Study on the Size Distribution and Similarity Law of Bubble Nuclei in Water

To study the distribution characteristics and similarity laws of nuclei under different pressures,based on the selfdesigned decompression chamber and the acoustic measuring system,the size distributions of nuclei in the degassed tap water under negative ambient pressures were measured.A number density distribution function of nuclei based on the modified Weibull distribution function was proposed and verified by the experimental measurement results and some published data of nuclei size distribution.Based on this nuclei number density distribution function,the similarity law of the nuclei size distribution was analyzed:in the scale experiment,the value of exponential in the similarity law of the nuclei number density should be determined by the nuclei size distribution of the water in the prototype experiment and the actual nuclei size distribution of the water in the model experiment.And a precondition is that the nuclei size distributions are similar.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

First proof-of-principle experiment with the post-accelerated isotope separator on-line beam at BRIF:measurement of the angular distribution of ^(23)Na+^(40)Ca elastic scattering

The reaction dynamics of exotic nuclei near the drip line is one of the main research topics of current interest.Elastic scattering is a useful probe for investigating the size and surface diffuseness of exotic nuclei.The development of rare isotope accelerators offers opportunities for such studies.To date,many relevant measurements have been performed at accelerators using the projectile fragmentation technique,while the measurements at accelerators using isotope separator on-line(ISOL)systems are still quite scarce.In this work,we present the first proof-of-principle experiment with a post-accelerated ISOL beam at the Beijing Radioactive Ion Beam Facility(BRIF)by measuring the angular distribution of elastic scattering for the stable nucleus^(23)Na from the doubly magic nucleus^(40)Ca at energies above the Coulomb barrier.The angular distribution measured by a silicon strip detector array in a scattering chamber using the ISOL beam at BRIF is in good agreement with that measured by the high-precision Q3 D magnetic spectrograph using the nonISOL beam at nearly the same energy.This work provides useful background for making BRIF a powerful tool for the investigation of the reaction dynamics of exotic nuclei.

Determination of drug,excipients and coating distribution in pharmaceutical tablets using NIR-CI

The growing interest of the pharmaceutical industry in Near Infrared-Chemical Imaging (NIR-CI) is a result of its high usefulness for quality control analyses of drugs throughout their production process (particularly of its non-destructive nature and expeditious data acquisition).In this work,the concentration and distribution of the major and minor components of pharmaceutical tablets are determined and the spatial distribution from the internal and external sides has been obtained.In addition,the same NIR-CI allowed the coating thickness and its surface distribution to be quantified.Images were processed to extract the target data and calibration models constructed using the Partial Least Squares (PLS) algorithms.The concentrations of Active Pharmaceutical Ingredient (API) and excipients obtained for uncoated cores were essentially identical to the nominal values of the pharmaceutical formulation.But the predictive ability of the calibration models applied to the coated tablets decreased as the coating thickness increased.

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.

Pairing effects on the fragment mass distribution of Th,U,Pu,and Cm isotopes

In this article,a comprehensive study of the fission process of Th,U,Pu,and Cm isotopes using a Yukawa-folded meanfield plus standard pairing model is presented.The study focused on analyzing the effects of the pairing interaction on the fragment mass distribution and its dependence on nuclear elongation.The significant role of pairing interactions in the fragment mass distributions of^(230)Th,^(234)U,^(240)Pu,and^(246)Cm was demonstrated.Numerical analysis revealed that increasing the pairing interaction strength decreased the asymmetric fragment mass distribution and increased the symmetric distribution.Furthermore,the odd-even mass differences at symmetric and asymmetric fission points were examined,highlighting their sensitivity to changes in the pairing interaction strength.Systematic analysis of the Th,U,Pu,and Cm isotope fragment mass distributions demonstrated the effectiveness of the model in reproducing the experimental data.In addition,the effects of the zero-point energy and half-width parameter on the fragment mass distribution for^(240)Pu were explored.Thus,this study provides valuable insights into the fission process by emphasizing the importance of pairing interactions and their relationship with nuclear elongation.

