Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered...Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.展开更多
The authors compute the quasiconvex envelope of certain functions defined on the space M,.mn of real m x n matrices via a homogeneous function on Mmn - They also deduce Invariance properties for various convex envelop...The authors compute the quasiconvex envelope of certain functions defined on the space M,.mn of real m x n matrices via a homogeneous function on Mmn - They also deduce Invariance properties for various convex envelopes from corresponding invariance properties satisfied by a function. Some applications related in particular to nonlinear elasticity arc given.展开更多
In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space resp...In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.展开更多
The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main r...The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.展开更多
By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist ...By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.展开更多
In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.W...In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).展开更多
In order to improve the functional affinity of the humanized VH single domain antibody against human lung cancer, the genes coding the homogenous dimers dihu3D3Vn and tetramers tehu3D3VH were constructed by fusing the...In order to improve the functional affinity of the humanized VH single domain antibody against human lung cancer, the genes coding the homogenous dimers dihu3D3Vn and tetramers tehu3D3VH were constructed by fusing the SV5-Cys short peptide and p53 tetramefization structural domain gene to hu3D3VH gene via recombinant PCR technique, respectively. Then, the dihu3D3VH and tehu3D3VH genes were cloned to the prokaryotic expression vector pET-22b（ ＋ ） and expressed in E. coli BL21 （DE3）. The proteins expressed were purified through Ni^2＋ -affinity chromatographic column. Meanwhile, the hu3D3VH, dihu3D3VH and tehu3D3VH proteins were labeled with FTTC, and their reactivity with antigen and specificity were analyzed by immunofluorescence assay. As to their functional affinities, it was analyzed and compared by flow cytometry. The results indicated that these two genes were expressed as monomers and mainly as inclusion bodies. After purification and renaturation, there were about 50% of dimers and 70% of tetramer remaining in the protein solution. In addition, the dihu3D3VH and tehu3D3VH proteins still remained the reactivity with antigen and specificity of hu3D3VH protein, and their functional affinities were increased about 60% or 100% respectively, compared with those of hu3D3VH protein. It is evident that the functional affinity of hu3D3VH protein can be greatly improved by increasing its binding valency.展开更多
Regional homogeneity（ReHo）and the amplitude of low-frequency fluctuation（ALFF）are two approaches to depicting different regional characteristics of resting-state functional magnetic resonance imaging（RS-fMRI）dat...Regional homogeneity（ReHo）and the amplitude of low-frequency fluctuation（ALFF）are two approaches to depicting different regional characteristics of resting-state functional magnetic resonance imaging（RS-fMRI）data.Whether they can complementarily reveal brain regional functional abnormalities in attention-deficit/hyperactivity disorder（ADHD）remains unknown.In this study,we applied ReHo and ALFF to 23 medication-na ve boys diagnosed with ADHD and 25 age-matched healthy male controls using whole-brain voxel-wise analysis.Correlation analyses were conducted in the ADHD group to investigate the relationship between the regional spontaneous brain activity measured by the two approaches and the clinical symptoms of ADHD.We found that the ReHo method showed widely-distributed differences between the two groups in the fronto-cingulo-occipitocerebellar circuitry,while the ALFF method showed a difference only in the right occipital area.When a larger smoothing kernel and a more lenient threshold were used for ALFF,more overlapped regions were found between ALFF and ReHo,and ALFF even found some new regions with group differences.The ADHD symptom scores were correlated with the ReHo values in the right cerebellum,dorsal anterior cingulate cortex and left lingual gyrus in the ADHD group,while no correlation was detected between ALFF and ADHD symptoms.In conclusion,ReHo may be more sensitive to regional abnormalities,at least in boys with ADHD,than ALFF.And ALFF may be complementary to ReHo in measuring local spontaneous activity.Combination of the two may yield a more comprehensive pathophy-siological framework for ADHD.展开更多
We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce ...We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.展开更多
The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equatio...The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.展开更多
文摘Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.
文摘The authors compute the quasiconvex envelope of certain functions defined on the space M,.mn of real m x n matrices via a homogeneous function on Mmn - They also deduce Invariance properties for various convex envelopes from corresponding invariance properties satisfied by a function. Some applications related in particular to nonlinear elasticity arc given.
