Weighting Function In Order Research Articles

An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step method with the first step as Traub–Steffensen iteration and the next two taken as Traub–Steffensen-like iteration with four functional evaluations per iteration. We compare our proposed method with the recent derivative-free methods using some chemical engineering problems modelled as nonlinear equations with simple and multiple roots. Stability of the presented family of methods is demonstrated by using the graphical tool known as basins of attraction.

Oscillatory shear flow between two parallel plates for viscoelastic constitutive model of distributed-order derivative

PurposeThe purpose of this study is to investigate viscoelastic properties for the constitutive equation in terms of distributed-order derivatives.Design/methodology/approachThe authors considered the steady oscillatory shear flow between two parallel plates (one is fixed and another oscillates in its own plane), and then examined the effects of different forms of the order-weight functions.FindingsThe constitutive equation in terms of distributed-order derivatives can characterize viscoelastic properties. The order-weight functions can effectively describe viscoelasticity.Originality/valueModel the viscoelastic constitutive equation in terms of distributed-order derivatives, where order-weight functions can select to respond viscoelastic properties.

Quantum Decision Theory, Bounded Rationality and the Ellsberg Paradox

We test a simple quantum decision model of the Ellsberg paradox. We find that the theoretical predictions of the model are in conformity with our experimental results. The predictions of our quantum model are not statistically significantly different from those of the source dependent model. The source dependent model requires the specification of probability weighting functions in order to fit the evidence. On the other hand, our quantum model makes no recourse to probability weighting functions. This suggests that much of what is normally attributed to probability weighting may actually be due to quantum probability. When we replace quantum probability by Kolmogorov probability in our model, then the Ellsberg paradox reemerges. Hence, we make essential use of quantum probability theory. All our development uses no more than standard linear algebra and real numbers, which are very familiar to economists. This makes our paper accessible to a wider audience than the quantum community.JEL Classification: D01, D81, D91

Prediction model for fatigue life and limit of steel based on small crack micromechanics

It is very important to predict fatigue life and limit of steels for material design and they are affected by microstructures. Although a model for the prediction based on microstructural information was proposed, such model doesn’t consider the other important factors, the stress distribution and the crack closure. This study employed the weight function in order to describe the effect of the stress distribution. For the crack closure, a crack closure equation for small fatigue cracks was employed. Also, tension/compression fatigue experiments using three different steels were carried out to validate this model. Predicted fatigue lives and limits showed good agreement with experimental results for all steels. These new extensions expanded the application of this model, e.g. bending conditions.

H∞ Robust Control of an LCL-Type Grid-Connected Inverter with Large-Scale Grid Impedance Perturbation

In the distributed power generation system (DPGS), there may be a large range perturbation values of equivalent grid impedance at the point of common coupling (PCC). Perturbation of the impedance will cause resonant frequency variation of the Inductance Capacitance Inductance (LCL) filter on a large scale, affecting the quality of the grid current of the grid-connected inverter (GCI) and even causing resonance. To deal with this problem, a novel H∞ robust control strategy based on mixed-sensitivity optimization is proposed in this paper. Its generalized controlled object is augmented by properly selecting weighting functions in order to consider both tracking performance around power frequency and the stability margin in a high frequency of the GCI. For convenient implementation, the H∞ robust controller is simplified by model reduction from the seventh order to the third order. By comparison with a traditional control strategy with a quasi-proportional resonance controller, the proposed H∞ robust control strategy avoids crossing 180 degrees at the resonant frequency point in the phase frequency characteristic of current loop, and moves the phase frequency characteristic left. It guarantees a sufficient margin of stability throughout the designed range of grid impedance perturbation values and avoids the difficulty of parameter setting. Finally, the experimental results support the theoretical analyses and demonstrate the feasibility of the proposed strategy.

Refined energy-conserving dissipative particle dynamics model with temperature-dependent properties and its application in solidification problem.

It has been observed previously that the physical behaviors of Schmidt number (Sc) and Prandtl number (Pr) of an energy-conserving dissipative particle dynamics (eDPD) fluid can be reproduced by the temperature-dependent weight function appearing in the dissipative force term. In this paper, we proposed a simple and systematic method to develop the temperature-dependent weight function in order to better reproduce the physical fluid properties. The method was then used to study a variety of phase-change problems involving solidification. The concept of the "mushy" eDPD particle was introduced in order to better capture the temperature profile in the vicinity of the solid-liquid interface, particularly for the case involving high thermal conductivity ratio. Meanwhile, a way to implement the constant temperature boundary condition at the wall was presented. The numerical solutions of one- and two-dimensional solidification problems were then compared with the analytical solutions and/or experimental results and the agreements were promising.

