VECTOR BUNDLE, KILLING VECTOR FIELD AND PONTRYAGIN NUMBERS

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.

Time evolution of a squeezed chaotic field in an amplitude damping channel when used as a generating field for a squeezed number state

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.

The Problem on Class Numbers of Quadratic Number Fields

It is a survey of the problem on class numbers of quadratic number fields.

The Tate Kernel of the Number Field Q (-3)

A complete characterization of Tate kernel of the number field Q (-3) is given.Our method can also be used in other fields.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

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,

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

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.

Establishment and Comparison of Pulsed-field Gel Electrophoresis,Multiple-locus Variable Number Tandem Repeat Analysis and Automated Ribotyping Methods for Subtyping of Citrobacter Strains

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.

On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields

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.

Relationship between the Sunspot Number and Solar Polar Field by Wavelet-Based Multifractal Analysis

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.

Effect of Trap Space Layout on Trapped Number of Spodoptera litura in Tobacco Field

[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.

On the Role of Chemical Potential in Determining the Temperature Dependent Critical Magnetic Field and the Penetration Depth of Superconductors

Dealing with both elemental and high-Tc superconductors (SCs) - Sn, Nb and Pb belonging to the former category, and MgB2 and different samples of YBCO to the latter - we show that the difference in the values of their critical magnetic field Hc1,c2 and the penetration depth λL(0) is, remarkably, attributable predominantly to the difference in the values of a single parameter, viz., the chemical potential (μ) close to their critical temperatures (Tcs). Based directly on the dynamics of pairing in a magnetic field and the corresponding number equation, our approach relates Hc1,c2 of an SC with the following set of its properties: S1 = {μ, Tc, Debye temperature, effective mass of the electron, magnetic interaction parameter, Landau index}. Hence, it provides an alternative to the approach followed by Talantsev [Mod. Phys. Lett. B 33, 1950195 (2019)] who has shown by ingeniously combining the results of various well-established theories that Hc2 of an SC can be calculated via four different equations, each of which invokes two or more properties from its sample-specific set S2 = {Tc, gap, coherence length, λL(0), jump in sp. ht.}, which is radically different from S1.

Effects of Blade Number on Characteristics of Centrifugal Pumps

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.

Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field

An analysis of Thermophoresis effect on unsteady magneto-hydrodynamic free convection flow over an inclined porous plate with time dependent suction in presence of magnetic field with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration profiles are then presented graphically for different values of the parameters entering into the problem. Finally, the effects of the pertinent parameters on the skin-friction coefficient, the rate of heat transfer (Nusselt number) and wall deposition flux (Stanton number), which are of physical interest, are exhibited in tabular form.

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

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.

TiO_2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

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.

ON THE EXCEPTIONAL FIELDS FOR A CLASS OF REAL QUADRATIC FIELDS

In this paper, we give a lower bound exp（2.2 × 10~8 ） for those discriminants of real quadratic fields Q（√ d） with d= N^2-4 and h（d）=1.

Field Electron Emission from Diamond - like Carbon Films

A low turn-on field electron emission from diamond-like carbon films has been observed for the first time to author’s knowledge.Carbon films were prepared by microwave plasma chemical vapor deposition (CVD).Special pretreatment ceramic substrates were used. The characteristics of the film have been identified by using X-ray diffraction(XRD),and Raman spectrum. The field emission experiment has been performed in a vacuum chamber with a base pressure of about 10 -5 Pa. The turn-on field of 1.2 V/μm,and the current density of 1.25 mA/cm 2 at electric field of 6 V/μm were obtained.

Modeling Density and Anisotropy of Energetic Electrons Along Magnetic Field Lines

The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. The variance of both the number density and anisotropy along the magnetic field line is evaluated systematically by modeling four typically prescribed distribution functions. It is shown that in the case of ＂the positive anisotropy＂ （namely, the perpendicular temperature T⊥ exceeds the parallel temperature T｜｜）, the number density of energetic electrons always decreases with the magnetic latitude for a regular increasing magnetic field and the maximum wave growth is therefore generally confined to the equator where the resonant energy is minimum, and the number density is the largest. However, the ＂loss-cone＂ anisotropy of the electrons with a ＂pancake＂ distribution or kappa distribution keeps invariant or nearly invariant, whereas the ＂temperature＂ anisotropy with a pure bi-Maxwellian distribution or Ashour-Abdalla and Kennel＇s distributions decreases with the magnetic latitude. The results may provide a useful approach to evaluating the number density and anisotropy of the energetic electrons at latitudes where the observation information is not available.

Lattice Models of Finite Fields

Finite fields form an important chapter in abstract algebra, and mathematics in general, yet the traditional expositions, part of Abstract Algebra courses, focus on the axiomatic presentation, while Ramification Theory in Algebraic Number Theory, making a suited topic for their applications, is usually a separated course. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a much larger audience, and bridging the above mentioned gap. Such lattice models of finite fields provide a good basis for later developing their study in a more concrete way, including decomposition of primes in number fields, Frobenius elements, and Frobenius lifts, allowing to approach more advanced topics, such as Artin reciprocity law and Weil Conjectures, while keeping the exposition to the concrete level of familiar number systems. Examples are provided, intended for an undergraduate audience in the first place.

A Fluid Dynamics Approach for the Computation of Nonlinear Force-Free Magnetic Field

Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.