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.

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

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.

A new zeta function for number fields

According to the idea of class field theory, the possible absolutely normal number fieldsare restricted in nature by the arithmetical properties of rational number field .Becausethe fundamental arithmetical property of is the distributive law of the prime numbers,

Interpretation of the short period variations in geomagnetic anomalies of Shaanxi region

A temporary profile from Shiquan in the southern part of Shaanxi Province to Ningxian in Gansu Province for observation of geomagnetic short period variations was set up. The characteristics of geomagnetic short period variations in the profile region was analyzed through geomagnetic transfer functions at measurement sites (Fan, et al, 1998). According to the theory of multi-scale analysis of wavelet transform, the components affected by regional origin in the region is extracted in this paper. The components of regional origin is used as original data in the inversion study for investigation of 2-D conductivity structure corresponding to the regional origin. The inversion method (Zhdanov, Traynin, 1997) which is based on the minimum of the total energy of the residual field between observational electro-magnetic field and the calculated theoretical field of conductivity model and the conception of migrated residual field is introduced into our inversion of the data of magneto-variation sounding. The result of the inversion gives the underground conductivity structure in depth range of 100 km beneath the profile, and shows that a high conductivity area is located under Wugong and Qianling. The main characteristics of the inversion method is briefly discussed, that is, it can reflect the depth and the distribution of anomalous conductivity area comparatively well, and large number of parameters of inversion model is allowed to be used in the Inversion.

Measurement and estimation of free field to eardrumtransfer function for virtual acoustic space research

Free field to Eardrum Thansfer Function (FETF) is one of the major factors influencing the identification of the sound source direction. FETF can be employed to generate a Virtual Acoustic Space (VAS) by computer and other equlpment. In this paper the methods to improve the measurement and estimation of FETF are approached. Least-mean-squares (LMS)method is much better than empirical FFT method. This paper also gives a sample description of excitation signals for measuring the impulse response of FETF.

Relation between sound transfer function from diffuse sound field to the eardrum and temporary threshold shift

Twelve volunteers with normal hearing (9 males and 3 females) participated in this work The sound transfer functions (STFS) from diffuse sound field to the subject's eardrums were measured and correlated to the temporary threshold shift (TTS) due to fiffuse-exposure.A probe tube with a miniature microphone was used for STF measurements in which successive 1/3 oct bandwidth random noise with central frequency from 0.25 kKz to 8 kHz were used. The subjects were divided into two groups, with the STF maxima at 2 kHz and 4 kHz respectively Pre- and post- exposure sweep Bekesy audiograms were recorded and the temporary thresh old shift calctilated as the difference between the two. Frequency of the maximum TTS was correlated to that of the maximum STF. The average TTS was very small or zero at frequen cies below the band noise exposure , but was noticeable even at the highest measured frequency (8 kHz) for beyond the noise band. Also individual differences in STF were found at frequencies between 2 kHz and 4 kHz

Application and measurement of underwater acoustic reciprocity transfer functions in reverberant sound field

The reciprocity measurement theory in anomalous reverberant sound fields was investigated.An improved method Was proposed due to the interrelated errors.The source volume velocity Was corrected by spatial average of measurement results and evaluation of the reverberant sound field influence on acoustic energy density.The result was validated in underwater experiment,corrected reciprocity measurement results were almost the same as direct measurement results.It indicates that reverberant sound field does not affect the validitv of the principle,but influences the obtainment of source volume velocity,then influences the measurement of transfer functions with the principle.The proposed method is simple and effective in anomalous reverberant sound fields.The study mav be valuable for the applications which are based on the principle.