Mixed Moments Research Articles

Вторые смешанные моментные функции решения двумерного уравнения диффузии

Вторые смешанные моментные функции решения двумерного уравнения диффузии

Optical conductivity of topological Kondo insulating states

Using real-space dynamical mean field quantum Monte Carlo simulations, we study the optical conductivity of two-dimensional topological Kondo insulating states. We consider model parameters which allow us to consider mixed valence and local moment regimes. The real space resolution inherent to our approach reveals a renormalization of the hybridization gap as one approaches the edge. Low energy transport is dominated by the helical edge state and the corresponding Drude weight scales as the coherence scale of the heavy fermion state. The concomitant renormalization of the edge state velocity leads to a constant edge local density of states. We discuss the implication of our results for the three dimensional case.

The United States of the United Races: A Utopian History of Racial Mixing GregCarter. New York: New York University Press, 2013.

United States of the United Races: A Utopian History of Racial Mixing Greg Carter. New York: New York University Press, 2013.In this seven-chapter history, Greg Carter traces the trajectory of political and philosophical conversations about Americans of mixed race (the term Carter prefers to use rather than multi-racial) since the post-revolutionary era of the United States. Taking inspiration for the book's title from Wendell Phillips's The United States of United Races essay (60), Carter aims to enumerate and examine the statesmen, writers, and other luminaries who praised mixture as a means to bring equality to all, and to fulfill an American destiny (3), a position that Carter suggests has been passed over by other historians (3).To a certain extent, the stakes that Carter outlines above are accurate. fact that Carter's study cites centuries of data regarding race mixture in the United States makes it unique, yet currently, broad considerations of racial mixture are numerous in scholarship. There are many general texts about racial relations as well as those with a specific focus, such as Renee C. Romano's Race Mixing: Black-White Marriage in Postwar America (2003), Lauren L. Basson's White Enough To Be American: Race Mixing, Indigenous People, and the Boundaries of State and Nation (2008), and Christina A. Sue's Land of the Cosmic Race: Race Mixture, Racism, and Blackness in Mexico (2013).The recent proliferation of scholarly interest in racial mixture takes impetus, perhaps, as Carter did, from the election of President Barack Obama and Obama's status as a mixed-race American. It would be difficult not to think of the President's genetics in tandem with Carter's discussion, since artist Ron English's fusion portrait Abraham Obama comprises the cover art of the book. work is well-chosen as a segue into the text, for it forces viewers into a visual double-take; mimicking a signature (192) that according to Carter, happens often in the lives of mixed race persons-the moment when asked 'What are you?' occurs (192).Carter differentiates his project by stating the study uncovers a narrative of positive notions just as important as the negative, and puts both the positive and the negative in the historical context, recovering past advocates for or against racial mixture and amplifying the resonances over time (5). Finally, Carter claims not to privilege one kind of racial mixing (for example, black and white) in the book but rather interrogates mixture in any configuration as an engine for positive change (5). …

POLSAR图像杂波L分布建模及其参数估计

The statistical modeling based on the product model is an effective method to analysis high-resolution POLSAR images, whlie the core is the selection of texture model. The generalized gamma distribution (GΓD) is a generic model which includes Weibull distribution, Gamma distribution and Inverse Gamma distribution. So we can expect that if we modeling the texture component with GΓD, the product model will not only accurate, but also generally to the POLSAR images modeling. In this paper, we firstly derive the high moments and matrix log-cumulants (MLCs) of the GΓD random variables. Then we find that we can model the POLSAR images with L-distribution when the GΓD is applied to the texture component of the product model. Also we get a novel estimation based on the MLCs of L-distributed random variables. In this paper, a parameter estimation method based on the mixed moments is proposed, in order to solve the problem that the estimation based on matrix log-cumulants is invalid when the number of samples is small. What is more, the manifolds of theoretical MLCs for several distributions show the intrinsic relationship of the widespread distribution and L-distribution which can prove the universal of the latter. Finally, the correctness of modeling with L-distribution and the validity of the derivation of the estimator are verified though simulated data and real data.

An Inspection Method of SMD Component Type Based on Moment Features and BP Neural Network

The type inspection of surface mounted devices (SMD) components is an important part of the numerical control (NC) placement machine’s vision system. In order to improve the detection speed, accuracy rate and versatility, a detection method based on moment features and neural network is proposed. Firstly, component images are preprocessed in order to eliminate the influence of non-uniform illumination and simplify the calculation, so component lead images can be obtained, and then seven invariant moments and a zero-order Zernike moment of the lead images are extracted. Next, the moment features are corrected and normalized. Finally, back propagation (BP) neural network based on the Levenberg-Marquardt algorithm is taken as a classifier for training and testing the 8-dimensional mixed moment feature vectors, 0 and 1 are used to represent the degree of belonging of each image. The experimental results show that this method doesn’t need complex lighting system and has good versatility, and the correct rate can be up to 100%.

