Convergence of a Sinusoidal Series with an Infinite Integral

In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.

Evaluation model of individual thermal comfort based on mean skin temperature

The local skin temperatures of 22 subjects at air temperatures of 21,24,26,29 ℃ are measured,and the mean skin temperatures are calculated by ten skin temperature measuring points.The thermal comfort levels and the thermal sensations of these subjects are also investigated by a questionnaire.The Mahalanobis distance discrimination method is applied to establish the evaluation model for the thermal comfort based on the mean skin temperature.The experimental results indicate that the difference of the mean skin temperatures between the comfort level and the discomfort level is significant.Using the evaluation model,the mean skin temperature at the thermal comfort level is 32.6 to 33.7 ℃,and the thermal comfort levels of 72% of the subjects are correctly evaluated.The accuracy of the evaluation model can be improved when the effects of sex of the subject on the mean skin temperature and the thermal comfort are considered.It can be concluded that the mean skin temperature can be used as an effective physiological indicator to evaluate human thermal comfort in a steady thermal environment.

Coal–rock interface detection on the basis of image texture features

Based on the stability and inequality of texture features between coal and rock,this study used the digital image analysis technique to propose a coal–rock interface detection method.By using gray level co-occurrence matrix,twenty-two texture features were extracted from the images of coal and rock.Data dimension of the feature space reduced to four by feature selection,which was according to a separability criterion based on inter-class mean difference and within-class scatter.The experimental results show that the optimized features were effective in improving the separability of the samples and reducing the time complexity of the algorithm.In the optimized low-dimensional feature space,the coal–rock classifer was set up using the fsher discriminant method.Using the 10-fold cross-validation technique,the performance of the classifer was evaluated,and an average recognition rate of 94.12%was obtained.The results of comparative experiments show that the identifcation performance of the proposed method was superior to the texture description method based on gray histogram and gradient histogram.

On the exact solutions to the long short-wave interaction system

The complete discrimination system for polynomial method is applied to the long-short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the （G~/G）-expansion method, we gain some new solutions.

Kernel Model Applied in Kernel Direct Discriminant Analysis for the Recognition of Face with Nonlinear Variations

A kernel-based discriminant analysis method called kernel direct discriminant analysis is employed, which combines the merit of direct linear discriminant analysis with that of kernel trick. In order to demonstrate its better robustness to the complex and nonlinear variations of real face images, such as illumination, facial expression, scale and pose variations, experiments are carried out on the Olivetti Research Laboratory, Yale and self-built face databases. The results indicate that in contrast to kernel principal component analysis and kernel linear discriminant analysis, the method can achieve lower （7%） error rate using only a very small set of features. Furthermore, a new corrected kernel model is proposed to improve the recognition performance. Experimental results confirm its superiority （1% in terms of recognition rate） to other polynomial kernel models.

Static Model Classification Status： Taking Into Account Emerging External Factors

Analysis of the problem of predicting bankruptcy shows that foreign and domestic models included only internal factors of enterprises. But the same indicators of internal factors in the rapidly changing external environment can lead to bankruptcy, and not in others. External factors are the most dangerous, because the possible influence on them is minimal and the impact of their implementation can be devastating. This paper focuses on the same factors to assess the impact of the macroeconomic indicators （extemal factors） on the parameters of static models predicting a local approximation of the crisis at the plant. To accomplish the purpose, a Spark set of 100 companies was compiled, including 50 companies which officially declared bankruptcy in the period of 2000-2009 and 50 stable operating companies with a random sample of the same time period. External factors were extracted from the Joint Economic and Social Data Archive1 The author compared two data sets： （1） microeconomic indicators--money to the total liabilities, retained earnings to total assets, net profit to revenue, Earnings Before Interest and Taxes （EBIT） to assets, net income to equity, net profit to total liabilities, current liabilities to total assets, the totality of short-term and long-term loans to total assets, current assets to current liabilities, assets to revenue, equity to total assets, and current assets to revenue; and （2） external factors--index of real gross domestic product （GDP）, industrial production index, the index of real cash incomes, an index of real investments, consumer price index, the refinancing rate, unemployment rate, the price of electricity, gas prices, oil price, gas price, dollar to ruble, ruble euro Standard ＆ Poor （S＆P） index, the Russian Trading System （RTS） index, and region. The aim of the comparison results paging classes ＂insolvent＂ and ＂non-bankrupt＂ is achieved using two methods： classification and discrimination. In both methods, computational procedures are realized with the use of algorithms linear regression, artificial neural network, and genetic algorithm. In the 2-m model, data set includes both internal and external factors. The results showed that the inclusion of only the microeconomic indicators, excluding external factors, impedes models about two times.

