In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof ...In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.展开更多
In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of ...In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.展开更多
The applicability of the density rule of Pathwardhan and Kumer and the rule based on the linear isopiestic relation is studied by comparison with experimental density data in the literature. Predicted and measured val...The applicability of the density rule of Pathwardhan and Kumer and the rule based on the linear isopiestic relation is studied by comparison with experimental density data in the literature. Predicted and measured values for 18 electrolyte mixtures are compared. The two rules are good for mixtures with and without common ions, including those containing associating ions. The deviations of the rule based on the linear isopiestic relation are slightly higher for the mixtures involving very strong ion complexes, but the predictions are still quite satisfactory.The density rule of Pathwardhan and Kumer is more accurate for these mixtures. However, it is not applicable for mixtures containing non-electrolytes. The rule based on the linear isopiestic relation is extended to mixtures involving non-electrolytes. The predictions for the mixtures containing both electrolytes and non-electrolytes and the non-electrolyte mixtures are accurate. All these results indicate that this rule is a widely applicable approach.展开更多
Fatty acids(FAs) provide energy and also can be used to trace trophic relationships among organisms.Sea cucumber Apostichopus japonicus goes into a state of aestivation during warm summer months.We examined fatty acid...Fatty acids(FAs) provide energy and also can be used to trace trophic relationships among organisms.Sea cucumber Apostichopus japonicus goes into a state of aestivation during warm summer months.We examined fatty acid profiles in aestivated and non-aestivated A.japonicus using multivariate analyses(PERMANOVA,MDS,ANOSIM,and SIMPER).The results indicate that the fatty acid profiles of aestivated and non-aestivated sea cucumbers differed significantly.The FAs that were produced by bacteria and brown kelp contributed the most to the differences in the fatty acid composition of aestivated and nonaestivated sea cucumbers.Aestivated sea cucumbers may synthesize FAs from heterotrophic bacteria during early aestivation,and long chain FAs such as eicosapentaenoic(EPA) and docosahexaenoic acid(DHA) that produced from intestinal degradation,are digested during deep aestivation.Specific changes in the fatty acid composition of A.japonicus during aestivation needs more detailed study in the future.展开更多
In this paper we use the simplex B-spline representation of polynomials or piecewise polynomials in terms of their polar forms to construct several differential or discrete bivariate quasi interpolants which have an o...In this paper we use the simplex B-spline representation of polynomials or piecewise polynomials in terms of their polar forms to construct several differential or discrete bivariate quasi interpolants which have an optimal approximation order.This method provides an efficient tool for describing many approximation schemes involving values and(or) derivatives of a given function.展开更多
Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C...Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.展开更多
Motivated by Sasaki＇s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynom...Motivated by Sasaki＇s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is etIicient, especially for sparse bivariate polynomials.展开更多
文摘In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.
基金Supported by the Scientific Research Fund of Zhejiang Province Education Depart-ment(200700190) Supported by the Science Technique Planed Item of Taizhou City(063KY08)Supported by Major Scientific Research Fund of Taizhou University(09ZD08)
文摘In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.
基金Supported by the Science Foundation of University of Petroleum (No. ZX9903), the Open Science Foundation of the State Key Laboratory of Heavy Oil Processing (No. 200005), and the National Natural Science Foundation of China (No. 20006010).
文摘The applicability of the density rule of Pathwardhan and Kumer and the rule based on the linear isopiestic relation is studied by comparison with experimental density data in the literature. Predicted and measured values for 18 electrolyte mixtures are compared. The two rules are good for mixtures with and without common ions, including those containing associating ions. The deviations of the rule based on the linear isopiestic relation are slightly higher for the mixtures involving very strong ion complexes, but the predictions are still quite satisfactory.The density rule of Pathwardhan and Kumer is more accurate for these mixtures. However, it is not applicable for mixtures containing non-electrolytes. The rule based on the linear isopiestic relation is extended to mixtures involving non-electrolytes. The predictions for the mixtures containing both electrolytes and non-electrolytes and the non-electrolyte mixtures are accurate. All these results indicate that this rule is a widely applicable approach.
基金Supported by the National Marine Public Welfare Research Project(No.201305043)the National Natural Science Foundation of China(No.41106134)the National Key Technology R&D Program of China(Nos.2011BAD13B02,2010BAC68B01)
文摘Fatty acids(FAs) provide energy and also can be used to trace trophic relationships among organisms.Sea cucumber Apostichopus japonicus goes into a state of aestivation during warm summer months.We examined fatty acid profiles in aestivated and non-aestivated A.japonicus using multivariate analyses(PERMANOVA,MDS,ANOSIM,and SIMPER).The results indicate that the fatty acid profiles of aestivated and non-aestivated sea cucumbers differed significantly.The FAs that were produced by bacteria and brown kelp contributed the most to the differences in the fatty acid composition of aestivated and nonaestivated sea cucumbers.Aestivated sea cucumbers may synthesize FAs from heterotrophic bacteria during early aestivation,and long chain FAs such as eicosapentaenoic(EPA) and docosahexaenoic acid(DHA) that produced from intestinal degradation,are digested during deep aestivation.Specific changes in the fatty acid composition of A.japonicus during aestivation needs more detailed study in the future.
文摘In this paper we use the simplex B-spline representation of polynomials or piecewise polynomials in terms of their polar forms to construct several differential or discrete bivariate quasi interpolants which have an optimal approximation order.This method provides an efficient tool for describing many approximation schemes involving values and(or) derivatives of a given function.
基金partly supported by the National Natural Science Foundation of China under Grant Nos.91118001 and 11170153the National Key Basic Research Project of China under Grant No.2011CB302400Chongqing Science and Technology Commission Project under Grant No.cstc2013jjys40001
文摘Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.
基金supported by National Natural Science Foundation of China(GrantNos.91118001 and 11170153)National Key Basic Research Project of China(Grant No.2011CB302400)Chongqing Science and Technology Commission Project(Grant No.cstc2013jjys40001)
文摘Motivated by Sasaki＇s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is etIicient, especially for sparse bivariate polynomials.
