Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.

Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by using NN and 3N potential models

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

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

A partial least squares and principal component regression study of quinone compounds with trypanocidal activity

A quantitative structure-activity relationship (QSAR) study of 19 quinone compounds with trypanocidal activity was performed by Partial Least Squares (PLS) and Principal Component Regression (PCR) methods with the use of leave-one-out crossvalidation procedure to build the regression models. The trypanocidal activity of the compounds is related to their first cathodic potential (Ep(c1)). The regression PLS and PCR models built in this study were also used to predict the Ep(c1) of six new quinone compounds. The PLS model was built with three principal components that described 96.50% of the total variance and present Q(2) = 0.83 and R-2 = 0.90. The results obtained with the PCR model were similar to those obtained with the PLS model. The PCR model was also built with three principal components that described 96.67% of the total variance with Q(2) = 0.83 and R-2 = 0.90. The most important descriptors for our PLS and PCR models were HOMO-1 (energy of the molecular orbital below HOMO), Q4 (atomic charge at position 4), MAXDN (maximal electrotopological negative difference), and HYF (hydrophilicity index).

Patients' Expectations of and Satisfaction with Implant-Supported Fixed Partial Dentures and Single Crowns

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

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Attentional disorders in patients with complex partial epilepsy

A study of concentrated attention patterns in epileptic patients was conducted with the objectives: characterization of the patients' epileptic condition; assessment of the concentrated attention levels in epileptic and nonepileptic individuals; comparison of the attention levels of the two groups. An evaluation was performed of 50 adult outpatients with complex partial seizures and 20 non-epileptic individuals (comparative group) at the Neuroepilepsy Ambulatory Unit, State University of Campinas SP, Brazil. Method: characterization of seizure types, frequency and duration; concentrated attention assessment (Concentrated Attention Test - Toulouse-Piéron); comparison of the epileptic with non-epileptic individuals. Results: A statistically significant difference was observed between the groups with regard to Correct Response, Wrong Response and No Response. A difference was observed in relation to Time, but it was statistically insignificant. The epileptic patients presented inferior cognitive performance in relation to concentrated attention when compared with the non-epileptic individuals, findings compatible with the clinical complaints.

Retention strength of cobalt-chromium vs nickel-chromium titanium vs Cp titanium in a cast framework association of removable partial overdenture

Aim: There is little information considering the framework association between cast clasps and attachments. The aim of this study was to evaluate the retention strength of frameworks match circumferential clasps and extra resilient attachment cast in three different alloys (cobalt-chromium, nickel-chromium titanium and commercially pure titanium), using two undercut (0.25 and 0.75 mm) and considering different period of time (0, 1/2, 1, 2, 3, 4 and 5 years). Methods: Using two metallic matrices, representing a partially edentulous mandibular right hemiarch with the first molar crown, canine root and without premolars, 60 frameworks were fabricated. Three groups (n = 20) of each metal were cast and each group was divided into two subgroups (n = 10), corresponding the molar undercut of 0.25 mm and 0.75 mm. The nylon male was positioned at the matrix and attached to the acrylic resin of the prosthetic base. The samples were subjected to an insertion and removal test under artificial saliva environment. Results: The data were analyzed and compared with ANOVAs and Tukey's test at 95% of probability. The groups cast in cobaltchromium and nickel-chromium-titanium had the highest mean retention strength (5.58 N and 6.36 N respectively) without significant difference between them, but statistically different from the group cast in commercially pure titanium, which had the lowest mean retention strength in all the periods (3.46 N). The association frameworks using nickel-chromium-titanium and cobalt-chromium could be used with 0.25 mm and 0.75 mm of undercut, but the titanium samples seems to decrease the retention strength, mainly in the 0.75 mm undercut. The circumferential clasps cast in commercially pure titanium used in 0.75 mm undercuts have a potential risk of fractures, especially after the 2nd year of use. Conclusion: This in vitro study showed that the framework association between cast clasp and an extra resilient attachment are suitable to the three metals evaluated, but strongly suggest extra care with commercially pure titanium in undercut of 0.75 mm. Clinical significance: Frameworks fabricated in Cp Ti tend to decrease in retentive strength over time and have a potential risk of fracture in less than 0.75 mm of undercut.