An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points

ABSTRACTIn this paper, we not only develop an optimal class of three-step eighth-order methods with higher order weight functions employed in the second and third sub-steps, but also investigate their dynamics underlying the purely imaginary extraneous fixed points. Their theoretical and computational properties are fully described along with a main theorem stating the order of convergence and the asymptotic error constant as well as extensive studies of special cases with rational weight functions. A number of numerical examples are illustrated to confirm the underlying theoretical development. Besides, to show the convergence behaviour of global character, fully explored is the dynamics of the proposed family of eighth-order methods as well as an existing competitive method with the help of illustrative basins of attraction.

Robust Stability Analysis of Distributed-Order Linear Time-Invariant Systems With Uncertain Order Weight Functions and Uncertain Dynamic Matrices

Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex plane defined by the upper and lower bounds of the order weight function. Thereby, sufficient conditions are obtained to ensure robust stability in distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices. Numerical examples are presented to verify the obtained results.

The angular distribution of sound incident on a panel or opening

A theoretical method has been developed for predicting the directivity of the sound that is radiated from a panel or opening excited by sound incident on the other side. This directivity needs to be known when predicting the sound level at a particular position due to sound radiation from a roof, wall, ventilating duct, or chimney flue. The method uses a two-dimensional strip model and the low-frequency result for a square piston. It was found necessary to use a weighting function in order to account for the angular distribution of the incident sound. Initially a cosine squared weighting function with a weighting angle parameter was chosen and the weighting angle parameter was varied in order to obtain the best agreement with experiment for the particular situation. This talk will describe the theoretical development of weighting functions, which are based on the actual physics of each situation. Situations that are covered include an opening or panel on the surface of a room and an opening at the end of a duct. The method will be compared with published experimental results on the directivity of the forced sound radiation from panels and the sound radiation from openings.

657 材料の弾塑性特性に応じた衝撃のゲインスケジュールド制御

In this paper we deal with the active control of shock caused by the collision between two objects so as to make the deformation of shock-receiving object large and deformation of shock-giving object small. Because the shockreceiving object deforms elast-plastically, we appliy gain-scheduled(GS) control to overcome the discontinuous input when the deformation of shock-receiving object change from the elastic range to plastic range. Moreover we utilize varying gain of a frequency weighting function in order to improve performance of shock control. Evaluation index of effectiveness of control is the plastic deformation ratio between the two objects. By carrying out experiment, it is verified that the GS controller designed is effective for active control of shock.

AR(1) 모형의 모수에 대한 L-추정법

In this study, a robust estimation method for the first-order autocorrelation coefficient in the time series model following AR(l) process with additive outlier(AO) is investigated. We propose the L-type trimmed least squares estimation method using the preliminary estimator (PE) suggested by Rupport and Carroll (1980) in multiple regression model. In addition, using Mallows` weight function in order to down-weight the outlier of X-axis, the bounded-influence PE (BIPE) estimator is obtained and the mean squared error (MSE) performance of various estimators for autocorrelation coefficient are compared using Monte Carlo experiments. From the results of Monte-Carlo study, the efficiency of BIPE(LAD) estimator using the generalized-LAD to preliminary estimator performs well relative to other estimators.

Weighted inequalities and applications to best local approximation in Luxemburg norm

In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ∈, when ∈→0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.

Implications for clinical pharmacodynamic studies of the statistical characterization of an in vitro antiproliferation assay.

Modeling of nonlinear pharmacodynamic (PD) relationships necessitates the utilization of a weighting function in order to compensate for the heteroscedasticity. The structure of the variance was studied for concentration-effect data generated in an in vitro 96-well plate cell growth inhibition assay, where data are numerous (480 data points per experiment) and replication is easy. From the five candidate models that were considered, the power function S2Y = phi 2Y phi 3, where Y is the sample mean and S2Y is the sample variance, was shown to be the most appropriate to describe the nonuniformity of the variance along the range of measured effect for 253 sets of (Y; S2Y) data. The Hill model was fit to the concentration-effect data with weighted nonlinear regression, where the weights were equal to the reciprocal of the predicted variance. The examination of the distribution of the 253 sets of parameters of the PD model showed that IC50 was lognormally distributed whereas the distribution of gamma was normal. The characterization of the appropriate variance function and concentration-effect function in a simple in vitro experimental setting with a large number of experiments, with each experiment including a large number of data points, will be useful for guiding similar in vitro concentration-effect studies where data are plentiful and for guiding PD modeling in complex clinical settings in which extensive data for model characterization is impossible to obtain.

