Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the...Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the Bott-Baum-Cheeger Theorem for vector bundle E.展开更多
We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also ...We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.展开更多
This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and order...This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
[Objectives] This study was to find out the effect of trap space layout on the trapped number of Spodoptera litura in tobacco field. [Methods]From2015 to 2017,investigations were made using different hanging heights,d...[Objectives] This study was to find out the effect of trap space layout on the trapped number of Spodoptera litura in tobacco field. [Methods]From2015 to 2017,investigations were made using different hanging heights,distances( densities) and equidistant plane layout in the tobacco planting area in central Guizhou Province. [Results] The trapped number of S. litura was different at different hanging heights of the trap,and some had the difference reached the5% significant level in the trapped number. The optimum hanging height was 1. 5-2. 0 m. The trapping effect was the best at the field layout distance of20. 0-30. 0 m( density of 5-8 traps/hm^2). Under the conditions of even distribution at the equal distance between traps of 40.0 m in the field,the accumulated trapped number of S. litura from April to August was in the order of outer ring > central ring > inner ring,presenting the zonal distribution. The difference in the trapped numbers was significant among different rings,reaching the 5% significant level. [Conclusions]This study provided theoretical bases for the physiochemical control of S. litura in tobacco field.展开更多
There is increasing interest in finding the relation between the sunspot number (SSN) and solar polar field. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such a...There is increasing interest in finding the relation between the sunspot number (SSN) and solar polar field. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigated the relations between the SSN and solar polar field by performing a multifractal analysis. To investigate the change in multifractality, we applied a wavelet transform to time series. When the SSN was maximum and minimum, the SSN showed monofractality or weak multifractality. The solar polar field showed weak multifractality when that was maximum and minimum. When the SSN became maximum, the fractality of the SSN changed from multifractality to monofractality. The multifractality of SSN became large before two years of SSN maximum, then that of the solar polar field became large and changed largely. It was found that the change in SSN triggered the change in the solar polar field. Hence, the SSN and solar polar field were closely correlated from the view point of fractals. When the maximum solar polar field before the maximum SSN was larger, the maximum SSN of the next cycle was larger. The formation of the magnetic field of the sunspots was correlated with the solar polar field.展开更多
Objective To establish and compare the pulsed-field gel electrophoresis （PFGE）, multiple-locus variable number tandem repeat analysis （MLVA） and automated ribotyping for subtyping of Citrobacter strains. Methods P...Objective To establish and compare the pulsed-field gel electrophoresis （PFGE）, multiple-locus variable number tandem repeat analysis （MLVA） and automated ribotyping for subtyping of Citrobacter strains. Methods PFGE protocol was optimized in terms of plug preparation procedure, restriction enzymes and configuration of electrophoretic parameters. MLVA method was evaluated by finding variable number tandem repeats in two genomes of Citrobacter strains. The ribotyping was performed by using the automated RiboPrinter system. Results We optimized the plug preparation procedure, focused on the cell suspension concentration （turbidity of 2.5 to 3.5）, SDS addition （no SDS needed） and lysis time （1 h）, and selected the appropriate restriction enzyme （Xbal） and the electrophoretic parameters （1.0 s-20.0 s for 19 h） of PFGE. There was nearly no discriminatory power of MLVA between Citrobacter strains. For 51 Citrobacter strains, automated ribotyping gave a D-value of 0.9945, while PFGE gave a D-value of 0.9969. Both PFGE and automated ribotyping clustered strains from the same sources （with the same species from the same place at the same time identified as the same source） and divided strains from different sources （from different years, places and hosts） into different subtypes. Conclusion PFGE protocol established in this paper and automated ribotyping are suitable for application in Citrobacter subtyping.展开更多
We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structure...We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structures of Mordell-Weil groups over some real quadratic fields via two-descent. We also prove similar results for the case of certain cubic fields. Especially, we give the first example of elliptic curve having everywhere good reduction over a pure cubic field using our method.展开更多
The monopile is the most common foundation to support offshore wind turbines.In the marine environment,local scour due to combined currents and waves is a significant issue that must be considered in the design of win...The monopile is the most common foundation to support offshore wind turbines.In the marine environment,local scour due to combined currents and waves is a significant issue that must be considered in the design of wind turbine foundations.In this paper,a full-scale numerical model was developed and validated based on field data from Rudong,China.The scour development around monopiles was investigated,and the effects of waves and the Reynolds number Re were analyzed.Several formulas for predicting the scour depth in the literature have been evaluated.It is found that waves can accelerate scour development even if the KC number is small(0.78<KC<1.57).The formula obtained from small-scale model tests may be unsafe or wasteful when it is applied in practical design due to the scale effect.A new equation for predicting the scour depth based on the average pile Reynolds number(Rea)is proposed and validated with field data.The equilibrium scour depth predicted using the proposed equation is evaluated and compared with those from nine equations in the literature.It is demonstrated that the values predicted from the proposed equation and from the S/M(Sheppard/Melville)equation are closer to the field data.展开更多
This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to al...This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field F<sub>p </sub>using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.展开更多
文摘Let E be a vector bundle over a compact Riemannian manifold M. We construct a natural metric on the bundle space E and discuss the relationship between the killing vector fields of E and M. Then we give a proof of the Bott-Baum-Cheeger Theorem for vector bundle E.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574647)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A16)the University Experimental Technology Foundation of Shandong Province of China(Grant No.S04W138)
文摘We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.
