence, a new tool for analytical and bioinformatics studies of peptides fractionation is proposed.