Gene selection (feature selection) is generally pertormed in gene space(feature space), where a very serious curse of dimensionality problem always existsbecause the number of genes is much larger than the number of s...Gene selection (feature selection) is generally pertormed in gene space(feature space), where a very serious curse of dimensionality problem always existsbecause the number of genes is much larger than the number of samples in gene space(G-space). This results in difficulty in modeling the data set in this space and the lowconfidence of the result of gene selection. How to find a gene subset in this case is achallenging subject. In this paper, the above G-space is transformed into its dual space,referred to as class space (C-space) such that the number of dimensions is the verynumber of classes of the samples in G-space and the number of samples in C-space isthe number of genes in G-space. it is obvious that the curse of dimensionality in C-spacedoes not exist. A new gene selection method which is based on the principle of separatingdifferent classes as far as possible is presented with the help of Principal ComponentAnalysis (PCA). The experimental results on gene selection for real data set areevaluated with Fisher criterion, weighted Fisher criterion as well as leave-one-out crossvalidation, showing that the method presented here is effective and efficient.展开更多
In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatte...In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.展开更多
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lore...In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.展开更多
In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonome...In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to t...This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.展开更多
The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and...The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO<sub>2</sub> per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.展开更多
In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. ...In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.展开更多
This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from...This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.展开更多
In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a n...In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.展开更多
文摘Gene selection (feature selection) is generally pertormed in gene space(feature space), where a very serious curse of dimensionality problem always existsbecause the number of genes is much larger than the number of samples in gene space(G-space). This results in difficulty in modeling the data set in this space and the lowconfidence of the result of gene selection. How to find a gene subset in this case is achallenging subject. In this paper, the above G-space is transformed into its dual space,referred to as class space (C-space) such that the number of dimensions is the verynumber of classes of the samples in G-space and the number of samples in C-space isthe number of genes in G-space. it is obvious that the curse of dimensionality in C-spacedoes not exist. A new gene selection method which is based on the principle of separatingdifferent classes as far as possible is presented with the help of Principal ComponentAnalysis (PCA). The experimental results on gene selection for real data set areevaluated with Fisher criterion, weighted Fisher criterion as well as leave-one-out crossvalidation, showing that the method presented here is effective and efficient.
文摘In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.
基金supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
基金supported by the Ministry of Education and Science of Republic Kazakhstan(Grant No.5129/GF4)partially by the Russian Academic Excellence Project(agreement between the Ministry of Education and Science of the Russian Federation and Ural Federal University No.02.A03.21.006 of August 27,2013)
文摘In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.
文摘In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
基金Work supported by National Natural Science Foundation of China.
文摘This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.
文摘The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO<sub>2</sub> per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.
文摘In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.
文摘In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.
