A Note On the Statistical Difference of Small Direct Products

We demonstrate that if two probability distributions D and E of sufficiently small min-entropy have statistical difference ε, then the direct-product distributions D^l and E^l have statistical difference at least roughly ε\s√l, provided that l is sufficiently small, smaller than roughly ε^{4/3}. Previously known bounds did not work for few repetitions l, requiring l>ε^2.

Boxicity and cubicity of product graphs

The boxicity (cubicity) of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in R-k. In this article, we give estimates on the boxicity and the cubicity of Cartesian, strong and direct products of graphs in terms of invariants of the component graphs. In particular, we study the growth, as a function of d, of the boxicity and the cubicity of the dth power of a graph with respect to the three products. Among others, we show a surprising result that the boxicity and the cubicity of the dth Cartesian power of any given finite graph is, respectively, in O(log d/ log log d) and circle dot(d/ log d). On the other hand, we show that there cannot exist any sublinear bound on the growth of the boxicity of powers of a general graph with respect to strong and direct products. (C) 2015 Elsevier Ltd. All rights reserved.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

La melancolía en Atlántida de Oscar Villegas : representación teatral del carácter nacional mexicano

Les images qui représentent le Mexicain le montrent habituellement sous les traits d’un être extrêmement mélancolique qui fait face à un destin tragique. Les nombreux mythes entourant le Mexicain, issus de la culture même, sont effectivement reliés de près ou de loin à la peur et la tristesse, soit deux composantes essentielles de la mélancolie. L’anthropologue Roger Bartra dans La jaula de la melancolía: identidad y metamorfosis del mexicano analyse ces éléments clés qui constitueraient la personnalité du Mexicain. L’objectif de cette recherche est de démontrer que Atlántida d’Oscar Villegas est l’œuvre par excellence qui représente cette mélancolie toute mexicaine. Dans sa pièce de théâtre, Villegas raconte l’histoire d’une jeune artiste de cabaret qui vit de nombreuses désillusions dans un monde vulgaire et pervers où les valeurs humaines font défaut. Le dramaturge met en scène le Mexico urbain des années quarante et montre le désespoir et l’impossibilité pour les habitants de ses quartiers pauvres de changer le cours de leur vie. En plus d’être une pièce de théâtre qui, tant au niveau de son contenu que de sa forme, porte en elle les marques de la mélancolie, Atlántida met en relief ces caractéristiques devenues au fil du temps représentatives de l’image nationale du Mexicain. L’étude de cette œuvre s’appuie sur les théories d’analyse du texte théâtral d’Anne Ubersfeld qui propose une approche centrée sur l’action et les conditions de communication contenues dans les dialogues. Faire le pont entre la pièce de théâtre de Villegas et l’essai de Bartra permet d’explorer le lien intrinsèque qui semble s’établir entre Mexicain et mélancolie.

Exam 2001 pdf

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Exam 2001

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Formulation of the standard model in terms of spinor fields

We propose an alternative formulation of the Standard Model which reduces the number of free parameters. In our framework, fermionic fields are assigned to fundamental representations of the Lorentz and the internal symmetry groups, whereas bosonic field variables transform as direct products of fundamental representations of all symmetry groups. This allows us to reduce the number of fundamental symmetries. We formulate the Standard Model by considering the SU(3) and SU(2) symmetry groups as the underlying symmetries of the fundamental interactions. This allows us to suggest a model, for the description of the interactions of the intermediate bosons among themselves and interactions of fermions, that makes use of just two parameters. One parameter characterizes the symmetric phase, whereas the other parameter (the asymmetry parameter) gives the breakdown strength of the symmetries. All coupling strengths of the Standard Model are then derived in terms of these two parameters. In particular, we show that all fermionic electric charges result from symmetry breakdown.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

Efeitos de inseticidas na sobrevivência e no comportamento de abelhas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Starch distribution in pear tree organs in relation to training systems, rootstocks and fruit quality

