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
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
Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aer...Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.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
[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
As we examine the behaviour of the number field sieve(NFS) in the medium prime case, we notice various patterns that can be exploited to improve the running time of the sieving stage. The contributions of these observ...As we examine the behaviour of the number field sieve(NFS) in the medium prime case, we notice various patterns that can be exploited to improve the running time of the sieving stage. The contributions of these observations to the computational mathematics community are twofold. Firstly, we clarify the understanding of the true practical effectiveness of the algorithm. Secondly, we propose a test for a better choice of the polynomials used in the NFS. These results are of particular interest to cryptographers as the run-time of the NFS directly determines the security level of some discrete logarithm problem based protocols.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
Static Random Access Memory(SRAM) based Field Programmable Gate Array(FPGA) is widely applied in the field of aerospace, whose anti-SEU(Single Event Upset) capability becomes more and more important. To improve anti-F...Static Random Access Memory(SRAM) based Field Programmable Gate Array(FPGA) is widely applied in the field of aerospace, whose anti-SEU(Single Event Upset) capability becomes more and more important. To improve anti-FPGA SEU capability, the registers of the circuit netlist are tripled and divided into three categories in this study. By the packing algorithm, the registers of triple modular redundancy are loaded into different configurable logic block. At the same time, the packing algorithm considers the effect of large fan-out nets. The experimental results show that the algorithm successfully realize the packing of the register of Triple Modular Redundancy(TMR). Comparing with Timing Versatile PACKing(TVPACK), the algorithm in this study is able to obtain a 11% reduction of the number of the nets in critical path, and a 12% reduction of the time delay in critical path on average when TMR is not considered. Especially, some critical path delay of circuit can be improved about 33%.展开更多
The blade number of impeller is an important design parameter of pumps,which affects the characteristics of pump heavily.At present,the investigation focuses mostly on the performance characteristics of axis flow pump...The blade number of impeller is an important design parameter of pumps,which affects the characteristics of pump heavily.At present,the investigation focuses mostly on the performance characteristics of axis flow pumps,the influence of blade number on inner flow filed and characteristics of centrifugal pump has not been understood completely.Therefore,the methods of numerical simulation and experimental verification are used to investigate the effects of blade number on flow field and characteristics of a centrifugal pump.The model pump has a design specific speed of 92.7 and an impeller with 5 blades.The blade number is varied to 4,6,7 with the casing and other geometric parameters keep constant.The inner flow fields and characteristics of the centrifugal pumps with different blade number are simulated and predicted in non-cavitation and cavitation conditions by using commercial code FLUENT.The impellers with different blade number are made by using rapid prototyping,and their characteristics are tested in an open loop.The comparison between prediction values and experimental results indicates that the prediction results are satisfied.The maximum discrepancy of prediction results for head,efficiency and required net positive suction head are 4.83%,3.9%and 0.36 m,respectively.The flow analysis displays that blade number change has an important effect on the area of low pressure region behind the blade inlet and jet-wake structure in impellers.With the increase of blade number,the head of the model pumps increases too,the variable regulation of efficiency and cavitation characteristics are complicated,but there are optimum values of blade number for each one.The research results are helpful for hydraulic design of centrifugal pump.展开更多
The authors exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers.They also prove the 3-divisibility of the plus part of the class number of another family consisting ...The authors exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers.They also prove the 3-divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields.At the end,they provide some numerical examples supporting our results.展开更多
By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
The TiO2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically s...The TiO2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically solved with the homotopy analysis method(HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO2nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO2nanoparticles increases. This confirms the fact that the occurrence of the TiO2nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased.An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water,while the Nusselt number of the nanofluid is larger than that of pure water. However,both the parameters increase if the magnetic field intensity increases.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.
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 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supported by the National Natural Science Foundation of China (Grant No. 52072267)Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems (Grant No. 23DZ2229029)
文摘Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.
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.
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As we examine the behaviour of the number field sieve(NFS) in the medium prime case, we notice various patterns that can be exploited to improve the running time of the sieving stage. The contributions of these observations to the computational mathematics community are twofold. Firstly, we clarify the understanding of the true practical effectiveness of the algorithm. Secondly, we propose a test for a better choice of the polynomials used in the NFS. These results are of particular interest to cryptographers as the run-time of the NFS directly determines the security level of some discrete logarithm problem based protocols.
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 the National Natural Science Foundation of China(No.61106033)
文摘Static Random Access Memory(SRAM) based Field Programmable Gate Array(FPGA) is widely applied in the field of aerospace, whose anti-SEU(Single Event Upset) capability becomes more and more important. To improve anti-FPGA SEU capability, the registers of the circuit netlist are tripled and divided into three categories in this study. By the packing algorithm, the registers of triple modular redundancy are loaded into different configurable logic block. At the same time, the packing algorithm considers the effect of large fan-out nets. The experimental results show that the algorithm successfully realize the packing of the register of Triple Modular Redundancy(TMR). Comparing with Timing Versatile PACKing(TVPACK), the algorithm in this study is able to obtain a 11% reduction of the number of the nets in critical path, and a 12% reduction of the time delay in critical path on average when TMR is not considered. Especially, some critical path delay of circuit can be improved about 33%.
基金supported by National Outstanding Young Scientists Founds of China(Grant No.50825902)Top talent Foundation of Jiangsu University of China(Grant No.2007001)
文摘The blade number of impeller is an important design parameter of pumps,which affects the characteristics of pump heavily.At present,the investigation focuses mostly on the performance characteristics of axis flow pumps,the influence of blade number on inner flow filed and characteristics of centrifugal pump has not been understood completely.Therefore,the methods of numerical simulation and experimental verification are used to investigate the effects of blade number on flow field and characteristics of a centrifugal pump.The model pump has a design specific speed of 92.7 and an impeller with 5 blades.The blade number is varied to 4,6,7 with the casing and other geometric parameters keep constant.The inner flow fields and characteristics of the centrifugal pumps with different blade number are simulated and predicted in non-cavitation and cavitation conditions by using commercial code FLUENT.The impellers with different blade number are made by using rapid prototyping,and their characteristics are tested in an open loop.The comparison between prediction values and experimental results indicates that the prediction results are satisfied.The maximum discrepancy of prediction results for head,efficiency and required net positive suction head are 4.83%,3.9%and 0.36 m,respectively.The flow analysis displays that blade number change has an important effect on the area of low pressure region behind the blade inlet and jet-wake structure in impellers.With the increase of blade number,the head of the model pumps increases too,the variable regulation of efficiency and cavitation characteristics are complicated,but there are optimum values of blade number for each one.The research results are helpful for hydraulic design of centrifugal pump.
基金supported by the SERB MATRICS Grant(No.MTR/2021/00762)the ANRF(SERB)Govt.of India Grant(No.CRG/2023/007323).
文摘The authors exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers.They also prove the 3-divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields.At the end,they provide some numerical examples supporting our results.
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
文摘The TiO2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically solved with the homotopy analysis method(HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO2nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO2nanoparticles increases. This confirms the fact that the occurrence of the TiO2nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased.An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water,while the Nusselt number of the nanofluid is larger than that of pure water. However,both the parameters increase if the magnetic field intensity increases.