Bootstrapping and Askey–Wilson polynomials

The mixed moments for the Askey–Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey–Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.

Comparative study for non-statistical fluctuation of net- proton, baryon, and charge multiplicities

We investigate the higher moments of net-proton, net-baryon, and net-charge event distributions in Au+Au collisions at from 11.5 to 200 GeV. The non-statistical moments are defined as the differences between the real event moments and mixed event moments. The real events are generated with the parton and hadron cascade model PACIAE, while the mixed events are constructed by combining particles randomly selected from different real events. It is found that the theoretical results of net-proton and net-charge real higher moment excitation functions of Sσ and κσ2 are consistent with the STAR data, and that the properties of higher moment excitation functions are significantly dependent on the window sizes. In addition, the centrality dependence of the net-proton, net-baryon, and net-charge non-statistical higher moments are also studied.

Gaps between zeros of Dedekind zeta-functions of quadratic number fields

Let K be a quadratic number field, and let ζK(s) denote the Dedekind zeta-function attached to K. Using the mixed second moments of derivatives of ζK(12+it), we prove the existence of gaps between consecutive zeros of ζK(s) on the critical line which are at least 6=2.44949… times the average spacing.

Transient Analysis of the M/M/k/N/N Queue using a Continuous Time Homogeneous Markov System with Finite State Size Capacity

In this article, the M/M/k/N/N queue is modeled as a continuous-time homogeneous Markov system with finite state size capacity (HMS/cs). In order to examine the behavior of the queue a continuous-time homogeneous Markov system (HMS) constituted of two states is used. The first state of this HMS corresponds to the source and the second one to the state with the servers. The second state has a finite capacity which corresponds to the number of servers. The members of the system which can not enter the second state, due to its finite capacity, enter the buffer state which represents the system's queue. In order to examine the variability of the state sizes formulae for their factorial and mixed factorial moments are derived in matrix form. As a consequence, the pmf of each state size can be evaluated for any t ∈ ℝ+. The theoretical results are illustrated by a numerical example.

On the Second Mixed Moment of the Characteristic Polynomials of 1D Band Matrices

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H N with independent Gaussian entries such that 〈H ij H lk 〉 = δ ik δ jl J ij , where $${J=(-W^2\triangle+1)^{-1}}$$ . Assuming that $${W^2=N^{1+\theta}}$$ , $${0 < \theta \leq 1}$$ , we show that the moment’s asymptotic behavior (as $${N\to\infty}$$ ) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.

Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker--Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy M${}_n$ models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They provide nonnegative distribution functions combined with an analytical closure. Numerical tests are performed with standard first-order finite volume schemes and compared with a finite difference Fokker--Planck scheme.

The Distribution of Directions in an Affine Lattice: Two-Point Correlations and Mixed Moments

We consider an affine Euclidean lattice and record the directions of all lattice vectors of length at most $T$. Strombergsson and the second author proved in [Annals of Math.~173 (2010), 1949--2033] that the distribution of gaps between the lattice directions has a limit as $T$ tends to infinity. For a typical affine lattice, the limiting gap distribution is universal and has a heavy tail; it differs distinctly from the gap distribution observed in a Poisson process, which is exponential. The present study shows that the limiting two-point correlation function of the projected lattice points exists and is Poissonian. This answers a recent question by Boca, Popa and Zaharescu [arXiv:1302.5067]. The existence of the limit is subject to a certain Diophantine condition. We also establish the convergence of more general mixed moments.

Percentile Estimation in Inverse Gaussian Distributions

This paper presents procedures for percentile estimation in the three-parameter inverse Gaussian (IG3) and the two-parameter inverse Gaussian (IG2) distributions. All procedures require first the estimation of distribution parameters and second the computation of the desired quantile at the estimated parameters. Parameter estimation is accomplished by maximum likelihood (ML) or a mixed moments (MXM) method. A Newton-Rahpson (NR) procedure is used for inverting the CDF. Simulation and asymptotic results are given for the resulting estimators. Two sets of real data are used to illustrate the procedures.

On Stuttering Hyper-Poisson Distribution and its Properties

Here we develop an order k version of the hyper-Poisson distribution and study some of its properties by deriving its probability mass function, mean, variance and recursion formulae for probabilities, raw moments and factorial moments. The estimation of the parameters of this class of distributions by the method of mixed moments and method of maximum likelihood is attempted and it is demonstrated with the help of a real data set that this order k version of the hyper-Poisson distribution fits the situations better than the existing model. DOI: http://dx.doi.org/10.4038/sljastats.v14i1.5876

THE YAGLOM LAW IN THE EXPANDING SOLAR WIND

We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els\"asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom's third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.