A generalisation of the Mantel-Haenszel test to bivariate failure time data

SUMMARY This paper presents a class of Mantel & Haenszel (1959) type statistics for testing independence between pairs of failure times. This class is extended to include a weight function in order to enhance test power. Large sample distributions of these statistics are given under the null hypothesis of independence. The paper also presents a simplified test, the covariance test, which is asymptotically equivalent to the Mantel-Haenszel-type test. In order to account for heterogeneity among subjects, both tests are generalised to include subject-specific covariates. In a simulation study, the weighted Mantel-Haenszel and covariance tests are shown to lead to an increase in power for detecting dependence, compared to unweighted tests and to a score test (Commenges & Andersen, 1995) that is based on a random effects model. An example is used to illustrate the methodology.

Eigenfunction Expansion and Higher Order Weight Functions of Interface Cracks

In this paper the properties of the eigenfunction expansion form in the interface crack problem of plane elasticity are discussed in detail. After using the Betti’s reciprocal theorem to the cracked dissimilar bonded body, several path-independent integrals are obtained. All the coefficients in the eigenfunction expansion form, including the K1 and K2 values, and the J-integral can be related to corresponding path independent integrals. Possibility for formulating the weight function is also suggested.

Transport in ordered and disordered porous media II: Generalized volume averaging

In this paper we develop the averaged form of the Stokes equations in terms of weighting functions. The analysis clearly indicates at what point one must choose a media-specific weighting function in order to achieve spatially smoothed transport equations. The form of the weighting function that produces the cellular average is derived, and some important geometrical theorems are presented.

The determination of the elastic T-term using higher order weight functions

It has been shown in a recent work [1] that the elastic T-term at the tip of a mixed mode crack can be determined by the so-called second order weight functions through a work-conjugate integral that is akin to that of the Bueckner-Rice weight function method for evaluating stress intensity factors. In this paper, the development of the second order weight functions is reviewed. These second order weight functions are determined using a unified finite element method introduced in [2]. The finite element procedure handles both traction and displacement boundaries and it permits the Bueckner-Rice weight functions and the second order weight functions for the elastic T-term to be determined in one single finite element run. The accuracy of the computed weight functions is assessed by comparing the computed results with special closed form solutions. The numerical values of the elastic T-term for single edge notch specimens under tension, pure bending and three-point bend are given. The corresponding second order weight functions are tabulated.

The theory of higher order weight functions for linear elastic plane problems

We generalize Bueckner's fundamental field concept and develop higher order weight functions for calculating power expansion coefficients of a regular elastic field in a two-dimensional body in the absence of body forces. Problems of the first and third kind are investigated. Integral formulas for the expansion coefficients are given for interior points and crack tips. In these formulas the integration is performed over the boundary of the body, crack faces included. The prescribed boundary data (tractions and/or displacements) of the regular field appear in the integrand in weighted form. The weights are derived from fundamental fields of universal character. The significance of these expansion coefficients in fracture analysis is also discussed.

The Backus-Gilbert method

The Backus-Gilbert method for linear moment problems is considered. Properties of the Backus-Gilbert inverse operator are derived. Results for convergence and order of convergence when the number of moment equations tends to infinity are proven. Special emphasis is put on the proper exponent in the weight function in order to get pointwise convergence and convergence with respect to the L2 norm.

Interdigital Transducer Models: Their Impact on Filter Synthesis

The characterization and comparison of various interdigital transducer (IDT) models used to analyze and design SAW transversal filters are facilitated by partitioning the overall periodic transducer re- sponse into an impulse function, a discrete time sampling function, and m acoustic weighting function in order to describe both wide-band and space harmonic responses. Through this formalism the analog char- acter of an IDT is accounted for by the use of an acoustic function a(f). This perspective is applied to five interdigital transducer models: namely, impulse (equivalent circuit), impulse (sine wave), modified delta function, spectral weighting and space harmonic. The models differ by their a(r) function. The spectral weighting model is de- scribed in detail for its application to apodized and withdrawal weighted transducer design. A new modified delta function model is shown to agree qualitatively with the spectral weighting model for single electrodes, Aperture weighting laws are derived for the models using sampling theory; it is shown that the cla~sicf;~/~ frequency de- pendence holds only for the narrow-band case f = fn and that, in gen- eral, compensation is required for the acoustic weighting function of the model used. Guidelines for evaluating whether or not compensa- tion is needed as well as compensation techniques and alternatives are described.