Research on Some Questions About Selection of Independent Variables

The paper studies four methods about selection of independent variables in multivariate analysis. In general condition, advanced statistical method and backward statistical method could not obtain the best subset of independent variables. It is possibly affected by the orders of variables or associations among variables. When multicollinearity is presented in a set of explanatory variables-abnormal state, it is not effective to use the method, although stepwise regression and optimum selecting method of total subsets is widely used.;According to this case, the paper proposes a new method which combines deleting variables with ingredient analysis and is used in research and science practically.;The important characteristic of this paper is that it gives some examples to support each conclusion.

NONLINEAR INTEGRAL INEQUALITY IN n INDEPENDENT VARIABLES WITH RETARDATION

In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.

INTEGRAL INEQUALITIES IN TWO INDEPENDENT VARIABLES AND THEIR APPLICATIONS

In this paper, we investigate some general integral inequalities in two independent variables which are used to solve some problems involving the theory of partial diferential and integral equations with time delays.

DISCRETE PHENOMENA IN THE UNIQUENESS OF THE CAUCHY PROBLEM IN MULTIPLE INDEPENDENT VARIABLES

This paper deals with discerete phenomena in uniqueness in the Cauchy problemsum from i?j=0 to n （i?j/0）aijuxixj+sum from i=0 to n（i/0）biuxi+cu=0,x0>0, u（0,x1,…,xn）=ux0（0,x1,…,xn） =0We prove that the problem only has trivial solutions in the neighbourhood of the origin, if bo（0）-Z sum from i=1 to n（i/1）（2ai + 1）λi≠0,λi>0 being the square roots of the eigenvalues of the product of matrices(?2aoo/?xi?xi（0）(i?j=i,….?and （aif（0））ii?f….,and ai being the arbitrarily non-negative integers.

The Relations of Change Rate of Constitutive Variables for the Freezing and Thawing of Water Saturated Porous Media

The relations of change rate of an independent variable, volumetric strain of the porous skeleton, with the change rates of a kind of constitutive variables, such as porosity, volumetric strain of the solid matrix, are derived from the definition of the porosity of water saturated porous media; and the relations of the change rates of another two independent variables, pressure of the pore liquid water and temperature, with the change rates of another kind of constitutive variables, such as pressure of the pore ice, average pressure of the pore liquid water and ice, and average stress of the solid matrix, are obtained from the Clausius Clapeyron relation in the process of freezing or thawing, definitions of the average pore pressure and effective stress. Based on the hypothesis of linear thermoelasticity, principle of effective stress and these relations, the change rates of all constitutive variables may be described with the change rates of the three independent variables.

Diabetes Risk Factor and Its Relationship to Increasing Coronavirus (COVID-19) Mortality Rate in United States in 2019-2022: An Epidemiological Study

As an effort to understand the effect of diabetes on the increasing rate of COVID-19 infection, we embarked upon a detailed statistical analysis of various datasets that include COVID-19 infection and mortality rate, diabetes and diseases that may contribute to the severity and risk factor of diabetes in individuals and this impact on COVID-19 and the mortality rate. These diseases include respiratory diseases, cardiovascular diseases, and obesity. Equally significant is the statistical analysis on ethnicity, age, and sex on COVID-19 infection as well as mortality rate. Their possible contributions to increasing the severity and risk factor of diabetes as a risk to mortality to individuals who have COVID-19. Objectives: The ultimate objectives of this investigation are as follow: 1) Is there a risk factor of diabetes on COVID-19 infection and increasing mortality rate? 2) To what extent do other disease conditions that include, obesity, heart failure, and respiratory diseases influence the severity and risk factor of diabetes on increasing COVID-19 infection and mortality rate? 3) To what extent does age, race, and gender increase the mortality of COVID-19 and increase the severity and risk factor of diabetes on COVID-19 mortality rate? 4) How and why COVID-19 virus increases the risk of diabetes in children? 5) Diabetes and COVID-19: Who is most at Risk? Lastly, understanding the misconception of COVID-19 and diabetes.

STUDY ON IRONING USING UPPER-BOUND APPROACH

An upper-bound model for ironing is proposed according to theupper-bound theorem. There are two independent parameters which are used tooptimize the upperbound approach in this model. Through calculation, the analyticalresults agree well with the expenmental results. Meanwhile, based on the proposedmodel, the influence on ironing force is analysed of the main technological parameterssuch as the ironing rate, semicone angle, the ratio of the inside radius to the outside ra-dius, the length of working land of die and friction factors existing between the billetand die.

On the Computation of Noether Normalization

This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.

