In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary a...In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.展开更多
Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjec...Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjecture (RC): All roots of ξ(z)are real. We have calculated ξand ζ, and found that ξ(z)is alternative oscillation, which intuitively implies RC, and the property of ζ(s)is not good. Therefore Riemann’s direction is correct, but he used the same notation ξ(t)=ξ1(t)to confuse two concepts. So the product expression only can be used in contraction. We find that if ξhas complex roots, then its structure is destroyed, so RC holds. In our proof, using Riemann’s four theorems is sufficient, needn’t cite other results. Hilbert (1900) proposed Riemann hypothesis (RH): The non-trivial roots of ζhave real part 1/2. Of course, RH also holds, but can not be proved directly by ζ(s).展开更多
AIM： To investigate the mechanism of fibroblast cell proliferation stimulated by the Opisthorchis viverrini excretory/secretory （ES） product. METHODS： NIH-3T3, mouse fibroblast cells were treated with O. viverrini...AIM： To investigate the mechanism of fibroblast cell proliferation stimulated by the Opisthorchis viverrini excretory/secretory （ES） product. METHODS： NIH-3T3, mouse fibroblast cells were treated with O. viverrini ES product by non-contact co-cultured with the adult parasites. Total RNA from NIH-3T3 treated and untreated with O. viverrini was extracted, reverse transcribed and hybridized with the mouse 15K complementary DNA （cDNA） array. The result was analyzed by ArrayVision version 5 and GeneSpring version 5 softwares. After normalization, the ratios of gene expression of parasite treated to untreated NIH-3T3 cells of 2-and more-fold upregulated was defined as the differentially expressed genes. The expression levels of the signal transduction genes were validated by semiquantitative SYBR-based real-time RT-PCR. RESULTS： Among a total of 15 000 genes/ESTs, 239 genes with established cell proliferation-related function were 2 fold-and more-up-regulated by O. viverrini ES product compared to those in cells without exposure to the parasitic product. These genes were classified into groups including energy and metabolism, signal transduction, protein synthesis and translation, matrix and structural protein, transcription control, cell cycle and DNA replication. Moreover, the expressions of serinethreonine kinase receptor, receptor tyrosine kinase and collagen production-related genes were up-regulated by O.viverrini ES product, The expression level of signal transduction genes, pkC, pdgfra, jak 1, eps 8, tgfβ 1/4,strap and h ras measured by real-time RT-PCR confirmed their expression levels to those obtained from cDNA array. However, only the up-regulated expression of pkC,eps 8 and tgfβ3 1/4 which are the downstream signaling molecules of either epidermal growth factor （EGF） or transforming growth factor-β （TGF-β） showed statistical significance （P 〈 0.05）.CONCLUSION： O. viverrini ES product stimulates the significant changes of gene expression in several functional categories and展开更多
An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds ...An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.展开更多
基金supported by the National Natural Science Foundation of China (No. 61174071)
文摘In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.
文摘Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjecture (RC): All roots of ξ(z)are real. We have calculated ξand ζ, and found that ξ(z)is alternative oscillation, which intuitively implies RC, and the property of ζ(s)is not good. Therefore Riemann’s direction is correct, but he used the same notation ξ(t)=ξ1(t)to confuse two concepts. So the product expression only can be used in contraction. We find that if ξhas complex roots, then its structure is destroyed, so RC holds. In our proof, using Riemann’s four theorems is sufficient, needn’t cite other results. Hilbert (1900) proposed Riemann hypothesis (RH): The non-trivial roots of ζhave real part 1/2. Of course, RH also holds, but can not be proved directly by ζ(s).
基金the Thailand Research Fund, Grant No. TRG4880004 and the Grants of Khon Kaen University 2004 and 2006 Grants-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan the Grant for Student of Liver Fluke and Cholangiocarcinoma Research Center, Faculty of Medicine, Khon Kaen University, 2003-2005
文摘AIM： To investigate the mechanism of fibroblast cell proliferation stimulated by the Opisthorchis viverrini excretory/secretory （ES） product. METHODS： NIH-3T3, mouse fibroblast cells were treated with O. viverrini ES product by non-contact co-cultured with the adult parasites. Total RNA from NIH-3T3 treated and untreated with O. viverrini was extracted, reverse transcribed and hybridized with the mouse 15K complementary DNA （cDNA） array. The result was analyzed by ArrayVision version 5 and GeneSpring version 5 softwares. After normalization, the ratios of gene expression of parasite treated to untreated NIH-3T3 cells of 2-and more-fold upregulated was defined as the differentially expressed genes. The expression levels of the signal transduction genes were validated by semiquantitative SYBR-based real-time RT-PCR. RESULTS： Among a total of 15 000 genes/ESTs, 239 genes with established cell proliferation-related function were 2 fold-and more-up-regulated by O. viverrini ES product compared to those in cells without exposure to the parasitic product. These genes were classified into groups including energy and metabolism, signal transduction, protein synthesis and translation, matrix and structural protein, transcription control, cell cycle and DNA replication. Moreover, the expressions of serinethreonine kinase receptor, receptor tyrosine kinase and collagen production-related genes were up-regulated by O.viverrini ES product, The expression level of signal transduction genes, pkC, pdgfra, jak 1, eps 8, tgfβ 1/4,strap and h ras measured by real-time RT-PCR confirmed their expression levels to those obtained from cDNA array. However, only the up-regulated expression of pkC,eps 8 and tgfβ3 1/4 which are the downstream signaling molecules of either epidermal growth factor （EGF） or transforming growth factor-β （TGF-β） showed statistical significance （P 〈 0.05）.CONCLUSION： O. viverrini ES product stimulates the significant changes of gene expression in several functional categories and
基金This work was supported partly by the National Natural Science Foundation of China(NSFC)(Nos.62073315,62103305)the Shanghai Pujiang Program(No.21PJ 1413100)China Postdoctoral Science Foundation(Nos.2021M703423,2022T150686).
文摘An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.
