Ideal Class Groups and Subgroups of Real Quadratic Function Fields

In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n.[

Lower Bound for Ideal Class Numbers of Real Quadratic Function Fields

In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more explicitly for six types of real quadratic function fields. As a consequence, six classes of real quadratic function fields with ideal class number greater than one are given.[

Parametrization of the Quadratic Function Fields Whose Divisor Class Numbers are Divisible by Three

A parametrization of quadratic function fields whose divisor class numbers are divisible by 3 is obtained by using free parameters when the characteristics of the fields are not 3.

Halton-type sequences from global function fields

For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.

SUBGROUPS OF CLASS GROUPS OF ALGEBRAIC QUADRATIC FUNCTION FIELDS

Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessaryand sufficient condition is given for the class group H(K) to contain a cyclic subgroup of anyorder n, which holds true for both real and imaginary fields K. Then several series of functionfields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, aregiven, for which the class groups H(K) are proved to contain cyclic subgroups of order n.

Bounds of the Ideal Class Numbers of Real Quadratic Function Fields

The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.

Heun Functions Describing Fermions Evolving in Parallel Electric and Magnetic Fields

The present work deals with the behavior of fermions moving in a static magnetic induction and a time-harmonic electric field, both oriented along Oz. For the ultra-relativistic particles described by a Heun double confluent equation, we derive the corresponding wave functions and the conserved current density components.

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.

The Analytical Potential Energy Function of NH Radical Molecule in External Electric Field

The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD （T） method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials, electric displacements, elastic deformations, and thermoelasticity, and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures （cylinder or sphere）, subjected to mechanical load and electric potential. The material properties, thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution. In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material, reinforced by elastic isotropic fibers, this material is considered as structurally anisotropic material. The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity, and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin＇s approximation method. Finally, numerical results are carried out and discussed.

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.

Stress Field Analyses of Functionally Gradient Ceramic Tool by FEM

The cutting properties of the functionally gradient ceramic cutting tools relate closely to the gradient distribution. A cutting model of the functionally gradient ceramic tool is firstly designed in the present paper. The optimum of gradient distribution is obtained by way of the FEM analyses.

Effect of gradient magnetic field on physiochemistry functions of rice seedlings

Rice varieties Handao 2,Zhongbai 4,Han-jingzi,and Akihikari were treated with gradi-ent magnetic fileld to study the effect of gradi-ent field on rice.The magnetic field was madeup of 12 plots magnetic plates arranged in eachother south and north pole.The magneticstrength was 0-40 mT.Each four varieties wasput under the magnetic plate 15 cm away,andwent through the magnetic field with the speedof 20 cm/s.The same varieties without thetreatment were used as CK.Both of the seedswere soaked in water for 48 h in room temper-ature,and then sprouted on the porcelain platewith absorbed water paper.When the

Molecular Dynamic Simulation of Melting Points of Trans-1,4,5,8- tetranitro-1,4,5,8-tetraazadacalin （TNAD） with Some Propellants

Molecular dynamic simulation was employed to predict the melting points Tm of TNAD/HMX, TNAD/RDX, TNAD/DINA, and TNAD/DNP systems （tans-1,4,5,8- tetranitro-1,4,5,8-tetraazadacalin （TNAD）, dinitropiperazine （DNP）, cyclotetramethylenetetranitroamine （HMX）, cyclotrimethylenetrinitramine （RDX）, and N-nitrodihydroxyethylaminedinitrate （DINA））. Tm was determined from the inflexion point on the curve of mean specific volume vs. temperature. The result shows that the Tm values of TNAD/HMX, TNAD/RDX, and TNAD/DINA systems are 500, 536, and 488 K, respectively. The TNAD/DNP system has no obvious Tm value, which shows the system is insoluble. Using Tm, the solubility of the four systems was analyzed. The radial distribution functions of the four systems were analyzed and the main intermolecular forces between TNAD and other energetic components are short-range interactions. The better the solubility is, the stronger the intermoleenlar interaction is. In addition, the force field energy at different temperature was also analyzed to predict Tm of the four systems.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

A RANDOM TRANSPORT-DIFFUSION EQUATION

In this paper we study the integral curve in a random vector field perturbed by white noise. It is related to a stochastic transport-diffusion equation. Under some conditions on the covariance function of the vector field, the solution of this stochastic partial differential equation is proved to have moments. The exact p-th moment is represented through integrals with respect to Brownian motions. The basic tool is Girsanov formula.