Hydrodynamic Characteristics of Square Heaving Plates with Opening Under Forced Oscillation

The existence of the heaving plates can improve the heaving motion performance of an offshore structure significantly by providing both extra added mass and damping.In the current research,numerical investigation is carried out on the hydrodynamic characteristics of both isolated square heaving plate and double square heaving plates with opening by an immersed boundary-lattice Boltzmann method.The effects on hydrodynamic performance of plates due to Keulegan-Carpenter(KC)number,frequency number,opening ratio,opening distribution and spacing of plates are examined.It is found that the heaving plates with optimized opening ratio can provide additional damping compared with the plates without opening.Better hydrodynamic characteristics of double plates can be obtained with the increase of plate spacing.

Near-infrared chemical imaging for quantitative analysis of chlorpheniramine maleate and distribution homogeneity assessment in pharmaceutical formulations

Near infrared chemical imaging(NIR-CI)combines conventional near infrared(NIR)spectros-copy with chemical imaging,thus provides spectral and spatial information simult aneously.It could be utilized to visualize the spatial distribution of the ingredients in a sample.The data acquired using NIR CI instrument are hyperspectral data cube(hypercube)containing thousands of spectra.Chemometric methodologies are necessary to transform spectral information into chemical information.Partial least squares(PLS)method was performed to extract chemical information of chlorpheniramine maleate in pharmaceutical formulations.A series of samples which consisted of different CPM concentrations(w/w)were compressed and hypercube data were measured.The spectra extracted from the hypercube were used to establish the PLS model of CPM.The results of the model were R^(2)_(val)0.981,RMSEC 0.384%,RMSECV 0.483%,RMSEP 0.631%,indicating that this model was reliable.

An Extended Bivariate T-Distribution Type Symmetry Model for Square Contingency Tables

The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.

Estimation under a Finite Mixture of Exponentiated Exponential Components Model and Balanced Square Error Loss

By exponentiating each of the components of a finite mixture of two exponential components model by a positive parameter, several shapes of hazard rate functions are obtained. Maximum likelihood and Bayes methods, based on square error loss function and objective prior, are used to obtain estimators based on balanced square error loss function for the parameters, survival and hazard rate functions of a mixture of two exponentiated exponential components model. Approximate interval estimators of the parameters of the model are obtained.

Partial Least Squares Regression Model to Predict Water Quality in Urban Water Distribution Systems

The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality.Partial least squares(PLS) regression model,in which the turbidity and Fe are regarded as control objectives,is used to establish the statistical model.The experimental results indicate that the PLS regression model has good predicted results of water quality compared with the monitored data.The percentages of absolute relative error(below 15%,20%,30%) are 44.4%,66.7%,100%(turbidity) and 33.3%,44.4%,77.8%(Fe) on the 4th sampling point;77.8%,88.9%,88.9%(turbidity) and 44.4%,55.6%,66.7%(Fe) on the 5th sampling point.

Least Squares Fitting Based Fault Classification in Distribution Systems

Power systems are the largest and most complex human made systems, consisting of thousands of electrical sources, loads, transmission and distribution lines, power transformers, circuit breakers, etc. where faults always occurred. Faults can cause personnel and equipment safety problems, and can result in significant disruption to power supply and thus financial losses. In this paper we will present comprehensive mathematical suite to detect and classify fault dependent models of various types of power systems. This work will extract fault unique signatures by using polarization ellipse during the healthy condition and the polarization will be circular shape with radius equal the rated voltage of the system, but during the fault condition the polarization will be ellipse shape and the fault signature will be defined according the ellipse parameters major axis, minor axis, ellipticity and orientation angle, by using least squares criterion will define the ellipse parameters this system will identify and classify. This paper will be a milestone for extended paper based on the proposed mathematical modelling and applying it to identify, classify and localize with simulation model.