Starch is the main form in which plants store carbohydrates reserves, both in terms of amounts and distribution among different plant species. Carbohydrates are direct products of photosynthetic activity, and it is well know that yield efficiency and production are directly correlated to the amount of carbohydrates synthesized and how these are distributed among vegetative and reproductive organs. Nowadays, in pear trees, due to the modernization of orchards, through the introduction of new rootstocks and the development of new training systems, the understanding and the development of new approaches regarding the distribution and storage of carbohydrates, are required. The objective of this research work was to study the behavior of carbohydrate reserves, mainly starch, in different pear tree organs and tissues: i.e., fruits, leaves, woody organs, roots and flower buds, at different physiological stages during the season. Starch in fruit is accumulated at early stages, and reached a maximum concentration during the middle phase of fruit development; after that, its degradation begins with a rise in soluble carbohydrates. Moreover, relationships between fruit starch degradation and different fruit traits, soluble sugars and organic acids were established. In woody organs and roots, an interconversion between starch and soluble carbohydrates was observed during the dormancy period that confirms its main function in supporting the growth and development of new tissues during the following spring. Factors as training systems, rootstocks, types of bearing wood, and their position on the canopy, influenced the concentrations of starch and soluble carbohydrates at different sampling dates. Also, environmental conditions and cultural practices must be considered to better explain these results. Thus, a deeper understanding of the dynamics of carbohydrates reserves within the plant could provide relevant information to improve several management practices to increase crop yield efficiency.

A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Direct Observation of Photodissociation Products from Phenylperoxyl Radicals Isolated in the Gas Phase

Gas phase peroxyl radicals are central to our chemical understanding of combustion and atmospheric processes and are typically characterized by strong absorption in the UV (lambda(max) approximate to 240 nm). The analogous maximum absorption feature for arylperoxyl radicals is predicted to shift to the visible but has not previously been characterized nor have any photoproducts arising from this transition been identified. Here we describe the controlled synthesis and isolation in vacuo of an array of charge-substituted phenylperoxyl radicals at room temperature, including the 4-(N,N,N-trimethylammonium)methyl phenylperoxyl radical cation (4-Me3N[+]CH2-C6H4OO center dot), using linear ion-trap mass spectrometry. Photodissociation mass spectra obtained at wavelengths ranging from 310 to 500 nm reveal two major photoproduct channels corresponding to homolysis of aryl-OO and arylO-O bonds resulting in loss of O-2 and O, respectively. Combining the photodissociation yields across this spectral window produces a broad (FWHM approximate to 60 nm) but clearly resolved feature centered at lambda(max) = 403 nm (3.08 eV). The influence of the charge-tag identity and its proximity to the radical site are investigated and demonstrate no effect on the identity of the two dominant photoproduct channels. Electronic structure calculations have located the vertical (B) over tilde <- (X) over tilde transition of these substituted phenylperoxyl radicals within the experimental uncertainty and further predict the analogous transition for unsubstituted phenylperoxyl radical (C6H5OO center dot) to be 457 nm (2.71 eV), nearly 45 nm shorter than previous estimates and in good agreement with recent computational values.

Isolation and characterization of charge-tagged phenylperoxyl radicals in the gas phase : direct evidence for products and pathways in low temperature benzene oxidation

The phenylperoxyl radical has long been accepted as a critical intermediate in the oxidation of benzene and an archetype for arylperoxyl radicals in combustion and atmospheric chemistry. Despite being central to many contemporary mechanisms underpinning these chemistries, reports of the direct detection or isolation of phenylperoxyl radicals are rare and there is little experimental evidence connecting this intermediate with expected product channels. We have prepared and isolated two charge-tagged phenyl radical models in the gas phase [i.e., 4-(N,N,N-trimethylammonium) phenyl radical cation and 4-carboxylatophenyl radical anion] and observed their reactions with dioxygen by ion-trap mass spectrometry. Measured reaction rates show good agreement with prior reports for the neutral system (k(2)[(Me3N+)C6H4 center dot + O-2] = 2.8 x 10(-11) cm(3) molecule(-1) s(-1), Phi = 4.9%; k(2)[(-O2C)C6H4 center dot + O-2] = 5.4 x 10(-1)1 cm(3) molecule(-1) s(-1), Phi = 9.2%) and the resulting mass spectra provide unequivocal evidence for the formation of phenylperoxyl radicals. Collisional activation of isolated phenylperoxyl radicals reveals unimolecular decomposition by three pathways: (i) loss of dioxygen to reform the initial phenyl radical; (ii) loss of atomic oxygen yielding a phenoxyl radical; and (iii) ejection of the formyl radical to give cyclopentadienone. Stable isotope labeling confirms these assignments. Quantum chemical calculations for both charge-tagged and neutral phenylperoxyl radicals confirm that loss of formyl radical is accessible both thermodynamically and entropically and competitive with direct loss of both hydrogen atom and carbon dioxide.