Effect of axial loads on implant-supported partial fixed prostheses by strain gauge analysis

Objectives: The present study used strain gauge analysis to perform an in vitro evaluation of the effect of axial loading on 3 elements of implant-supported partial fixed prostheses, varying the type of prosthetic cylinder and the loading points. Material and methods: Three internal hexagon implants were linearly embedded in a polyurethane block. Microunit abutments were connected to the implants applying a torque of 20 Ncm, and prefabricated Co-Cr cylinders and plastic prosthetic cylinders were screwed onto the abutments, which received standard patterns cast in Co-Cr alloy (n = 5). Four strain gauges (SG) were bonded onto the surface of the block tangentially to the implants, SG 01 mesially to implant 1, SG 02 and SG 03 mesially and distally to implant 2, respectively, and SG 04 distally to implant 3. Each metallic structure was screwed onto the abutments with a 10 Ncm torque and an axial load of 30 kg was applied at five predetermined points (A, B, C, D, E). The data obtained from the strain gauge analyses were analyzed statistically by RM ANOVA and Tukey's test, with a level of significance of p<0.05. Results: There was a significant difference for the loading point (p=0.0001), with point B generating the smallest microdeformation (239.49 με) and point D the highest (442.77 με). No significant difference was found for the cylinder type (p=0.748). Conclusions: It was concluded that the type of cylinder did not affect in the magnitude of microdeformation, but the axial loading location influenced this magnitude.

Detecção e localização de descargas parciais em transformadores de potência utilizando sinais acústicoas transitórios e o método GSPS

Neste trabalho, é desenvolvido um método de localização de descargas parciais, em transformadores de potência, baseado no algoritmo GPS (Global Positioning System). Para a análise da estrutura, foi desenvolvido um solftware, no qual as equações diferenciais que representam a propagação de ondas acústicas são resolvidas numericamente através do método Acoustic Finite Difference Time Domain (AFDTD), cujo domínio computacional é truncado através da técnica CPML (Convolutional Perfectly Matched Layer). Os resultados obtidos são comparados a estimativas produzidas utilizando-se sinais elétricos relativos às descargas.

Microstrain Around Dental Implants Supporting Fixed Partial Prostheses Under Axial and Non-Axial Loading Conditions, In Vitro Strain Gauge Analysis

The current study used strain gauge analysis to perform an in vitro evaluation of the effect of axial and non-axial loading on implant-supported fixed partial prostheses, varying the implant placement configurations and the loading points. Three internal hexagon implants were embedded in the center of each polyurethane block with in-line and offset placements. Microunit abutments were connected to the implants using a torque of 20 N.cm, and plastic prosthetic cylinders were screwed onto the abutments, which received standard patterns cast in Co-Cr alloy (n = 10). Four strain gauges (SGs) were bonded onto the surfaces of the blocks, tangentially to the implants: SG 01 mesially to implant 1, SG 02 and SG 03 mesially and distally to implant 2, respectively, and SG 04 distally to implant 3. Each metallic structure was screwed onto the abutments using a 10-N.cm torque, and axial and non-axial loads of 30 kg were applied at 5 predetermined points. The data obtained from the strain gauge analyses were analyzed statistically through the repeated measures analysis of variance and the Tukey test, with a conventional level of significance of P < 0.05. The results showed a statistically significant difference for the loading point (P = 0.0001), with point E (nonaxial) generating the highest microstrain (327.67 mu epsilon) and point A (axial) generating the smallest microstrain (208.93 mu epsilon). No statistically significant difference was found for implant placement configuration (P = 0.856). It was concluded that the offset implant placement did not reduce the magnitude of microstrain around the implants under axial and non-axial loading conditions, although loading location did influence this magnitude.

Clinical evaluation of failures in removable partial dentures

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

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.