Inelastic electron and Raman scattering from the collective excitations in quantum wires: Zero magnetic field

The nanofabrication technology has taught us that an m-dimensional confining potential imposed upon an n-dimensional electron gas paves the way to a quasi-(n-m)-dimensional electron gas, with m ⩽n and 1 ⩽ n, m ⩽ 3. This is the road to the(semiconducting) quasi-n dimensional electron gas systems we have been happily traversing on now for almost two decades. Achieving quasi-one dimensional electron gas (Q-1DEG) [or quantum wire(s) for more practical purposes] led us to some mixed moments in this journey: while the reduced phase space for the scattering led us believe in the route to the faster electron devices, the proximity to the 1D systems left us in the dilemma of describing it as a Fermi liquid or as a Luttinger liquid. No one had ever suspected the potential of the former, but it took quite a while for some to convince the others on the latter. A realistic Q-1DEG system at the low temperatures is best describable as a Fermi liquid rather than as a Luttinger liquid. In the language of condensed matter physics, a critical scrutiny of Q-1DEG systems has provided us with a host of exotic(electronic, optical, and transport) phenomena unseen in their higher- or lower-dimensional counterparts. This has motivated us to undertake a systematic investigation of the inelastic electron scattering (IES) and the inelastic light scattering(ILS) from the elementary electronic excitations in quantum wires. We begin with the Kubo's correlation functions to derive the generalized dielectric function, the inverse dielectric function,and the Dyson equation for the dynamic screened potential in the framework of Bohm-Pines’random-phase approximation. These fundamental tools then lead us to develop methodically the theory of IES and ILS for the Q-1DEG systems. As an application of the general formal results, which know no bounds regarding the subband occupancy, we compute the density of states, the Fermi energy, the full excitation spectrum[comprised of intrasubband and intersubband single-particle as well as collective excitations], the loss functions for the IES and the Raman intensity for the ILS. We observe that it is the collective (plasmon)excitations that largely contribute to the predominant peaks in the energy-loss and the Raman spectra. The inductive reasoning is that the IES can be a potential alternative of the overused ILS for investigating collective excitations in quantum wires. We trust that this research work shall be useful to all – from novice to expert and from theorist to experimentalist – who believe in the power of traditional science.

Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from the Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the large-value tail of the inter-tracer distance probability distribution. At large times this tail is found to be closer to a pure exponential than to the form obtained from the Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson’s distribution.

On the Moments of Ratio of Quadratic Forms in Normal Random Variables

In this paper, we present both integral and infinite series expressions of mixed moments of two quadratic forms in normal random variables. We also present efficient numerical methods for computing the mixed moments under each approach.

Testing the Equality and Exchangeability of Bivariate Distributions

We consider three methods (oments, cut-points, and ranks) for testing the hypotheses of equality of two bivariate distribution functions (H 0a ) and exchangeability (H 0b ). To test H 0a , the asymptotic normality of the vector of mixed moments provides a statistic with an asymptotic chi-square distribution. With every observation, method of cut-points associates three 2 × 2 tables to record the proportions of the X, Y, and the combined samples that fall in the four regions around the observation. We measure the total squared deviations of the proportions in the combined sample from X and Y samples. The two methods are compared with the method of ranks based on the Puri and Sen (1971) multivariate two-sample rank test for location. To test H 0b we identify two bivariate distributions, one above and the other below the line of symmetry X = Y, to which a test of H 0a is applied. Under H 0b , matrix of mixed moments is symmetric and a quadratic form in differences of (r,s)-th and (s, r)-th mixed moments provides an asymptotic chi-square distribution. A permutation test is devised to apply the method of cut-points to the observations above and below the line of symmetry after they are folded. We also describe an adaption of the Puri-Sen rank test to assess H 0b . To estimate the power of the above methods under different types of alternatives and compare them to existing tests, we report on a Monte Carlo experiment that evaluates the finite-sample performance of these methods under the Plackett's family of bivariate distributions.

On multivariate truncated generalized Cauchy distribution

In this paper, a multivariate form of truncated generalized Cauchy distribution (TGCD), which is denoted by (MVTGCD), is introduced. The joint density function, conditional density function, moment generating function and mixed moments of order $${b=\sum_{i=1}^{k}b_{i}}$$ are obtained. Making use of the mixed moments formula, skewness and kurtosis in case of the bivariate case are obtained. Also, all parameters of the distribution are estimated using the maximum likelihood and Bayes methods. A real data set is introduced and analyzed using three models. The first model is the bivariate Cauchy distribution, the second is the truncated bivariate Cauchy distribution and the third is the bivariate truncated generalized Cauchy distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic to emphasize that the bivariate truncated generalized Cauchy model fits the data better than the other models.