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We study the spectroscopy of the one-dimensional Dirac oscillator perturbed by a chain of delta-shaped potentials. We consider two cases: scalar and vector couplings. The transfer matrix method is used for the determination of the...
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We study the spectroscopy of the one-dimensional Dirac oscillator perturbed by a chain of delta-shaped potentials. We consider two cases: scalar and vector couplings. The transfer matrix method is used for the determination of the general condition of quantization of energy, and a detailed example is presented.
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In this paper we first approximate a 'nearly singular' function, which tends to be the Dirac-delta function, to high degree of accuracy by using a recently developed Delta-shaped basis function. The Hermite-based meshless collocat...
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In this paper we first approximate a 'nearly singular' function, which tends to be the Dirac-delta function, to high degree of accuracy by using a recently developed Delta-shaped basis function. The Hermite-based meshless collocation method based on radial basis functions is then applied to solve a default barrier model, which is a time-dependent boundary value problem with a singularity at the initial condition. For numerical verification on the accuracy and efficiency of the newly proposed method, we compare the results with an analytical solution of the default barrier model under an assumption on the affine boundary. Numerical results indicate that the proposed method has potential advantage to solve problems with Dirac-type singularities.
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In order to predict the noise performance of a digital capacitive MEMS accelerometer and optimize the parameters of circuits, an improved quantization noise model is presented in this paper. Considering the distortion produced by ...
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In order to predict the noise performance of a digital capacitive MEMS accelerometer and optimize the parameters of circuits, an improved quantization noise model is presented in this paper. Considering the distortion produced by the nonlinear characteristic of a quantizer, a system model of the Sigma-Delta (Sigma Delta) accelerometer is established on the basis of describing function method model of a 1-bit quantizer. On the basis of this model, the formula of quantization noise before noise shaping, the transfer function of quantization noise and its expression in the signal band are presented. The model of quantization noise proposed in this paper includes the influence of sensing element parameters and the high non linearity of a 1-bit quantizer. DC and AC simulation results show that the model can forecast the quantization noise in the signal band more accurately, compared with the models based on linear and quasi-linear model of a quantizer. The influences of electronic noise and sampling frequency on quantization noise are also analyzed. The results show that in Sigma Delta MEMS accelerometer, electronic noise will lead to a reduction of the quantization gain and impact the noise shaping ability seriously. Increasing sampling frequency cannot effectively reduce the output quantization noise, but it will decline with sampling frequency at the slope of 3 dB/oct. (C) 2015 Elsevier Ltd. All rights reserved.
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This article considers statistical inference for consistent estimators of generalized Gini indices of inequality, poverty, and welfare. Our method does not require grouping the population into a fixed number of quantiles. The empi...
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This article considers statistical inference for consistent estimators of generalized Gini indices of inequality, poverty, and welfare. Our method does not require grouping the population into a fixed number of quantiles. The empirical indices are shown to be asymptotically normally distributed using functional limit theory. Easily computed asymptotic variance expressions are obtained using influence functions. Inference based on first-order asymptotics is then compared with the grouped method and various bootstrap methods in simulations and with U.S. income data. The bootstrap-t method based on our asymptotic theory is found to have superior size and power properties in small samples.
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This paper explores two wavelet-based energy-conserving algorithms for the Gross-Pitaevskii equation with delta potentials in Bose-Einstein condensates, named modified Crank-Nicolson wavelet method and time-splitting wavelet metho...
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This paper explores two wavelet-based energy-conserving algorithms for the Gross-Pitaevskii equation with delta potentials in Bose-Einstein condensates, named modified Crank-Nicolson wavelet method and time-splitting wavelet method, respectively. Both proposed methods can preserve the intrinsic properties of original problems as much as possible. Meanwhile, the rigorous error estimates and some conservative properties are investigated. They are proved to preserve the charge conservation exactly. The global energy conservation laws can be preserved under several conditions. In practical computations, to avoid a large drift in energy values caused by discontinuous potential well, an improved discrete delta function is implemented. Numerical experiments for attractive and repulsive cases are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis. (C) 2017 Elsevier Inc. All rights reserved.
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We present a simple influence function based approach for computing the variances of estimates of absolute risk and functions of absolute risk. We apply this approach to criteria that assess the impact of changes in the risk facto...
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We present a simple influence function based approach for computing the variances of estimates of absolute risk and functions of absolute risk. We apply this approach to criteria that assess the impact of changes in the risk factor distribution on absolute risk for an individual and at the population level. As an illustration we use an absolute risk prediction model for breast cancer that includes modifiable risk factors in addition to standard breast cancer risk factors. Influence function based variance estimates for absolute risk and the criteria are compared to bootstrap variance estimates.
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Let S:[0,1] → [0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P _S:L ~1(0,1)→ L ~1(0,1) has a stationary density f*. We develop a piecewise constant method for the numerical computatio...
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Let S:[0,1] → [0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P _S:L ~1(0,1)→ L ~1(0,1) has a stationary density f*. We develop a piecewise constant method for the numerical computation of f*, based on the approximation of Dirac's delta function via pulse functions. We show that the numerical scheme out of this new approach is exactly the classic Ulam's method. Numerical results are given for several one dimensional test mappings.
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This paper revisits the problem first studied by Jaworski and Dowell, namely, the free vibration of multi-step beams. Previous authors utilized approximate method of Ritz as well as the finite element method with attendant compari...
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This paper revisits the problem first studied by Jaworski and Dowell, namely, the free vibration of multi-step beams. Previous authors utilized approximate method of Ritz as well as the finite element method with attendant comparison with the experimental results. This study provides the exact solution for the Jaworski and Dowell problem in terms of Krylov-Duncan functions. Additionally, the Galerkin method is applied and contrasted with the exact solution. It is shown that the straightforward implementation of the Galerkin method, as it is usually performed in the literature, does not lead to results obtained by Jaworski and Dowell using the Ritz method. Moreover, the straightforward application of the Galerkin method does not tend to the results obtained by either exact solution or experiments. A modification of the Galerkin method is proposed by introducing generalized functions to describe both mass and stiffness of the stepped beam. Specifically, the unit step function, Dirac's delta function and the doublet function, are utilized for this purpose. With this modification, the Galerkin method yields results coinciding with those derived by the Ritz method, and turn out to be in close vicinity with those produced by the exact solution as well as experiments.
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After reviewing the algebraic derivation of the Doppler factor in the Lienard-Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying...
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After reviewing the algebraic derivation of the Doppler factor in the Lienard-Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying the weak definition, non-zero in an infinitesimal neighborhood, and not the one obeying the strong definition, non-zero in a point. This conclusion emerges from our analysis of (a) the derivation of an important Dirac delta function identity, which generates the Doppler factor, (b) the linear superposition principle implicitly used by the Green function method, and (c) the two equivalent formulations of the Schwarzschild-Tetrode-Fokker action. As a consequence, in full agreement with our previous discussion of the geometrical origin of the Doppler factor, we conclude that the electromagnetic interaction takes place not between points in Minkowski space, but between corresponding infinitesimal segments along the worldlines of the particles.
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We revisit Munshi's proof of the t-aspect subconvex bound for GL(3) L-functions, and we are able to remove the "conductor lowering" trick. This simplification along with a more careful stationary phase analysis allows us to improv...
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We revisit Munshi's proof of the t-aspect subconvex bound for GL(3) L-functions, and we are able to remove the "conductor lowering" trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi's bound toL(1/2 + it,pi) << (pi, epsilon) (1 + vertical bar t vertical bar)(3/4-3/40+epsilon).
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