Malcev dialgebras

We apply Kolesnikov's algorithm to obtain a variety of nonassociative algebras defined by right anticommutativity and a "noncommutative" version of the Malcev identity. We use computer algebra to verify that these identities are equivalent to the identities of degree up to 4 satisfied by the dicommutator in every alternative dialgebra. We extend these computations to show that any special identity for Malcev dialgebras must have degree at least 7. Finally, we introduce a trilinear operation which makes any Malcev dialgebra into a Leibniz triple system.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

Functionalization of gold and silver nanoparticles with diphenyl dichalcogenides probed by surface enhanced Raman scattering

This paper describes a surface-enhanced Raman scattering (SERS) systematic investigation regarding the functionalization of gold (Au) and silver (Ag) nanoparticles with diphenyl dichalcogenides, i.e. diphenyl disulfide, diphenyl diselenide, and diphenyl ditelluride. Our results showed that, in all cases, functionalization took place with the cleavage of the chalcogenchalcogen bond on the surface of the metal. According to our density functional theory calculations, the molecules assumed a tilted orientation with respect to the metal surface for both Au and Ag, in which the angle of the phenyl ring relative to the metallic surface decreased as the mass of the chalcogen atom increased. The detected differences in the ordinary Raman and SERS spectra were assigned to the distinct stretching frequencies of the carbonchalcogen bond and its relative contribution to the ring vibrational modes. In addition, the SERS spectra showed that there was no significant interaction between the phenyl ring and the surface, in agreement with the tilted orientation observed from our density functional theory calculations. The results described herein indicate that diphenyl dichalcogenides can be successfully employed as starting materials for the functionalization of Au nanoparticles with organosulfur, organoselenium, and organotellurium compounds. On the other hand, diphenyl disulfide and diphenyl diselenide could be employed for the functionalization of Ag nanoparticles, while the partial oxidation of the organotellurium unit could be detected on the Ag surface. Copyright (C) 2011 John Wiley & Sons, Ltd.

ON THE RADICAL OF A FREE MALCEV ALGEBRA

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

Directed Flow of Identified Particles in Au plus Au Collisions at root S-NN=200 GeV at RHIC

STAR's measurements of directed flow (v(1)) around midrapidity for pi(+/-), K-+/-, K-S(0), p, and (p) over bar in Au + Au collisions at root s(NN) = 200 GeV are presented. A negative v(1) (y) slope is observed for most of produced particles (pi(+/-), K-+/-, K-S(0), p, and (p) over bar). In 5%-30% central collisions, a sizable difference is present between the v(1)(y) slope of protons and antiprotons, with the former being consistent with zero within errors. The v(1) excitation function is presented. Comparisons to model calculations (RQMD, UrQMD, AMPT, QGSM with parton recombination, and a hydrodynamics model with a tilted source) are made. For those models which have calculations of v(1) for both pions and protons, none of them can describe v(1()y) forpions and protons simultaneously. The hydrodynamics model with a tilted source as currently implemented cannot explain the centrality dependence of the difference between the v(1)(y) slopes of protons and antiprotons.

Counting singularities via fitting ideals

The stable singularities of differential map germs constitute the main source of studying the geometric and topological behavior of these maps. In particular, one interesting problem is to find formulae which allow us to count the isolated stable singularities which appear in the discriminant of a stable deformation of a finitely determined map germ. Mond and Pellikaan showed how the Fitting ideals are related to such singularities and obtain a formula to count the number of ordinary triple points in map germs from C-2 to C-3, in terms of the Fitting ideals associated with the discriminant. In this article we consider map germs from (Cn+m, 0) to (C-m, 0), and obtain results to count the number of isolated singularities by means of the dimension of some associated algebras to the Fitting ideals. First in Corollary 4.5 we provide a way to compute the total sum of these singularities. In Proposition 4.9, for m = 3 we show how to compute the number of ordinary triple points. In Corollary 4.10 and with f of co-rank one, we show a way to compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. Furthermore, we show in some examples how to calculate the number of isolated singularities using these results.

Study of postures in sugarcane cutters in the Pontal of Paranapanema-SP, Brazil

The expansion of sugarcane monoculture in Brazil in the last decades has pointed out to the necessity of considering the question of sugarcane cutters occupational health. In this work we present a cross-sectional study aiming to examine the occupational posture of a group of sugarcane cutters, which work in a cane field located in the region of Pontal do Paranapanema-SP, Brazil. The study was made using the Ergonomic Analysis of Work - EAW methodology and the postural analysis method by Win-OWAS. Through the obtained records of postures, it was observed that during a workday the sugarcane cutters remain standing erect on two legs or in one leg 66% of the time and that their trunk remain tilted and in rotation, according to 63% of the positions categorized. It was also observed that the sugarcane cutter trunk performs repetitive and boundless movements during his routine of work, which can expose this individual to additional wear of their musculoskeletal functions. The activities in which the individual engages have favorable or adverse influence on his posture. The repetitive movements involved in specialized occupations are equivalent to repeated exercises, thus may be responsible for the excessive development of certain muscle groups. The study suggests that the postures adopted by sugarcane cutters can overload their musculoskeletal system and predispose the cutters to work-related musculoskeletal diseases.

delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras

In the paper, a complete description of the delta-derivations and the delta-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p not equal 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

Partial projective representations and partial actions II

This paper is a continuation of Dokuchaev and Novikov (2010) [8]. The interaction between partial projective representations and twisted partial actions of groups considered in Dokuchaev and Novikov (2010) [8] is treated now in a categorical language. In the case of a finite group G, a structural result on the domains of factor sets of partial projective representations of G is obtained in terms of elementary partial actions. For arbitrary G we study the component pM'(G) of totally-defined factor sets in the partial Schur multiplier pM(G) using the structure of Exel's semigroup. A complete characterization of the elements of pM'(G) is obtained for algebraically closed fields. (C) 2011 Elsevier B.V. All rights reserved.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

Rappresentazioni lineari di SL3(C)

Espongo i fatti di base della teoria delle rappresentazioni con lo scopo di indagare i possibili modi in cui un dato gruppo di Lie o algebra di Lie agisce su uno spazio vettoriale di dimensione finita. Tali risultati verranno applicati all'algebra di Lie del gruppo speciale lineare.

Liquid crystal polymer brushes and their application as alignment layers in liquid crystal cells

Liquid Crystal Polymer Brushes and their Application as Alignment Layers in Liquid Crystal Cells Polymer brushes with liquid crystalline (LC) side chains were synthesized on planar glass substrates and their nematic textures were investigated. The LC polymers consist of an acrylate or a methacrylate main chain and a phenyl benzoate group as the mesogenic unit which is connected to the main chain via a flexible alkyl spacer composed of six CH2 units. The preparation of the LC polymer brushes was carried out according to the “grafting from” technique: polymerization is carried out from azo-initiators that have been previously self-assembled on the substrate. LC polymer brushes with a thickness from a few nm to 230 nm were synthesized by varying the monomer concentration and the polymerization time. The LC polymer brushes were thick enough to allow for direct observation of the nematic textures with a polarizing microscope. The LC polymer brushes grown on untreated glass substrates exhibited irregular textures (“polydomains”). The domain size is in the range of some micrometers and depends only weakly on the brush thickness. The investigations on the texture-temperature relationship of the LC brushes revealed that the brushes exhibit a surface memory effect, that is, the identical texture reappears after the LC brush sample has experienced a thermal isotropization or a solvent treatment, at which the nematic LC state has been completely destroyed. The surface memory effect is attributed to a strong anchoring of the orientation of the mesogenic units to heterogeneities at the substrate surface. The exact nature of the surface heterogeneities is unknown. The effect was observed for the LC brushes swollen with low molecular weight nematic molecules, as well. Rubbing the glass substrate with a piece of velvet cloth prior to the surface modification with the initiator and the brush growth gives rise to the formation of homogenous alignment of the mesogenic units in the LC polymer side chains. Monodomain textures were obtained for these LC brushes. The mechanism for the homogeneous alignment is based on the transfer of Nylon fibers during the rubbing process. A surfactant was mixed with the azo-initiator in modifying rubbed substrates for subsequent brush generation. Such brushes exhibited biaxial optical properties. Hybrid LC cells made from a substrate modified with biaxial brushes and a rubbed glass substrate show an orientation with a tilt angle of a = –15.6 . This work shows that LC brushes grown on rubbed surfaces fulfill the important criteria for alignment layers: the formation of macroscopic monodomains. First results indicate that by diluting the brush with molecules which are also covalently bound to the surface but induce a different orientation, a system is obtained in which the two conflicting alignment mechanisms can be used to generate a tilted alignment. In order to allow for an application of the alignment layers into a potential product, subsequent work should focus on the questions how easy and in which range the tilt angle can be controlled.

Expressiveness in biologically inspired languages

A very recent and exciting new area of research is the application of Concurrency Theory tools to formalize and analyze biological systems and one of the most promising approach comes from the process algebras (process calculi). A process calculus is a formal language that allows to describe concurrent systems and comes with well-established techniques for quantitative and qualitative analysis. Biological systems can be regarded as concurrent systems and therefore modeled by means of process calculi. In this thesis we focus on the process calculi approach to the modeling of biological systems and investigate, mostly from a theoretical point of view, several promising bio-inspired formalisms: Brane Calculi and k-calculus family. We provide several expressiveness results mostly by means of comparisons between calculi. We provide a lower bound to the computational power of the non Turing complete MDB Brane Calculi by showing an encoding of a simple P-System into MDB. We address the issue of local implementation within the k-calculus family: whether n-way rewrites can be simulated by binary interactions only. A solution introducing divergence is provided and we prove a deterministic solution preserving the termination property is not possible. We use the symmetric leader election problem to test synchronization capabilities within the k-calculus family. Several fragments of the original k-calculus are considered and we prove an impossibility result about encoding n-way synchronization into (n-1)-way synchronization. A similar impossibility result is obtained in a pure computer science context. We introduce CCSn, an extension of CCS with multiple input prefixes and show, using the dining philosophers problem, that there is no reasonable encoding of CCS(n+1) into CCSn.