Implicit differential equations with impasse singularities and singular perturbation problems

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

Extension of the Nambu-Jona-Lasinio model predictions at high densities and temperatures using an implicit regularization scheme

Traditional cutoff regularization schemes of the Nambu-Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study quark matter with Fermi momenta larger than the cutoff. In the present work, an extension of the model to high temperatures and densities recently proposed by Casalbuoni, Gatto, Nardulli, and Ruggieri is used in connection with an implicit regularization scheme. This is done by making use of scaling relations of the divergent one-loop integrals that relate these integrals at different energy-momentum scales. Fixing the pion decay constant at the chiral symmetry breaking scale in the vacuum, the scaling relations predict a running coupling constant that decreases as the regularization scale increases, implementing in a schematic way the property of asymptotic freedom of quantum chromodynamics. If the regularization scale is allowed to increase with density and temperature, the coupling will decrease with density and temperature, extending in this way the applicability of the model to high densities and temperatures. These results are obtained without specifying an explicit regularization. As an illustration of the formalism, numerical results are obtained for the finite density and finite temperature quark condensate and applied to the problem of color superconductivity at high quark densities and finite temperature.

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier-Stokes equations of fluid motion coupled with Maxwell's equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function-vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magneto hydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases. (c) 2007 Elsevier B.V. All rights reserved.

DUCTAL CARCINOMA IN-SITU OF THE BREAST - HISTOLOGIC CATEGORIZATION AND ITS RELATIONSHIP TO PLOIDY AND IMMUNOHISTOCHEMICAL EXPRESSION OF HORMONE RECEPTORS, P53, AND C-ERBB-2 PROTEIN

Background. Ductal carcinoma in situ (DCIS) of the breast has been diagnosed increasingly since the advent of mammography. However, the natural history of these lesions remains uncertain. Ductal carcinoma in situ of the breast does not represent a single entity but a heterogeneous group with histologic and clinical differences. The histologic subtype of DCIS seems to have an influence on its biologic behavior, but there are few studies correlating subtype with biologic markers.Methods. The authors studied a consecutive series of 40 cases of DCIS and after its histologic categorization verified its relationship with ploidy using image analysis and analyzing estrogen receptor (ER), progesterone receptor (PR), p53 and c-erbB-2 expression using immunohistochemistry.Results. The three groups proposed according to the grade of malignancy were correlated significantly with some of the additional parameters studied, including aneuploidy and c-erB-2 expression. Aneuploidy was detected in 77.5% of cases of DCIS mainly in high and intermediate grade subtypes (100% and 80% vs. 35.7% in low grade) whereas immunoreactivity for c-erbB-2 was detected in 45% of cases of DCIS mainly in the high grade group. Expression of ER and PR were observed frequently in this study (63.9% and 65.7% respectively), but without correlation with the histologic subtype of DCIS, although we found a somewhat significant association between high grade DCIS and lack of ER. p53 protein expression was detected in 36.8% of these cases, but no relationship between this expression and histologic subtype or grading of DCIS was found.Conclusions. These results provide further evidence for the morphologic and biologic heterogeneity of DCIS. Besides histologic classification and nuclear grading, some biologic markers such as aneuploidy and c-erbB-2 expression constitute additional criteria of high grade of malignancy.

An implicit BEM formulation to model strong discontinuities in solids

A boundary element method (BEM) formulation to predict the behavior of solids exhibiting displacement (strong) discontinuity is presented. In this formulation, the effects of the displacement jump of a discontinuity interface embedded in an internal cell are reproduced by an equivalent strain field over the cell. To compute the stresses, this equivalent strain field is assumed as the inelastic part of the total strain. As a consequence, the non-linear BEM integral equations that result from the proposed approach are similar to those of the implicit BEM based on initial strains. Since discontinuity interfaces can be introduced inside the cell independently on the cell boundaries, the proposed BEM formulation, combined with a tracking scheme to trace the discontinuity path during the analysis, allows for arbitrary discontinuity propagation using a fixed mesh. A simple technique to track the crack path is outlined. This technique is based on the construction of a polygonal line formed by segments inside the cells, in which the assumed failure criterion is reached. Two experimental concrete fracture tests were analyzed to assess the performance of the proposed formulation.

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Image categorization through optimum path forest and visual words

Different from the first attempts to solve the image categorization problem (often based on global features), recently, several researchers have been tackling this research branch through a new vantage point - using features around locally invariant interest points and visual dictionaries. Although several advances have been done in the visual dictionaries literature in the past few years, a problem we still need to cope with is calculation of the number of representative words in the dictionary. Therefore, in this paper we introduce a new solution for automatically finding the number of visual words in an N-Way image categorization problem by means of supervised pattern classification based on optimum-path forest. © 2011 IEEE.

Implicit R&D strategy and investment-linked R&D: a study of the R&D programme of the Argentina steel firm Acindar, SA

Includes bibliography

Eigenvalue analyses for non-transposed three-phase transmission line considering non-implicit ground wires

This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency range considered in this case. This transformation matrix is an approximation to the exact transformation matrix. For those elements related to the phases of the considered system, the transformation matrix is composed of the elements of Clarke's matrix. In part related to the ground wires, the elements of the transformation matrix must establish a relationship with the elements of the phases considering the establishment of a single homopolar reference in the mode domain. In the case of three-phase lines with the presence of two ground wires, it is unable to get the full diagonalization of the matrices Z and Y in the mode domain. This leads to the second proposal for the composition of real transformation matrix: obtain such transformation matrix from the multiplication of two real and constant matrices. In this case, the inclusion of a second matrix had the objective to minimize errors from the first proposal for the composition of the transformation matrix mentioned. © 2012 IEEE.

Public institutions and explicit and implicit environmental policies

Includes bibliography

Explicit and implicit knowledge of environment states induce adaptation in postural control

The aim of this study was to investigate the effects of explicit and implicit knowledge about visual surrounding manipulation on postural responses. Twenty participants divided into two groups, implicit and explicit, remained in upright stance inside a moving room. In the fourth trial participants in the explicit group were informed about the movement of the room while participants in the implicit group performed the trial with the room moving at a larger amplitude and higher velocity. Results showed that postural responses to visual manipulation decreased after participants were told that the room was moving as well as after increasing amplitude and velocity of the room, indicating decreased coupling (down-weighting) of the visual influences. Moreover, this decrease was even greater for the implicit group compared to the explicit group. The results demonstrated that conscious knowledge about environmental state changes the coupling to visual information, suggesting a cognitive component related to sensory re-weighting. Re-weighting processes were also triggered without awareness of subjects and were even more pronounced compared to the first case. Adaptive re-weighting was shown when knowledge about environmental state was gathered explicitly and implicitly, but through different adaptive processes. (C) 2014 Elsevier Ireland Ltd. All rights reserved.

A simple application of implicit function theorem

In this note we show that the roots of a polynomial are C∞ depend of the coefficients. The main tool to show this is the Implicit Function Theorem.

On symmetries of singular implicit ODEs

We study implicit ODEs, cubic in derivative, with infinitesimal symmetry at singular points. Cartan showed that even at regular points the existence of nontrivial symmetry imposes restrictions on the ODE. Namely, this algebra has the maximal possible dimension 3 iff the web of solutions is flat. For cubic ODEs with flat 3-web of solutions we establish sufficient conditions for the existence of nontrivial symmetries at singular points and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling is some coordinates. We use this symmetry to find first integrals of the ODE.

On the solvability of implicit differential inclusions

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.