Unifying distribution functions: some lesser known distributions

We show that there is a way to unify distribution functions that describe simultaneously a classical signal in space and (spatial) frequency and position and momentum for a quantum system. Probably the most well known of them is the Wigner distribution function. We show how to unify functions of the Cohen class, Rihaczek's complex energy function, and Husimi and Glauber-Sudarshan distribution functions. We do this by showing how they may be obtained from ordered forms of creation and annihilation operators and by obtaining them in terms of expectation values in different eigenbases.     

Sparse shifts for univariate polynomials

Letf(x) be a polynomial of degreed with rational coefficients and lett be a positive integer deg(f). We consider the problem of finding at-sparse shift forf(x). The problem is to find an a, if one exists (in some algebraic extension of the rationals), such that in the representation off(x) in the basis 1,x – , (x – )²,..., i.e., at most t of the coefficients f_i are non-zero. We derive explicit conditions for the uniqueness and rationality of at-sparse shift forf(x) and provide an efficient algorithm for computing a sparse shift when one exists. We also point out an application of our result to the problem of constructing sparse decompositions of univariate polynomials.Work by Y. N. Lakshman was supported by NSF grant CCR-9203062Work by B. D. Saunders was supported by NSF grant CCR-9123666     

On stochastic comparisons of finite mixtures for some semiparametric families of distributions

In this paper, we consider the classical finite mixture model, which is an effective tool for modeling lifetime distributions for random samples from heterogeneous populations. We discuss new results on stochastic comparison for two finite mixtures when each of them is drawn from one of the following semiparametric families, i.e., proportional hazards, accelerated lifetime and proportional reversed hazards.     

Longitudinal and lateral distributions of medium energy heavy ions in some semiconductor films

The depth distributions of Bi⁺ and Fe⁺ ions implanted into SiN_1.375H_0.603, α-Si, Si₃N₄ and SiO₂ films at different angles were measured by Rutherford backscattering technique. The results show that: (1) the experimental mean projected range R_p is in agreement with the calculated value by TRIM'98 within 9% for SiN_1.375H_0.603, Si₃N₄ α-Si cases; (2) the experimental range straggling ΔR_p is larger than the calculated value by TRIM'98, the reason is not known; and (3) the depth distributions of implanted ions at different angles in all cases exhibit nearly Gaussian behaviour; the agreement of the extracted lateral spread with the calculated value is best for the case of Bi⁺ ions implanted into SiO₂.     

A note on the polya-eggenberger distributions with s=1 and some applications

Although cumulative probabilities for the Pólya-Eggenberger distributions can be easily found on modern computing facilities, the special casess=1 can be handled with hypergeometric tables. Applications are mentioned.     

Sequence of polyhedral relaxations for nonlinear univariate functions

Optimization and Engineering - Given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear...     

Structural reliability analysis by univariate decomposition and numerical integration

This paper presents a new and alternative univariate method for predicting component reliability of mechanical systems subject to random loads, material properties, and geometry. The method involves novel function decomposition at a most probable point that facilitates the univariate approximation of a general multivariate function in the rotated Gaussian space and one-dimensional integrations for calculating the failure probability. Based on linear and quadratic approximations of the univariate component function in the direction of the most probable point, two mathematical expressions of the failure probability have been derived. In both expressions, the proposed effort in evaluating the failure probability involves calculating conditional responses at a selected input determined by sample points and Gauss–Hermite integration points. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure.     

Pharmaceutical quantification with univariate analysis using transmission Raman spectroscopy

The purpose of this study was to investigate the quantification performance of transmission Raman spectroscopy with univariate analysis. Model dosage forms containing acetaminophen and an excipient, lactose monohydrate, were prepared. The Raman spectra of the tablets were obtained using the modes of transmission, backscattering micro-spectroscopy, and wide area illumination. Calibration curves for quantification of acetaminophen in the tablets were created using peak heights of the Raman spectra. Of the three modes of measurement, the quantitative results by transmission had the highest correlation with those by conventional UV–vis methods. In the validation of quantification by the transmission mode with univariate analysis, a certain degree of daily variation was confirmed. Additionally, quantitative results using peak heights were compared with those of partial least squares (PLSs) multivariate analysis. The root mean square error of prediction (RMSEP) suggested that quantification using PLS provided better precision than the peak height method as expected. However, content uniformity test using large sample sizes by the Raman spectra is not required to be very highly predictive because they usually employ non-parametric criteria and include wide specification ranges. Therefore, univariate analysis using transmission Raman spectroscopy was a suitable quantitative method for conducting content uniformity tests of large sample sizes.     