2D-and 3D-QSBR Studies on the Relationship between Structure and Biodegradability of Phthalates

Nine phthalates were calculated at the B3LYP/6-311G＊＊ level using DFT method. The corresponding linear relationship equations （R2 were 0.853 and 0.936 respectively） for the biodegradation rate （Kb） and half-life time （h/2） of biodegradation were obtained with the structural parameters as theoretical descriptors. Furthermore, CoMFA method was also applied to establish 3D models which revealed the fields influencing these properties. The relationship between the properties and the structure was obtained. The correlation coefficients of the models were 0.992 and 0.999, respectively. Analyses of 2D and 3D models demonstrated that the molecular volume was an important factor affecting the biodegradability of these compounds.

Changes of soil microbial communities during decomposition of straw residues under different land uses

Monitoring soil microbial communities can lead to better understanding of the transformation processes of organic carbon in soil. The present study investigated the changes of soil microbial communities during straw decomposition in three fields, i.e., cropland, peach orchard and vineyard. Straw decomposition was monitored for 360 d using a mesh-bag method. Soil microbial metabolic activity and functional diversity were measured using the Biolog-Eco system. In all three fields, dried straws with a smaller size decomposed faster than their fresh counterparts that had a larger size. Dried corn straw decomposed slower than dried soybean straw in the early and middle stages, while the reverse trend was found in the late stage. The cropland showed the highest increase in microbial metabolic activity during the straw decomposition, whereas the peach orchard showed the lowest. There was no significant change in the species dominance or evenness of soil microbial communities during the straw decomposition. However, the species richness fluctuated significantly, with the peach orchard showing the highest richness and the cropland the lowest. With different carbon sources, the peach orchard utilised carbon the most, followed by the cropland and the vineyard. In all three fields, carbon was utilized in following decreasing order： saccharides〉amino acids〉polymers〉polyamines〉carboxylic acids〉aromatic compounds. In terms of carbon-source utilization, soil microbial communities in the peach orchard were less stable than those in the cropland. The metabolic activity and species dominance of soil microbial communities were negatively correlated with the straw residual percentage. Refractory components were primarily accumulated in the late stages, thus slowing down the straw decomposition. The results showed that dried and crushed corn straw was better for application in long-term fields. The diversity of soil microbial communities was more stable in cropland than in orchards during the straw decomposition.

Characterization of deep ground geothermal field in Jiahe Coal Mine

Research into the characteristics of geothermal fields is important for the control of heat damage in mines. Based on measured geothermal data of boreholes from 200 m to 1200 m in a Jiahe Coal Mine, we demonstrate non-linear but increasing relations of both geo-temperatures and geothermal gradients with increases depth. Numerically, we fitted the relationship between geo-temperatures and depth, a first-order exponential decay curve, formulated as: T(h) = 4.975 + 23.08 exp(h/1736.1).

Numerical analysis of elastic coated solids in line contact

A line contact model of elastic coated solids is presented based on the influence coefficients(ICs) of surface displacement and stresses of coating-substrate system and the traditional contact model. The ICs of displacement and stresses are obtained from their corresponding frequency response functions(FRF) by using a conversion method based on fast Fourier transformation(FFT). The contact pressure and the stress field in the subsurface are obtained by employing conjugate gradient method(CGM) and discrete convolution fast Fourier transformation(DC-FFT). Comparison of the contact pressure and subsurface stresses obtained by the numerical method with the exact analytical solutions for Hertz contact is conducted, and the results show that the numerical solution has a very high accuracy and verify the validity of the contact model. The effect of the stiffness and thickness of coatings is further numerically studied. The result shows that the effects on contact pressure and contact width are opposite for hard and soft coatings and are intensified with the increase of coating thickness; the locations of crack initiation and propagation are different for soft and hard coatings; the risk of cracks and delaminations of coatings can be brought down by improving the lubrication condition or optimizing the non-dimensional parameter h/bh. This research offers a tool to numerically analyze the problem of elastic coated solids in line contact and make the blindness and randomness of trial-type coating design less.