Formal multiplications, bialgebras of distributions and nonassociative Lie theory

We describe the general nonassociative version of Lie theory that relates unital formal multiplications (formal loops), Sabinin algebras and nonassociative bialgebras.     

On Ovals of Riemann Surfaces of Even Genera

Let X be a Riemann surface of genus g2. A symmetry of of X is an antiholomorphic involution acting of X. A classical theorem of Harnack states that the set Fix () of fixed points of is either emplty or it consists of g+1 disjoint simple closed curves called, following Hilberts terminology, the ovals of . A Riemann surface admitting a symmetry corresponds to a real algebraic curve and nonconjugate symmetries correspond to different real models of the curve. The number of ovals of the symmetry equals the number of connected components of the corresponding real model. It is well known that two symmetries of a Riemann surface of genus g have at most 2g+2 ovals, and the bound is attained for every genus and just for commuting symmetries. Natanzon showed that three and four nonconjugate symmetries of a Riemann surface of genus g have at most 2g+4 and 2g+8 ovals respectively, and these bounds are attained for every odd genus and for commuting symmetries. Natanzon found that a Riemann surface of genus g has at most 2( +1) nonconjugate symmetries and, again, this bound is attained for infinitely many of g. Recently we have showed that a Riemann surface of even genus g admits at most four symmetries. Our aim here is to show, using NEC groups and combinatorial methods, that three nonconjugate symmetries of a surface of even genus g has at most 2g+3 ovals and, surprisingly, if such a surface admits four nonconjugate symmetries then its total number of ovals does not exceed 2g+2. Furthermore, we show that this last bound is sharp for every even genus g and for surfaces with automorphism group D _n × Z₂, for each n dividing 2g.     

Real forms of a Riemann surface of even genus

Natanzon proved that a Riemann surface of genus has at most conjugacy classes of symmetries, and this bound is attained for infinitely many genera . The aim of this note is to prove that a Riemann surface of even genus has at most four conjugacy classes of symmetries and this bound is attained for an arbitrary even as well. An equivalent formulation in terms of algebraic curves is that a complex curve of an even genus has at most four real forms which are not birationally equivalent.

     

C18 solid-phase isolation and high-performance liquid chromatography/ultraviolet diode array determination of fully methoxylated flavones in citrus juices

A new analytical methodology for the determination of fully methoxylated flavones (FMFs) in citrus juices is described. Isolation of the FMFs is carried out by percolation of 30 mL of clarified citrus juice (to which tetramethyl-o-kaempferol is previously added as internal standard) through a C18 Sep-Pak cartridge, washing with 3 mL of water followed by 5 mL of water/acetonitrile (3:1), and selective elution of the retained FMFs with 5 mL of water/acetonitrile (9:11). Determination of the isolated FMFs is carried out by reversed-phase high-performance liquid chromatography (HPLC) and UV diode array detection (DAD). Signals at wavelengths 320, 335, and 345 nm (bandwidth 4 nm) are simultaneously acquired, stored, plotted, and integrated. The column used is a microbore (200 x 2.1-mm) Hypersil ODS 5 microns. Elution is in gradient mode, using a ternary mobile phase (water/acetonitrile/tetrahydrofuran). Column temperature is 40 degrees C. Recovery yields are nearly 100% for all the FMFs detected and identified: isosinensetin, hexamethyl-o-gossypetin, sinensetin, tetramethyl-o-isoscutellarein, hexamethyl-o-quercetagetin, nobiletin, tetramethyl-o-scutellarein, heptamethoxyflavone, and tangeretin. Chromatographic separation of the FMFs is extremely dependent upon the minor changes of the mobile phase composition and percentages, gradient rate, and temperature. The UV spectra (230 to 400 nm) of the FMFs obtained under chromatographic conditions are given. The FMFs relative response factors at 320, 335, and 345 nm and their concentrations in hand-squeezed and commercial concentrated orange and mandarin juices are tabulated. The FMF concentration differences found among samples are discussed.     

14-helical folding in a cyclobutane-containing beta-tetrapeptide

The efficient synthesis of tetrapeptide 5 containing, in alternation, cyclobutane and beta-alanine residues is described. NMR experiments both at low temperature in CDCl(3) and at 298 K in DMSO-d(6) solutions show the contribution of a strong hydrogen bond in the folded major conformation of 5. Temperature coefficients and diffusion times point out a hydrogen bond involving the NH proton from the cyclobutane residue 1 whereas NOEs manifest the high rigidity of the central fragment of the molecule and are compatible with a 14-membered macrocycle. Theoretical calculations predict a most stable folded conformation corresponding to a 14-helix stabilized by a hydrogen bond between NH(10) in the first residue and OC(25) in the third residue. This structure remains unaltered during the molecular dynamics simulation at 298 K in chloroform. All these results provide evidence for a 14-helical folding and reveal the ability of cis-2-aminocyclobutane carboxylic acid residues to promote folded conformations when incorporated into beta-peptides.     

Changing shapes: adiabatic dynamics of composite solitary waves

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite nonlinear non-dispersive waves points to variations in shape.     

Identification of surgical practice patterns using evolutionary cluster analysis

Modern data analysis and machine learning are strongly dependent on efficient search techniques. However, in general, further exploration into high-dimensional and multi-modal spaces is needed, and moreover, many real-world problems exhibit inaccurate, noisy, discrete and complex data. Thus, robust methods of optimization are often required to generate results suitable for these data. Some algorithms that imitate certain natural principles, namely the so-called evolutionary algorithms, have been used in different fields with great success. In this paper, we apply a variant of Particle Swarm Optimization (PSO), recently introduced by the authors, to partitional clustering of a real-world data set to distinguish between perioperative practices and associate them with some unknown relevant facts. Our data were obtained from a survey conducted in Spain based on a pool of colorectal surgeons. The PSO derivative we consider here: (i) is adapted to consider mixed discrete-continuous optimization, with statistical clustering criteria arranged to take these types of mixed measures; (ii) is able to find optimum or near-optimum solutions much more efficiently and with considerably less computational effort because of the richer population diversity it introduces; and (iii) is able to select the right parameter values through self-adaptive dynamic parameter control, thus overcoming the cumbersome aspect common to all metaheuristics.     

Solvent extraction of zinc with 5,7-dichloro-2-methyl-8-hydroxyquinoline into chloroform

The distribution equilibria of the zinc complex with 5,7-dichloro-2-methyl-8-hydroxyquinoline in the water-chloroform system have been studied at 25 degrees . The influence of pH, reagent and metal concentrations, and the presence of sodium perchlorate in the aqueous phase has been determined. From quantitative evaluation of the extraction equilibrium data, it has been deduced that the complex extracted is the simple 1:2 chelate, ZnR(2), although at ligand concentrations higher than 0.3M, the self-adduct complex seems to begin to form. The extraction constant of the ZnR(2) species, refined by means of the program Letagrop-Distribution, has the value log K(ex) = - 6.15 +/- 0.07.     

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat-kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero-energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat-kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey–DeWitt heat-kernel expansion.