知觉闲散、自我控制与反生产行为的关系研究

为了探究知觉闲散、自我控制和员工反生产行为之间存在的关系,本文采用本土企业的领导及其直接下属作为配对样本的调查方式,调查了来自21个企业的31位管理者和137位员工,结果发现:知觉闲散和员工反生产行为显著正相关;而员工的自我控制能力对其反生产行为产生负向影响;员工的自我控制能力在知觉闲散和反生产行为的关系中起到了负向调节作用。     

应用RAMP分子标记探讨仲彬草属的种间关系

对仲彬草属Kengyilia14个种和1个变种进行了RAMP分析。结果表明物种间遗传差异明显。40个引物组合产生的254条DNA扩增片段中，216条(85．0％)具有多态性，每个引物组合可扩增出l一9条多态性带，平均5．4条。遗传相似系数变化范围为0．327—0．886，平均值为0．549。同时，形态相似、地理分布一致的物种有一定的亲缘关系，聚类在一起。这与RAPD、形态学和细胞学等分析结果基本一致。因此，RAMP评分子标记是评价仲彬草属种间关系十分有效的方法。     

On changing points of mean residual life and failure rate function for some generalized Weibull distributions

The failure rate function and mean residual life function are two important characteristics in reliability analysis. Although many papers have studied distributions with bathtub-shaped failure rate and their properties, few have focused on the underlying associations between the mean residual life and failure rate function of these distributions, especially with respect to their changing points. It is known that the change point for mean residual life can be much earlier than that of failure rate function. In fact, the failure rate function should be flat for a long period of time for a distribution to be useful in practice. When the difference between the change points is large, the flat portion tends to be longer. This paper investigates the change points and focuses on the difference of the changing points. The exponentiated Weibull, a modified Weibull, and an extended Weibull distribution, all with bathtub-shaped failure rate function will be used. Some other issues related to the flatness of the bathtub curve are discussed.     

A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics

This paper presents a new, univariate dimension-reduction method for calculating statistical moments of response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of a multi-dimensional response function into multiple one-dimensional functions, an approximation of response moments by moments of single random variables, and a moment-based quadrature rule for numerical integration. The resultant moment equations entail evaluating N number of one-dimensional integrals, which is substantially simpler and more efficient than performing one N-dimensional integration. The proposed method neither requires the calculation of partial derivatives of response, nor the inversion of random matrices, as compared with commonly used Taylor expansion/perturbation methods and Neumann expansion methods, respectively. Nine numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the proposed method. Results indicate that the univariate dimension-reduction method provides more accurate estimates of statistical moments or multidimensional integration than first- and second-order Taylor expansion methods, the second-order polynomial chaos expansion method, the second-order Neumann expansion method, statistically equivalent solutions, the quasi-Monte Carlo simulation, and the point estimate method. While the accuracy of the univariate dimension-reduction method is comparable to that of the fourth-order Neumann expansion, a comparison of CPU time suggests that the former is computationally far more efficient than the latter.     

Iterative univariate optimization of nonlinear trusses with fuzzy strain constraints

A univariate iterative method for the optimization of nonlinear trusses with fuzzy constraints is proposed. The method is based on the control of elemental strains rather than stresses and hence it is called the desirable strain design criteria method. The objective of the fuzzy optimization is to find a design so that the weight or volume of the truss as well as all of the constraints on the elemental strains and joint deflections are desirable and satisfactory according to the fuzzy designer expressions. Such expressions are made in the form of fuzzy membership functions. Two illustrative examples, a 3- and a 10-bar truss, are optimized by the proposed method, where it is shown that in both cases the method monotonically converges to the highest desirability.     

