The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of ...The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.展开更多
Identifying disease-relevant genes and functional modules, based on gene expression pro- files and gene functional knowledge, is of high im- portance for studying disease mechanisms and sub- typing disease phenotypes....Identifying disease-relevant genes and functional modules, based on gene expression pro- files and gene functional knowledge, is of high im- portance for studying disease mechanisms and sub- typing disease phenotypes. Using gene categories of biological process and cellular component in Gene Ontology, we propose an approach to selecting func- tional modules enriched with differentially expressed genes, and identifying the feature functional modules of high disease discriminating abilities. Using the differentially expressed genes in each feature module as the feature genes, we reveal the relevance of the modules to the studied diseases. Using three data- sets for prostate cancer, gastric cancer, and leukemia, we have demonstrated that the proposed modular approach is of high power in identifying functionally integrated feature gene subsets that are highly rele- vant to the disease mechanisms. Our analysis has also shown that the critical disease-relevant genes might be better recognized from the gene regulation network, which is constructed using the characterized functional modules, giving important clues to the concerted mechanisms of the modules responding to complex disease states. In addition, the proposed approach to selecting the disease-relevant genes byjointly considering the gene functional knowledge suggests a new way for precisely classifying disease samples with clear biological interpretations, which is critical for the clinical diagnosis and the elucidation of the pathogenic basis of complex diseases.展开更多
In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[...In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.展开更多
文摘The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.30170515,30370388,30370798,30570424&30571034)the National High Tech Development Project of China(Grant Nos.2003AA2Z2051&2002AA2Z2052)+3 种基金Heilongjiang Science&Technology Key Project(Grant No.GB03C602-4)Harbin(City)Science&Technology Key Project(Grant No.2003AA3CS113)the Natural Science Foundation of Heilongjiang Province(Grant No.F0177)0utstanding 0verseas Scientist Foundation of Education Department of Heilongjiang Province(Grant No.1055HG009).
文摘Identifying disease-relevant genes and functional modules, based on gene expression pro- files and gene functional knowledge, is of high im- portance for studying disease mechanisms and sub- typing disease phenotypes. Using gene categories of biological process and cellular component in Gene Ontology, we propose an approach to selecting func- tional modules enriched with differentially expressed genes, and identifying the feature functional modules of high disease discriminating abilities. Using the differentially expressed genes in each feature module as the feature genes, we reveal the relevance of the modules to the studied diseases. Using three data- sets for prostate cancer, gastric cancer, and leukemia, we have demonstrated that the proposed modular approach is of high power in identifying functionally integrated feature gene subsets that are highly rele- vant to the disease mechanisms. Our analysis has also shown that the critical disease-relevant genes might be better recognized from the gene regulation network, which is constructed using the characterized functional modules, giving important clues to the concerted mechanisms of the modules responding to complex disease states. In addition, the proposed approach to selecting the disease-relevant genes byjointly considering the gene functional knowledge suggests a new way for precisely classifying disease samples with clear biological interpretations, which is critical for the clinical diagnosis and the elucidation of the pathogenic basis of complex diseases.
基金Supported by National Natural Science Foundation of China (Grant No. 10961021)
文摘In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.