Numerical Simulation on the Impact of A Liquid Square on Rigid Plate and Liquid Layer

Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice,including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal structures,emergency landing of aircrafts at sea as well as impact of ultra-cold droplets and ice lumps under aviation conditions.In this paper, a two dimensional (2-D) solver for Navier-Stokes equations is developed and applied in the numerical simulation of the impact on a rigid plate by a liquid square. The computational domain is discretized by Finite Volume Method (FVM). The Volume of Fluid (VOF) technique is used to track the free surface and the PiecewiseLinear Interface Construction (PLIC) is used for reconstruction. The Continuum Surface Force (CSF) model is used to account for the surface tension. The convective term and the diffusive term are upwind and centrally differenced respectively. The Inner Doubly Iterative Efficient Algorithm for Linked Equations (IDEAL) is used to decouple the pressure and velocity. Based on the proposed techniques, collapse of water column is simulated and convergence study is performed for the validation of the numerical solver. Then the impact of a free falling liquid body is simulated, and the effect of volume and initial height of the liquid body is analyzed. In addition, the impact on a plate with a liquid layer is also simulated to study the effect of falling height on a liquid floor.

Review of Trends in State Estimation of Power Distribution Networks

Distribution network state estimation provided complete and reliable information for the distribution management system (DMS) and was a prerequisite for other advanced management and control applications in the power distribution network. This paper first introduced the basic principles of the state estimation algorithm and sorted out the research status of the distribution network state estimation from least squares, gross error resistance etc. Finally, this paper summarized the key problems faced by the high-dimensional multi-power flow active distribution network state estimation and discussed prospects for future research hotspots and developments.

Application of Pareto Distribution in Wage Models

This paper deals with the use of Pareto distribution in models of wage distribution. Pareto distribution cannot generally be used as a model of the whole wage distribution, but only as a model for the distribution of higher or of the highest wages. It is usually about wages higher than the median. The parameter b is called the Pareto coefficient and it is often used as a characteristic of differentiation of fifty percent of the highest wages. Pareto distribution is so much the more applicable model of a specific wage distribution, the more specific differentiation of fifty percent of the highest wages will resemble to differentiation that is expected by Pareto distribution. Pareto distribution assumes a differentiation of wages, in which the following ratios are the same： ratio of the upper quartile to the median; ratio of the eighth decile to the sixth decile; ratio of the ninth decile to the eighth decile. This finding may serve as one of the empirical criterions for assessing, whether Pareto distribution is a suitable or less suitable model of a particular wage distribution. If we find only small differences between the ratios of these quantiles in a specific wage distribution, Pareto distribution is a good model of a specific wage distribution. Approximation of a specific wage distribution by Pareto distribution will be less suitable or even unsuitable when more expressive differences of mentioned ratios. If we choose Pareto distribution as a model of a specific wage distribution, we must reckon with the fact that the model is always only an approximation. It will describe only approximately the actual wage distribution and the relationships in the model will only partially reflect the relationships in a specific wage distribution.

Chi-Square Distribution: New Derivations and Environmental Application

We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.

A MORE GENERAL FORM OF ERROR DISTRIBUTION

This paper deduced a more general error distribution,the p-th pow-er norm distribution,based on the foundational properties of random errors.

Overlapped peaks resolution for linear sweep polarography using Gaussian-like distribution

A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.

α-synuclein C端截短体的胞内分布

目的研究α-synuclein的4种C端截短体胞内的表达分布情况。方法PCR法获得α-synuclein的4个C端截短体基因片段,分别克隆入pEGFP-N1载体,并转染MN9D细胞、PC12细胞及SH-SY5Y细胞,于Confocal荧光显微镜下观察α-synuclein 4个C端截短体胞内的表达分布情况。结果α-synuclein的不同C端截短体胞内分布明显不一致,表现为随着C端部分的增长,α-synuclein截短体向核分布的趋势增强。结论α-synuclein的胞内定位与其C端密切相关,并且整个C端序列都可能在其核分布中发挥重要作用。