The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets...The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.展开更多
A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some f...A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.展开更多
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas ar...A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.展开更多
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary an...This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.展开更多
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational inter...At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.展开更多
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.展开更多
In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is establis...In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.展开更多
The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary ...The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary structure. So development of an accurate prediction method ofβ-turn types is very necessary. In this paper, we used the composite vector with position conservation scoring function, increment of diversity and predictive secondary structure information as the input parameter of support vector machine algorithm for predicting theβ-turn types in the database of 426 protein chains, obtained the overall prediction accuracy of 95.6%, 97.8%, 97.0%, 98.9%, 99.2%, 91.8%, 99.4% and 83.9% with the Matthews Correlation Coefficient values of 0.74, 0.68, 0.20, 0.49, 0.23, 0.47, 0.49 and 0.53 for types I, II, VIII, I’, II’, IV, VI and nonturn respectively, which is better than other prediction.展开更多
We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.
By the Plemelj formula and the compressed fixed point theorem,this paper discusses a kind of boundary value problem for hypermonogenic function vectors in Clifford analysis.And the paper proves the existence and uniqu...By the Plemelj formula and the compressed fixed point theorem,this paper discusses a kind of boundary value problem for hypermonogenic function vectors in Clifford analysis.And the paper proves the existence and uniqueness of the solution to the boundary value problem for hypermonogenic function vectors in Clifford analysis.展开更多
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular in...This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.展开更多
基金supported by the National Natural Science Foundation of China(11201395)supported by the Science Foundation of Educational Commission of Hubei Province(Q20132801)
文摘The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
文摘The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.
文摘A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
基金The work is supported by the National Natural Science Foundation of China (10271074).
文摘A new vector-valued Pad′e-type approximation is defined by introducing a gener- alized vector-valued linear functional from a scalar polynomial space to a vector space. Some algebraic properties and error formulas are presented. The expressions of this Pad′e-type ap- proximants are provided with the generating function form and the determinant form.
基金Supported by Natural Science Foundation of Henan Province（0511013500）
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
文摘This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.
基金Supported by Shanghai Natural Science Foundation (Grant No.10ZR1410900)Key Disciplines of Shanghai Mu-nicipality (Grant No.S30104)+1 种基金the Anhui Provincial Natural Science Foundation (Grant No.070416227)Stu-dents’ Innovation Foundation of Hefei University of Technology (Grant No.XS08079)
文摘At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
基金the Natural Science Foundation of Zhejiang Province,China(M103089)
文摘In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.
文摘The structure and function of proteins are closely related, and protein structure decides its function, therefore protein structure prediction is quite important.β-turns are important components of protein secondary structure. So development of an accurate prediction method ofβ-turn types is very necessary. In this paper, we used the composite vector with position conservation scoring function, increment of diversity and predictive secondary structure information as the input parameter of support vector machine algorithm for predicting theβ-turn types in the database of 426 protein chains, obtained the overall prediction accuracy of 95.6%, 97.8%, 97.0%, 98.9%, 99.2%, 91.8%, 99.4% and 83.9% with the Matthews Correlation Coefficient values of 0.74, 0.68, 0.20, 0.49, 0.23, 0.47, 0.49 and 0.53 for types I, II, VIII, I’, II’, IV, VI and nonturn respectively, which is better than other prediction.
文摘We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.
基金Supported by the National Natural Science Foundation of China (Grant No.10801043)the Natural Science Foundation of Hebei Province (Grant No.A2010000346)the Foundation of Hebei Normal University (GrantNo.L200902)
文摘By the Plemelj formula and the compressed fixed point theorem,this paper discusses a kind of boundary value problem for hypermonogenic function vectors in Clifford analysis.And the paper proves the existence and uniqueness of the solution to the boundary value problem for hypermonogenic function vectors in Clifford analysis.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 10961015, 11261023, 10871024, 10931001, 11561057） and the Key Laboratory of Mathematics and Complex System, Ministry of Education, China.
文摘This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar＇s inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.
