Let { E i∶i∈I } be a family of Archimedean Riesz algebras.The product of Riesz algebras is denoted by Π i∈I E i .The main result in this paper is the following conclusion:there ...Let { E i∶i∈I } be a family of Archimedean Riesz algebras.The product of Riesz algebras is denoted by Π i∈I E i .The main result in this paper is the following conclusion:there exists a completely regular Hausdorff space X such that Π i∈I E i is Riesz algebra isomorphic to C(X) if and only if for every i∈I there exists a completely regular Hausdorff space X i such that E i is Riesz algebra isomorphic to C(X i) .展开更多
Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). T...Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.展开更多
AIM TO detect significant clusters of co-expressed genes associated with tumorigenesis that might help to predict stomach adenocarcinoma （SA） prognosis.METHODS The Cancer Genome Atlas database was used to obtain RNA...AIM TO detect significant clusters of co-expressed genes associated with tumorigenesis that might help to predict stomach adenocarcinoma （SA） prognosis.METHODS The Cancer Genome Atlas database was used to obtain RNA sequences as well as complete clinical data of SA and adjacent normal tissues from patients. Weighted gene co-expression network analysis （WGCNA） was used to investigate the meaningful module along with hub genes. Expression of hub genes was analyzed in 362 paraffin-embedded SA biopsy tissues by immunohistochemical staining. Patients were classified into two groups （according to expression of hub genes）： Weak expression and over-expression groups. Correlation of biomarkers with clinicopathological factors indicated patient survival.RESULTS Whole genome expression level screening identified 6,231 differentially expressed genes. Twenty-four co- expressed gene modules were identified using WGCNA. Pearson＇s correlation analysis showed that the tan module was the most relevant to tumor stage （r = 0.24, P = 7 × 10 -6）. In addition, we detected sorting nexin （SNX）10 as the hub gene of the tan module. SNX10 expression was linked to T category （P = 0.042, x2= 8.708）, N category （P = 0.000, x2= 18.778）, TNM stage （P = 0.001, x2 = 16.744） as well as tumor differentiation （P = 0.000,x2= 251.930）. Patients with high SNX10 expression tended to have longer diseasefree survival （DFS; 44.97 mo vs 33.85 mo, P = 0.000） as well as overall survival （OS; 49.95 vs 40.84 mo, P = 0.000） in univariate analysis. Multivariate analysis showed that dismal prognosis could be precisely predicted clinicopathologically using SNX10 [DFS： P = 0.014, hazard ratio （HR） = 0.698, 95% confidence interval （CI）： 0.524-0.930, OS： P = 0.017, HR = 0.704, 95%CI： 0.528-0.940].CONCLUSION This study provides a new technique for screening prognostic biomarkers of SA. Weak expression of SNX10 is linked to poor prognosis, and is a suitable prognostic biomarker of SA.展开更多
The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies...The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies the relations among some conditions used therein.展开更多
文摘Let { E i∶i∈I } be a family of Archimedean Riesz algebras.The product of Riesz algebras is denoted by Π i∈I E i .The main result in this paper is the following conclusion:there exists a completely regular Hausdorff space X such that Π i∈I E i is Riesz algebra isomorphic to C(X) if and only if for every i∈I there exists a completely regular Hausdorff space X i such that E i is Riesz algebra isomorphic to C(X i) .
文摘Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.
文摘AIM TO detect significant clusters of co-expressed genes associated with tumorigenesis that might help to predict stomach adenocarcinoma （SA） prognosis.METHODS The Cancer Genome Atlas database was used to obtain RNA sequences as well as complete clinical data of SA and adjacent normal tissues from patients. Weighted gene co-expression network analysis （WGCNA） was used to investigate the meaningful module along with hub genes. Expression of hub genes was analyzed in 362 paraffin-embedded SA biopsy tissues by immunohistochemical staining. Patients were classified into two groups （according to expression of hub genes）： Weak expression and over-expression groups. Correlation of biomarkers with clinicopathological factors indicated patient survival.RESULTS Whole genome expression level screening identified 6,231 differentially expressed genes. Twenty-four co- expressed gene modules were identified using WGCNA. Pearson＇s correlation analysis showed that the tan module was the most relevant to tumor stage （r = 0.24, P = 7 × 10 -6）. In addition, we detected sorting nexin （SNX）10 as the hub gene of the tan module. SNX10 expression was linked to T category （P = 0.042, x2= 8.708）, N category （P = 0.000, x2= 18.778）, TNM stage （P = 0.001, x2 = 16.744） as well as tumor differentiation （P = 0.000,x2= 251.930）. Patients with high SNX10 expression tended to have longer diseasefree survival （DFS; 44.97 mo vs 33.85 mo, P = 0.000） as well as overall survival （OS; 49.95 vs 40.84 mo, P = 0.000） in univariate analysis. Multivariate analysis showed that dismal prognosis could be precisely predicted clinicopathologically using SNX10 [DFS： P = 0.014, hazard ratio （HR） = 0.698, 95% confidence interval （CI）： 0.524-0.930, OS： P = 0.017, HR = 0.704, 95%CI： 0.528-0.940].CONCLUSION This study provides a new technique for screening prognostic biomarkers of SA. Weak expression of SNX10 is linked to poor prognosis, and is a suitable prognostic biomarker of SA.
文摘The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies the relations among some conditions used therein.