文摘This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
基金Supported by the Science and Technology Project of Guizhou Tobacco Company,China(201510)
文摘[Objectives] This study was to find out the effect of trap space layout on the trapped number of Spodoptera litura in tobacco field. [Methods]From2015 to 2017,investigations were made using different hanging heights,distances( densities) and equidistant plane layout in the tobacco planting area in central Guizhou Province. [Results] The trapped number of S. litura was different at different hanging heights of the trap,and some had the difference reached the5% significant level in the trapped number. The optimum hanging height was 1. 5-2. 0 m. The trapping effect was the best at the field layout distance of20. 0-30. 0 m( density of 5-8 traps/hm^2). Under the conditions of even distribution at the equal distance between traps of 40.0 m in the field,the accumulated trapped number of S. litura from April to August was in the order of outer ring > central ring > inner ring,presenting the zonal distribution. The difference in the trapped numbers was significant among different rings,reaching the 5% significant level. [Conclusions]This study provided theoretical bases for the physiochemical control of S. litura in tobacco field.
文摘There is increasing interest in finding the relation between the sunspot number (SSN) and solar polar field. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigated the relations between the SSN and solar polar field by performing a multifractal analysis. To investigate the change in multifractality, we applied a wavelet transform to time series. When the SSN was maximum and minimum, the SSN showed monofractality or weak multifractality. The solar polar field showed weak multifractality when that was maximum and minimum. When the SSN became maximum, the fractality of the SSN changed from multifractality to monofractality. The multifractality of SSN became large before two years of SSN maximum, then that of the solar polar field became large and changed largely. It was found that the change in SSN triggered the change in the solar polar field. Hence, the SSN and solar polar field were closely correlated from the view point of fractals. When the maximum solar polar field before the maximum SSN was larger, the maximum SSN of the next cycle was larger. The formation of the magnetic field of the sunspots was correlated with the solar polar field.
基金supported by the project (grant 2005CB522904 and 2005CB522905) from the Ministry of Scientific Technologythe project (grant 2008ZX10004-001, 2008ZX10004-008, and 2009ZX10004-101) from the Ministry of Scientific Technology and the Ministry of Health of the People’s Republic of China
文摘Objective To establish and compare the pulsed-field gel electrophoresis （PFGE）, multiple-locus variable number tandem repeat analysis （MLVA） and automated ribotyping for subtyping of Citrobacter strains. Methods PFGE protocol was optimized in terms of plug preparation procedure, restriction enzymes and configuration of electrophoretic parameters. MLVA method was evaluated by finding variable number tandem repeats in two genomes of Citrobacter strains. The ribotyping was performed by using the automated RiboPrinter system. Results We optimized the plug preparation procedure, focused on the cell suspension concentration （turbidity of 2.5 to 3.5）, SDS addition （no SDS needed） and lysis time （1 h）, and selected the appropriate restriction enzyme （Xbal） and the electrophoretic parameters （1.0 s-20.0 s for 19 h） of PFGE. There was nearly no discriminatory power of MLVA between Citrobacter strains. For 51 Citrobacter strains, automated ribotyping gave a D-value of 0.9945, while PFGE gave a D-value of 0.9969. Both PFGE and automated ribotyping clustered strains from the same sources （with the same species from the same place at the same time identified as the same source） and divided strains from different sources （from different years, places and hosts） into different subtypes. Conclusion PFGE protocol established in this paper and automated ribotyping are suitable for application in Citrobacter subtyping.
文摘We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structures of Mordell-Weil groups over some real quadratic fields via two-descent. We also prove similar results for the case of certain cubic fields. Especially, we give the first example of elliptic curve having everywhere good reduction over a pure cubic field using our method.
基金Supported by NNSF of China and SF of Chinese Education Committee ,and has been done when the author visited the Department of Mathematics of Purduc Unuversity in 1993
文摘It is a survey of the problem on class numbers of quadratic number fields.
基金financially supported by the National Natural Science Foundation of China (Grant No.52378329)。
文摘The monopile is the most common foundation to support offshore wind turbines.In the marine environment,local scour due to combined currents and waves is a significant issue that must be considered in the design of wind turbine foundations.In this paper,a full-scale numerical model was developed and validated based on field data from Rudong,China.The scour development around monopiles was investigated,and the effects of waves and the Reynolds number Re were analyzed.Several formulas for predicting the scour depth in the literature have been evaluated.It is found that waves can accelerate scour development even if the KC number is small(0.78<KC<1.57).The formula obtained from small-scale model tests may be unsafe or wasteful when it is applied in practical design due to the scale effect.A new equation for predicting the scour depth based on the average pile Reynolds number(Rea)is proposed and validated with field data.The equilibrium scour depth predicted using the proposed equation is evaluated and compared with those from nine equations in the literature.It is demonstrated that the values predicted from the proposed equation and from the S/M(Sheppard/Melville)equation are closer to the field data.
文摘This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field F<sub>p </sub>using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.
