The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separ...The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separation are given according to - screen and - screen.展开更多
Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient ...Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient and the relation theorem of heredity-variation. The attribute dependence of f-variation coefficient and the relation of heredity-variation are important characteristics of S-rough sets. From such discussion, this paper puts forward the heredity mining off-knowledge and the algorithm of heredity mining, also gives its relative application.展开更多
As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the ...As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.展开更多
In this paper, we prove Legendre’s conjecture: There is a prime number between n<sup>2</sup> and (n +1)<sup>2</sup> for every positive integer n. We also prove three related conjectures. The m...In this paper, we prove Legendre’s conjecture: There is a prime number between n<sup>2</sup> and (n +1)<sup>2</sup> for every positive integer n. We also prove three related conjectures. The method that we use is to analyze binomial coefficients. It is developed by the author from the method of analyzing binomial central coefficients, that was used by Paul Erdős in his proof of Bertrand’s postulate - Chebyshev’s theorem.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs...In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs with a fag-transitive and point-imprimitive automorphism group.展开更多
In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we...In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we prove that 5 - 4 distribution of critical points for cubic system is impossible by using the method of basic triangle and index formula. Then we discuss the possible distributions of cubic systems with eight, seven or six finite critical points.展开更多
文摘The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separation are given according to - screen and - screen.
基金This project was supported by the National Natural Science Foundation of China (60364001), the Shandong ProvincialNatural Science Foundation of China (Y2004A04) and Fujian Provincial Education Foundation of China(JA04268).
文摘Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient and the relation theorem of heredity-variation. The attribute dependence of f-variation coefficient and the relation of heredity-variation are important characteristics of S-rough sets. From such discussion, this paper puts forward the heredity mining off-knowledge and the algorithm of heredity mining, also gives its relative application.
文摘As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.
文摘In this paper, we prove Legendre’s conjecture: There is a prime number between n<sup>2</sup> and (n +1)<sup>2</sup> for every positive integer n. We also prove three related conjectures. The method that we use is to analyze binomial coefficients. It is developed by the author from the method of analyzing binomial central coefficients, that was used by Paul Erdős in his proof of Bertrand’s postulate - Chebyshev’s theorem.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
基金Zhilin Zhang was supported by the National Natural Science Foundation of China(12001204)Shenglin Zhou was supported by the National Natural Science Foundation of China(12271173).
文摘In this paper we present two new families of 2-(v,k,λ)designs with a flag-transitive and point-primitive automorphism group of product action type.More sur-prisingly,one of them is still a family of 2-(v,k,λ)designs with a fag-transitive and point-imprimitive automorphism group.
文摘In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we prove that 5 - 4 distribution of critical points for cubic system is impossible by using the method of basic triangle and index formula. Then we discuss the possible distributions of cubic systems with eight, seven or six finite critical points.
