ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

熔融纺丝法研究聚乙烯熔体的拉伸流变性能

采用熔融纺丝法研究了低密度聚乙烯(PE-LD)、线形低密度聚乙烯(PE-LLD)和高密度聚乙烯(PE-HD)熔体的拉伸流变性能。结果表明,PE-LD、PE-LLD和PE-HD熔体的熔体强度都随温度的升高而下降;随着拉伸应变速率和温度的升高,PE-LD、PE-LLD和PE-HD熔体的拉伸黏度下降;随着挤出速率的提高,相同应变速率下,PE-LD、PE-LLD和PE-HD熔体的拉伸应力和拉伸黏度都有所降低。

EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.

Pore shrinkage capacity of Shajiang black soils(Vertisols)on the North China Plain and its influencing factors

Different pore sizes present different pore shrinkage capacities in a nonrigid soil.However,the shrinkage capacities of different pore sizes and their influencing factors are not clear.We aimed to quantify the shrinkage capacities of different pore sizes(large pores,>50μm;medium pores,0.2-50μm;fine pores,<0.2μm)and determine how soil properties impact soil shrinkage capacity at the regional scale.Two sampling transects from west to east(360 km long,35 samples)and from north to south(190 km long,29 samples)were selected to investigate soil shrinkage capacity and physicochemical properties of at0-20 cm depth in the Vertisol(locally known as Shajiang black soil)region of the North China Plain.The results showed that soil total shrinkage capacity,indicated by the coefficient of linear extensibility(COLE),had a mean value of 0.041-0.051 in the west-east and north-south transects.Large pores had higher pore shrinkage index(PSI)values(0.103-0.109)than medium(0.077-0.096)and fine(0.087-0.091)pores.The PSI of fine pores showed a fluctuating increasing trend from northwest to southeast,and the fine pore shrinkage capacity determined the COLE(r^(2)=0.789,P<0.001).The PSI of large pores had a significant relationship with soil bulk density(r=0.281,P<0.05)and organic carbon(r=-0.311,P<0.05),whereas those of medium and fine pores were correlated with soil clay content(r=0.381 and 0.687,respectively,P<0.001).In addition,the PSI of fine pores was also correlated with montmorillonite content(r=0.387,P<0.01).It can be concluded that the PSI of large pores is related to anthropogenically influenced soil properties with low stability,whereas those of medium and fine pores are related to pedogenic properties.The high variability in anthropogenic and pedogenic factors explains the spatial pattern of Vertisol shrinkage capacity on the North China Plain.

Computational Complexity of a Solution for Directed Graph Cooperative Games

Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.

Orthogonal Discriminant Improved Local Tangent Space Alignment Based Feature Fusion for Face Recognition

Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.

Shrinkage Characteristics of Lime Concretion Black Soil as Affected by Biochar Amendment

Studies have reported that biochar is a sustainable amendment that improves the chemical and physical properties of soil.In this study,an incubation experiment was conducted to investigate the effects of different application rates of biochar on the cracking pattern and shrinkage characteristics of lime concretion black soil after three wetting and drying cycles.Biochar derived from the corn straw and peanut shell mixture was applied to the soil at rates of 0,50,100,and 150 g kg^(-1)dry weight,representing the treatments T_(0),T_(50),T_(100),and T_(150),respectively.During the wetting and drying cycles,the cracking pattern and shrinkage characteristics of the unamended and amended soil samples were recorded.Application of biochar significantly increased soil organic carbon content in the samples.During soil desiccation,biochar significantly reduced the rate of water loss.Cracks propagated slowly and stopped due to the relatively higher water content in the soil applied with biochar.The cracking area density(ρ_c),equivalent width,fractal dimension,and cracking connectivity index decreased during the drying process with increasing application rate of biochar.Theρ_(c )value of the T_(50),T_(100),and T_(150) treatments decreased by 33.6%,52.1%,and 56.9%,respectively,after three wetting and drying cycles,whereas the T_(0) treatment exhibited a marginal change.The coefficient of linear extensibility,an index used to describe onedimentional shrinkage,of the unamended soil sample(T_(0))was approximately 0.23.Application of 100 and 150 g kg^(-1)biochar to the soil significantly reduced the shrinkage capacity by 41.45%and 45.54%,respectively.The slope of the shrinkage characteristics curve,which indicates the ralationship between soil void ratio and moisture ratio,decreased with increase in the application rate of biochar.Furthermore,compared with the T_(0) treatment,the proportional shrinkage zone of the shrinkage characteristic curve of the T_(50),T_(100),and T_(150) treatments decreased by 5.8%,13.1%,and 12.1%,respectively.Differences were not observed in the moisture ratio at the maximum curvature of the shrinkage characteristic curve among the treatments.The results indicate that biochar can alter the cracking pattern and shrinkage characteristics of lime concretion black soil.However,the effects of biochar on the shrinkage of lime concretion black soil are dependent on the number of wetting and drying cycles.

OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A_(T,S)^(2)

This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.