基金Supported by Natural Science Foundation of Yunnan University (Grant No. 2007Z005C)National Natural Science Foundation of China (Grant No. 10761012)
文摘In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.
基金Supported by the NNSF of China (10371092)the Foundation of Wuhan University.
文摘The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.
文摘By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
文摘A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
基金This work was financially supported by the National United University[Grant Numbers T110M20600].
文摘In this paper,we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data.We also add the average classification as an approximate solution to the nonlinear operator part,without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution.The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function,which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid.Besides,note that the new homogenization functions method(HFM)does not require dealing with the regularization and highly nonlinear equations.The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region,even though a very large level of noise 50%is imposed on the over specified Neumann conditions.The numerical errors of our scheme are in the order of O(10^(−1))-O(10^(−4)).
文摘In order to improve the functional affinity of the humanized VH single domain antibody against human lung cancer, the genes coding the homogenous dimers dihu3D3Vn and tetramers tehu3D3VH were constructed by fusing the SV5-Cys short peptide and p53 tetramefization structural domain gene to hu3D3VH gene via recombinant PCR technique, respectively. Then, the dihu3D3VH and tehu3D3VH genes were cloned to the prokaryotic expression vector pET-22b（ ＋ ） and expressed in E. coli BL21 （DE3）. The proteins expressed were purified through Ni^2＋ -affinity chromatographic column. Meanwhile, the hu3D3VH, dihu3D3VH and tehu3D3VH proteins were labeled with FTTC, and their reactivity with antigen and specificity were analyzed by immunofluorescence assay. As to their functional affinities, it was analyzed and compared by flow cytometry. The results indicated that these two genes were expressed as monomers and mainly as inclusion bodies. After purification and renaturation, there were about 50% of dimers and 70% of tetramer remaining in the protein solution. In addition, the dihu3D3VH and tehu3D3VH proteins still remained the reactivity with antigen and specificity of hu3D3VH protein, and their functional affinities were increased about 60% or 100% respectively, compared with those of hu3D3VH protein. It is evident that the functional affinity of hu3D3VH protein can be greatly improved by increasing its binding valency.
基金supported by the Commonwealth Sciences Foundation, Ministry of Health, China (200802073)the National Basic Research Development Program, Ministry of Science and Technology, China (2007BAI17B03)+1 种基金the National Natural Sciences Foundation of China (30970802, 81000593, 81020108022, 81271652)the Open Research Fund of the State Key Laboratory of Cognitive Neuroscience and Learning
文摘Regional homogeneity（ReHo）and the amplitude of low-frequency fluctuation（ALFF）are two approaches to depicting different regional characteristics of resting-state functional magnetic resonance imaging（RS-fMRI）data.Whether they can complementarily reveal brain regional functional abnormalities in attention-deficit/hyperactivity disorder（ADHD）remains unknown.In this study,we applied ReHo and ALFF to 23 medication-na ve boys diagnosed with ADHD and 25 age-matched healthy male controls using whole-brain voxel-wise analysis.Correlation analyses were conducted in the ADHD group to investigate the relationship between the regional spontaneous brain activity measured by the two approaches and the clinical symptoms of ADHD.We found that the ReHo method showed widely-distributed differences between the two groups in the fronto-cingulo-occipitocerebellar circuitry,while the ALFF method showed a difference only in the right occipital area.When a larger smoothing kernel and a more lenient threshold were used for ALFF,more overlapped regions were found between ALFF and ReHo,and ALFF even found some new regions with group differences.The ADHD symptom scores were correlated with the ReHo values in the right cerebellum,dorsal anterior cingulate cortex and left lingual gyrus in the ADHD group,while no correlation was detected between ALFF and ADHD symptoms.In conclusion,ReHo may be more sensitive to regional abnormalities,at least in boys with ADHD,than ALFF.And ALFF may be complementary to ReHo in measuring local spontaneous activity.Combination of the two may yield a more comprehensive pathophy-siological framework for ADHD.
基金This work is supported by the National Natural Science Foundation of China(10471001)
文摘We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from R^m／{0} to R^n. By the well-known representation of Clifford algebras, we find an abundance of the new 2/3 （m ＋ 1）-harmonic morphism Ф： R^m／{0} → R^n where m = 2κδ（n - 1）.
文摘The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.