Comparison of Snowfall Variations over China Identified from Different Snowfall/Rainfall Discrimination Methods

Based on the snowfall observations at 836 surface weather stations in China and the Daily Surface Climate Variables of China version 3.0 dataset for 1961–2013, capability of five methods with different objective criteria for identifying wintertime snowfall is evaluated, to provide reference for application of these methods in snowfall/rainfall discrimination. Methods Ⅰ, Ⅱ, Ⅲ, Ⅳ, and Ⅴuse the daily average surface air temperature(Ta), wet-bulb temperature(Tw), dynamic threshold Tw, 0-cm ground temperature, and 700–850-hPa thickness, respectively, to identify the snowfall. The results show that the climatological distribution of snowfall can be well produced by Methods Ⅰ, Ⅱ, and Ⅲ. Method Ⅳ underestimates the snowfall days in eastern Tibetan Plateau(ETP), and Method Ⅴ cannot yield the actual large numbers of snowfall days and amounts. Accordingly, the linear trends of snowfall days estimated from Methods Ⅰ, Ⅱ, and Ⅲ largely agree with the observations, while a discrepancy is found in the linear trend of snowfall amounts over southeastern China(SEC). For interannual and decadal variations of snowfall, Method Ⅴ shows the worst performance. It is more reasonable to use Tw to distinguish snowfall from rainfall instead of Ta, 0-cm ground temperature, and 700–850-hPa thickness;and the reference thresholds of Tw in northeastern China(NEC), northwestern China(NWC), ETP, and SEC are-1.5,-1.5,-0.4, and-0.3°C, respectively. The above results are beneficial to identifying snowfall in short-term climate prediction.

Study of n-γ discrimination in low energy range(above 40 keVee) by charge comparison method with a BC501A liquid scintillation detector

A VME-based experiment system for n-y discrimination using the charge comparison method was established.A data acquisition program for controlling the programmable modules and processing data online via VME64X bus was developed through the use of Lab VIEW.The two-dimensional（2D） scatter plots of the charge in the slow component vs.the total charge from ^（241）Am-Be and 252Cf neutron sources are presented.The 2D scatter plots of the energy vs.the ratio of the charge in the slow component to the total charge of the pulses are also presented.The quality of n-γ discrimination was checked by the figure-of-merit,and the results showed good performance of n-γ discrimination at the low energy range.Neutrons and γ-rays were separated above 50 keVee（electron-equivalent energy）.The quality of n-γ discrimination has been improved compared with others＇ results at five energies（150,250,350,450,550 keVee）.

Discriminating among tectonic settings of spinel based on multiple machine learning algorithms

In geochemistry,researchers usually discriminate among tectonic settings by analyzing the chemistry elements of minerals.Previous studies have generally taken spinel and monoclinic pyroxene as subjects.Therefore,in this research,we took spinel as a breakthrough.Totally 1898 spinel samples with 14-dimension chemistry elements were collected from three different tectonic settings,including ocean island,convergent margin,and spreading center.In the experiment,20 classification algorithms were conducted in the classification learner application of MATLAB.The validation accuracies,receiver operating characteristic curves(ROCs),and the areas under ROC curve(AUCs)show that the Bag Ensemble Classifier has the best performance in the problem.Its validation accuracy is 86.3%,and the average AUC is 0.957.For further analysis,we studied the importance of different major elements in discriminating.It has been found that TiO2 has the best impact on discrimination,and FeOT,Al2O3,Cr2O3,MgO,MnO,and ZnO are of less importance.Based on the Bag Ensemble Classifier,a MATLAB plug-in application named Discriminator of Spinel Tectonic Setting(DSTS)has been developed for promoting the usage of machine learning in geochemistry and facilitating other researchers to use our achievements.

Comprehensive Application of Multiple Genetic Markers in a Case of Half‑Siblings with the Same Father and Different Mothers and an Avuncular Relationship

Half-sibling(HS)kinship testing is more difficult and complicated.This article describes a case where we sought to establish if three children with different mothers(one boy and two girls),shared a common father.The three children and their mother,as well as the suspected father’s elder brother took part in the identification.To investigate the application of multiple genetic markers in HS kinship testing,autosomal STR,Y-STR,and X-STR was performed on blood samples from the individuals of interest C1(female),M1(mother of C1),C2(male),M2(mother of C2),C3(female),M3(mother of C3),and UC(elder brother of the suspected biological father).The 24 Y-STR haplotypes of C2 and UC were identical,confirming that they come from the same paternal line.Among the 27 X-STRs tested in C1 and C3,18 of them had different paternal alleles,so C1 and C3 were excluded as half-sibling kinship.39 autosomal STR were calculated by ITO method,the HSI(or AI)of the pairs C1-C3,C2-C3,and C3-UC are<1,so HS kinship between C1 and C3,and between C2 and C3 can be excluded and avuncular kinship between C3 and UC can be excluded.The HSI(or AI)of the pairs C1-C2,C1-UC,and C2-UC are much>1,which may supports HS kinship between C1 and C2 and avuncular kinship between C1 and UC,and between C2 and UC.15 autosomal STR were calculated by discriminant function,DHS3>DR3 between C1 and C2,and thus they could be HS.DHS3<DR3 between C1 and C3,and between C2 and C3,so C1 and C3,and C2 and C3 may be unrelated individuals.Based on the above results,we can conclude that a HS relationship may be existed between C1 and C2.There may be a avuncular relationships between C1 and UC and between C2 and UC.HS relationships between C3 and C1 and between C3 and C2 as well as an avuncular relationship between C3 and UC were not supported by this study.The application of multiple genetic marker testing should be more regularly applied in the evaluation of HS and avuncular relationships.Increasing the number of related individuals tested when evaluating kinship relationships provides more data for better identification.