Search results for "Weight function"

An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds

2003

For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…

Simulation investigations of the position of Fatigue Fracture Plane in materials with biaxial loads

1989

In the paper three methods of determination of the expected fatigue fracture plane position under random triaxial stress state have been presented. They are: weight function method, variance method and damage cumulation method. The weight function method for biaxial cyclic loadings has been analysed with digital simulation. The fatigue fracture plane position has been determined with mean values of the direction cosines of principal stress axes. Averaging has been done at angle values with use of weights. Eleven various weights have been presented and their usability has been analysed on the basis of experimental results obtained by Rotvel, and Nishihara-Kawamoto. The weights with good agre…

Holder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order

2001

Gaussian quadrature rule for arbitrary weight function and interval

2005

Abstract A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature. Program summary Title of program: AWGQ Catalogue identifier:ADVB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVB Program obtained from: CPC Program Library, Queens University, Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Pentium IV 1.7 GHz processor Ins…

COMPARISON OF EXPERIMENTS WITH WEIGHTED DISTRIBUTIONS

1989

In this paper the standard statistical experiment in which a random sample is drawn from some distribution involving an unknown parameter θ is compared with experiments in which samples are obtained from different weighted versions of that distribution, so that the underlying probability of entering the sample is multiplied by some weight function. This comparison is carried out by means of the concepts of sufficiency and pairwise sufficiency as developed in Blackwell's theory of the comparison of statistical experiments. Many examples are presented which illustrate the wide variety of effects that weight functions can have on the information about θ.

Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method

1999

As has been observed experimentally by many authors, the position of the fatigue fracture plane appears to strongly depend on the directions of the principal stresses or strains. In Part I of the present work the expected principal stress directions under multiaxial random loading are theoretically obtained by averaging the instantaneous values of the three Euler angles through some suitable weight functions which are assumed to take into account the main factors influencing fatigue behaviour. Then, in Part II, it is examined how such theoretical principal directions determined by applying the proposed procedure are correlated to the position of the experimental fracture plane for some fati…

Fatigue fracture planes and expected principal stress directions under biaxial variable amplitude loading

2005

Fatigue behaviour under multiaxial variable amplitude loading can be examined by applying the failure criteria based on the critical plane approach. Positions of the critical plane can be determined in relation to the principal stress or strain directions. In the present paper, the expected directions of the principal stresses under proportional and non-proportional loading have been obtained by averaging the instantaneous values of the Euler angles through special weight functions. The known weight functions based on stress parameters appear not to be efficient for each loading or material being analysed. Thus, the authors consider new weight functions based on energy parameters. The prese…

Restricted Decontamination for the Imbalanced Training Sample Problem

2003

The problem of imbalanced training data in supervised methods is currently receiving growing attention. Imbalanced data means that one class is much more represented than the others in the training sample. It has been observed that this situation, which arises in several practical domains, may produce an important deterioration of the classification accuracy, in particular with patterns belonging to the less represented classes. In the present paper, we report experimental results that point at the convenience of correctly downsizing the majority class while simultaneously increasing the size of the minority one in order to balance both classes. This is obtained by applying a modification o…

Characterization of the human visual system threshold performance by a weighting function in the Gabor domain

1997

Abstract As evidenced by many physiological and psychophysical reports, the receptive fields of the first-stage set of mechanisms of the visual process fit to two-dimensional (2D) compactly supported harmonic functions. The application of this set of band-pass filter functions to the input signal implies that the visual system carries out some kind of conjoint space/spatial frequency transform. Assuming that a conjoint transform is carried out, we present in this paper a new characterization of the visual system performance by means of a weighting function in the conjoint domain. We have called this weighting function (in the particular case of the Gabor transform) the Gabor stimuli Sensiti…

An alternative space-time meshless method for solving transient heat transfer problems with high discontinuous moving sources

2016

International audience; The aim of this work is the development of a space-time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space-time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.