工作特征、职业倦怠与工作绩效的关系研究

本文以石化行业员工工作绩效为焦点,探讨工作特征对员工职业倦怠及工作绩效的影响,运用问卷调查法对某石化企业188名操作员工(男147人,女41人)进行调查,结果表明:工作要求(工作环境、工作安全感、身体负荷、设备条件)显著影响职业倦怠中的耗竭和疏离感维度;工作资源(同事支持、上级支持、培训、管理制度)对职业倦怠中的职业效能维度有显著的影响,并通过影响职业效能对关系绩效影响显著;此外工作资源直接对任务绩效有显著的影响;职业倦怠中耗竭和疏离感维度对职业效能维度有负向影响,表明石化行业员工的工作特征对其职业倦怠及工作绩效有良好的预测作用.     

Investigation on Relationships among Deformation, Texture and Properties of TA16 Alloy Tube

The relationships among the deformation, texture and properties of TA16 alloy tube were investigated, an optimum processing parameter was obtained. High Q (the ratio of reduction of diameter to reduction of wall thickness) values increase tensile, flaring properties and reduce flattening; high Q values increase tensile strength, flattening, flaring. and decrease tensile elonga. tion. The main circular textures of rolling tubes are basal (0001) and pyramidal {1015}, {1014}, {1013} etc., and the main axial textures are prism {1010} and pyramidal {1120}, {2131}, {2021} etc. under different Q and E values. There are greater changes in the grain size under different E values, compared with that under different Q values.     

A univariate Chebyshev polynomials method for structural systems with interval uncertainty

This paper presents an effective univariate Chebyshev polynomials method (UCM) for interval bounds estimation of uncertain structures with unknown-but-bounded parameters. The interpolation points required by the conventional collocation methods to generate the surrogate model are the tensor product of each one-dimensional (1D) interpolating point. Therefore, the computational cost is expensive for uncertain structures containing more interval parameters. To deal with this issue, the univariate decomposition is derived through the higher-order Taylor expansion. The structural system is decomposed into a sum of several univariate subsystems, where each subsystem only involves one uncertain parameter and replaces the other parameters with their midpoint value. Then the Chebyshev polynomials are utilized to fit the subsystems, in which the coefficients of these subsystems are confirmed only using the linear combination of 1D interpolation points. Next, a surrogate model of the actual structural system composed of explicit univariate Chebyshev functions is established. Finally, the extremum of each univariate function that is obtained by the scanning method is substituted into the surrogate model to determine the interval ranges of the uncertain structures. Numerical analysis is conducted to validate the accuracy and effectiveness of the proposed method.     

On the determination of grain-size distributions from intercept distributions

A matrix formulation for determining the spatial grain-size distribution of tetrakaidecahedral grains from linear-intercept data is developed. The truncation effect (which stems from the fact that the intersection of single-size grains by a test line gives rise to intercepts of different length) and the sampling effect (which results as a consequence of bigger grains being intersected more frequently than smaller ones) are separately taken into account. The derivation procedure of this formulation is applicable to any other convex shape, provided the linear intercept distribution for single-size grains of the corresponding shape is known. The percentage spatial grain-size distributions obtained by the formulation derived here are similar to those estimated by the Spektor's chord method for spherical grains.     

Families of distributions arising from distributions of order statistics

Consider starting from a symmetric distributionF on ℜ and generating a family of distributions from it by employing two parameters whose role is to introduce skewness and to vary tail weight. The proposal in this paper is a simple generalisation of the use of the collection of order statistic distributions associated withF for this purpose; an alternative derivation of this family of distributions is as the result of applying the inverse probability integral transformation to the beta distribution. General properties of the proposed family of distributions are explored. It is argued that two particular special cases are especially attractive because they appear to provide the most tractable instances of families with power and exponential tails; these are the skewt distribution and the logF distribution, respectively. Limited experience with fitting the distributions to data in their four-parameter form, with location and scale parameters added, is described, and hopes for their incorporation into complex modelling situations expressed. Extensions to the multivariate case and to ℜ⁺ are discussed, and links are forged between the distributions underlying the skewt and logF distributions and Tadikamalla and Johnson'sL _U family.