Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Influence of image filters on the reproducibility of measurements of alveolar bone loss

The reproducibility of measurements of alveolar bone loss on radiographs may be a problem on epidemiologic studies, as they are based on comparisons of the diagnosis of various examiners. The aim of the present research paper was to assess the inter- and intra-examiner reproducibility of measurements of the interproximal alveolar bone loss on non-manipulated digital radiographs and after the application of image filters. Five Oral Radiologists measured the distance between the cementoenamel junction (CEJ) to the alveolar crest or to the deepest point of the bony defect on 12 interproximal digital radiographs of molars and bicuspids of a dry human skull. The digital manipulation and the linear measurements were obtained with the Trophy Windows software (Throphy®). For each image, six different versions were created: 1) non-manipulated; 2) bright-contrast adjustment; 3) negative; 4) negative with brightness-contrast adjustment; 5) pseudo-colored; 6) pseudo-colored with brightness-contrast adjustment. In order to prevent interpretation bias because of the repetition of measurements, the examiners measured the radiographs in a random sequence. The two-way ANOVA test at 5% level of significance to compare the means of readings of the same operator with each filter indicated p<0.05 for the majority of operators, while the comparison between the mean values of operators using the same filter indicated p>0.05 for all filters. Based on the results, we concluded that linear measurements of interproximal alveolar bone loss on digital radiographs are highly reproducible among examiners. Nevertheless, the application of image filters significantly influenced the degree of intra-examiner reproducibility. Some filters even reduced the reproducibility of intra-examiner readings.

Nilpotency of the b ghost in the non-minimal pure spinor formalism

The b ghost in the non-minimal pure spinor formalism is not a fundamental field. It is based on a complicated chain of operators and proving its nilpotency is nontrivial. Chandia proved this property in arXiv:1008.1778, but with an assumption on the nonminimal variables that is not valid in general. In this work, the b ghost is demonstrated to be nilpotent without this assumption. © 2013 SISSA, Trieste, Italy.

Semigrupos de operadores lineares aplicados às equações diferenciais parciais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um modelo matemático de suspensão de pontes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Semigrupos de operadores lineares e equações diferenciais em espaços de Banach

Pós-graduação em Matemática Universitária - IGCE

Semigrupos de operadores lineares e aplicações

Pós-graduação em Matemática Universitária - IGCE

Context-sensitive analysis of x86 obfuscated executables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Existência de soluções para equações integrodiferenciais em epaços de Banach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

A squeezed state holomorphic phase space representation of equations of motion

A mapping scheme is presented which takes quantum operators associated to bosonic degrees of freedom into complex phase space integral kernel representatives. The procedure consists of using the Schrödinger squeezed state as the starting point for the construction of the integral mapping kernel which, due to its inherent structure, is suited for the description of second quantized operators. Products and commutators of operators have their representatives explicitly written which reveal new details when compared to the usual q-p phase space description. The classical limit of the equations of motion for the canonical pair q-p is discussed in connection with the effect of squeezing the quantum phase space cellular structure. © 1993.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.