Will Political Stability Factors Influence FDI Inflow？

In this paper, the authors discuss whether political stability would influence Foreign Direct Investment （FDI） inflow. There is an increasing interest among scholars about FDI since it has been considered as a way to offer abundant foreign capital, high skills, and new jobs throughout developing countries. Foreign companies pay more attention to the institutional properties and time horizon of the government leader. From historical experience, autocratic countries attract more FDI because of their flexibility and powerfulness. Hence, the research assumes that political stability as well as other factors like GDP, OMI, and interest rate probably would increase FDI inflow. Stata and Eviews have been used for regressing the independent variables and dependent variable. Correlation between each individual variable was calculated, and Least Squares method was used for investigating whether the linear correlation is significant. Finally, carefully analysing each indicator and ploting the graphs, things were found that there is no significant correlation between political stability factors of a country and FDI inflow. There are several explanations about the failure of hypothesis. First, the 10-year span is not long enough to prove the relationship. Then, the countries picked are most on the transition from autocracies to democracies. All the factors might influence the result of the correlation. Specific external factors such as economic conditions of investors need to be explored to see if it would probably determine the strong or weak of FDI.

Establishment and evaluation of operation function model for cascade hydropower station

Toward solving the actual operation problems of cascade hydropower stations under hydrologic uncertainty, this paper presents the process of extraction of statistical characteristics from long-term optimal cascade operation, and proposes a monthly operation function algorithm for the actual operation of cascade hydropower stations through the identification, processing, and screening of available information during long-term optimal operation. Applying the operation function to the cascade hydropower stations on the Jinshajiang-Yangtze River system, the modeled long-term electric generation is shown to have high precision and provide benefits. Through comparison with optimal operation, the simulation results show that the operation function proposed retains the characteristics of optimal operation. Also, the inadequacies and attribution of the algorithm are discussed based on case study, providing decision support and reference information for research on large-scale cascade operation work.

A LIL for independent non-identically distributed random variables in Banach space and its applications

In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.

Optimizing process of preparing artificial-similar material for rocky slope with uniform formula design

The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.

Sharp large deviation results for sums of independent random variables

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).

Predicting equations of main factors affecting regional climate in the"Three-North" Protective Forest Area

The relationship between the change of forest resources and climatic factor in the, “Three-North” region of China were studied in this paper. The predicting equations of climatic factor (dependent variable) with regional independent variable (longitude, latitude and altitude) and stand independent variable (forest coverage rate), were developed by extensively using the linear and nonlinear regression methods. With these models, we can calculate the ecological benefit of Shelter-belt forest.

On Random Taylor Series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.

NOTES ON ERDOS' CONJECTURE

Let Xn,n ≥ 1, be a sequence of independent random variables satisfying P(Xn = 0) = 1 - P(Xn = an) = 1 - 1/Pn, where an,n ≥ 1, is a sequence of real numbers, and Pn is the nth prime,set FN(x) = P (N Xn ≤ x). The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent, it is both sufficient and necessary that there exist three numbers X0 and X1 < X2 such that limsup(FN(X2) - FN(X1)) > 0 holds, and Lo = N→ ∞ lim FN(X0) exists. Moreover, the authors point out that they can also obtain the same result in the weakened case of lim inf P(Xn = 0) > 0.

Extended Rama Distribution:Properties and Applications

In this paper,the Rama distribution(RD)is considered,and a new model called extended Rama distribution(ERD)is suggested.The new model involves the sum of two independent Rama distributed random variables.The probability density function(pdf)and cumulative distribution function(cdf)are obtained and analyzed.It is found that the new model is skewed to the right.Several mathematical and statistical properties are derived and proved.The properties studied include moments,coefficient of variation,coefficient of skewness,coefficient of kurtosis and moment generating function.Some simulations are undertaken to illustrate the behavior of these properties.In addition,the reliability analysis of the distribution is investigated through the hazard rate function,reversed hazard rate function and odds function.The parameter of the distribution is estimated based on the maximum likelihood method.The distributions of order statistics for ERD are also presented.The performance of the suggested model is compared with several other lifetime distributions based on some goodness of fit tests on a real dataset.It turns out that the suggested model is more flexible than its competitors considered in this study,for modeling real lifetime data.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

The determinants of shareholders＇ wealth of acquiring firms in India

Corporate restructuring has become a major component in the financial and economic environment all over the world. Industrial restructuring has raised important issues for business decisions as well as for public policy formulation. Since 1991, Indian industries have been increasingly exposed to both domestic and international competition and competitiveness. The companies started restructuring there operations around their core business there M ＆ A. But M ＆ A is an area of potential good and harm in corporate strategy including manufacturing industry. Therefore, an attempt has been made to analyze the security returns and to find out the net wealth increase or decrease to the shareholders of acquiring firms. In India, there are totally 58 manufacturing companies which have undergone mergers and acquisitions during 2000, 2001 ＆ 2002. Thirty percentage from the total population was taken as sample size （i.e., 17 companies out of 58）. The present study is mainly based on secondary data. The Market Model and Market Adjusted Returns Model analysis are used as tools of analysis.

On Some New Integral Inequalities for Functions in One and Two Variables

In this paper, we consider a bound on a general version of the integralinequalities for functions and also study the qualitative behavior of the solutions of certainclasses of the hyperbolic partial delay differential equations under the integral inequalities.