In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison...In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.展开更多
Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ c...Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
The paper gives a brief analysis of the color harmony aesthetic measure of Spencer which was emerged in the industry art age, and points out shortcomings of the early studies. It studies order factors which affect the...The paper gives a brief analysis of the color harmony aesthetic measure of Spencer which was emerged in the industry art age, and points out shortcomings of the early studies. It studies order factors which affect the color harmony aesthetic measure based on the psychophysical method, and presents a continuous curve of the order factors. These are necessary for true color CAD, and are an essential research for automatic design leading to economic and social benefits. Key words paired comparison - color harmony - aesthetic measure - order factor展开更多
Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to i...Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.展开更多
文摘In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.
基金the National Natural Science Foundation of China( 1 0 371 1 0 9)
文摘Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘The paper gives a brief analysis of the color harmony aesthetic measure of Spencer which was emerged in the industry art age, and points out shortcomings of the early studies. It studies order factors which affect the color harmony aesthetic measure based on the psychophysical method, and presents a continuous curve of the order factors. These are necessary for true color CAD, and are an essential research for automatic design leading to economic and social benefits. Key words paired comparison - color harmony - aesthetic measure - order factor
基金The National Natural Science Foundation of China(No.50778111)The Key Project of Fund of Science and Technology Development of Shanghai(No.07JC14023)
文摘Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.
