一些循环代数函数域的不分明理想类

本文研究了一些l次循环函数域的理想类群的不分明理想类的结构问题.利用函数域的素理想分解理论和理想的一阶上同调理论,得到了这几类循环函数域的理想类群的l-秩的下界.进一步,我们还得了一些不分明理想类中不含不分明理想的域的充分条件.     

整体函数域素数次循环扩域的类群

设K/F是整体函数域的素数l次循环扩张,F是有理函数域F_q(T)上的有限可分扩域.利用函数域的Conner-Hurrelbrink正合六边形与源于短正合列的正合六边形,本文在l整除与不整除基域F的理想类数的情形下,分别研究函数域K理想类群的Sylow l-子群的结构.同时,利用得到的结果,本文给出了基域F的单位为K中元素norm的若干条件.     

Hyperelliptic curves and homomorphisms to ideal class groups of quadratic number fields

For the function field K of hyperelliptic curves over Q we define a subgroup of the ideal class group called the group of Z-primitive ideals. We then show that there are homomorphisms from this subgroup to ideal class groups of certain quadratic number fields.     

Mathematical Problems of Tomography and Hyperbolic Mappings

We consider a new class of mathematical problems related to interpretation of tomography data. The main assumption is that the sought distribution of absorption is an identically one function in the domain to be determined. These problems are connected with three known directions of mathematical physics: the Dirichlet problems for hyperbolic equations, the problems of small oscillations of a rotating fluid, and the problems of supersonic flows of an ideal gas.     

On conformal Killing symmetric tensor fields on Riemannian manifolds

A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free conformal Killing tensor fields on some closed manifolds.     

Powerful Necessary Conditions for Class Number Problems

We give a necessary condition for the ideal class group of a CM-field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM - fields of some types (e. g. the imaginary cyclic non -quadratic number fields of 2 - power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non - CM - fields to have class number one.     

Quadratic vector fields in ℂP2 with solvable monodromy group at infinity

Quadratic vector fields for which the line at infinity is a phase curve with three different singular points are considered. It is assumed that the characteristic numbers of these singular points are not multiples of 1/4 or 1/6. It is shown that among the fields with fixed characteristic numbers satisfying this assumption, one can choose seven fields such that any other field with solvable noncommutative monodromy group at infinity is affine equivalent to one of the chosen fields. In addition, quadratic vector fields with commutative monodromy group at infinity are described.     

Exponents of the ideal class groups of CM number fields

Since class numbers of CM number fields of a given degree go to infinity with the absolute values of their discriminants, it is reasonable to ask whether the same conclusion still holds true for the exponents of their ideal class groups. We prove that under the assumption of the Generalized Riemann Hypothesis this is indeed the case. Received: 8 May 2001; in final form: 15 April 2002/Published online: 8 November 2002     

Subgroups of ideal class groups of real quadratic algebraic function fields

Necessary and sufficient condition on real quadratic algebraic function fields K is given for their ideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic function fields K are obtained whose ideal class groups contain cyclic subgroups of order n. In particular, the ideal class numbers of these function fields are divisible by n.     

Covariant and dynamical reduction for principal bundle field theories

Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.     

Model testing for multivariate censored data

Summary. In the fields like Astronomy and Ecology, the need for proper statistical analysis of data that are censored is being increasingly recognized. Such data occur when, due to noise or other factors, instruments fail to detect low luminosities of celestial objects, or low concentrations of certain pollutants. For multivariate censored data sets there are very few distribution free methods available and researchers in the various fields often impose an assumption on the joint distribution, such as multivariate normality, and carry out parametric inferences. Under censoring, however, such parametric inferences are asymptotically wrong if the imposed assumption is incorrect. In this paper we propose a class of goodness-of-fit procedures for testing assumptions about the multivariate distribution under random censoring. The test procedures generalize Pearson's goodness-of-fit test in the sense that they are based on the concept of observed-minus-expected frequencies. The theory of the test statistic, however, differs from that for the classical Pearson test due to the accommodation of censored data. Received: 24 May 1994 / In revised form: 3 March 1996     

A Renormalization Group Method by Harmonic Extensions and the Classical Dipole Gas

In this paper, we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals of small perturbations of Gaussian fields. In this new method, one integrates Gaussian fields inside domains at all scales conditioning on the fields outside these domains, and by the variation principle solves local elliptic problems. It does not rely on an a priori decomposition of the Gaussian covariance. We apply this method to the model of classical dipole gas on the lattice, and show that the scaling limit of the generating function with smooth test functions is the generating function of the renormalized Gaussian free field.     

Class field towers of imaginary quadratic fields

In their 1934 paper, Scholz and Taussky defined the notion of capitulation type for imaginary quadratic fields whose ideal class group has a Sylow 3-subgroup which is elementary abelian of order 3². For one particular capitulation type (type D) they prove that the 3-class field tower of the quadratic field has length 2. They briefly indicate how a similar result can be shown to hold for capitulation type E. In this paper we give a simpler proof of their type D result and we construct a group theoretic counterexample to their type E assertion.     

Advanced finite element formulations for modeling thin piezoelectric structures

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imaginary Quadratic Fields with Ono Number 3

In this article, we prove that an imaginary quadratic field F has the ideal class group isomorphic to ?/2? ⊕ ?/2? if and only if the Ono number of F is 3 and F has exactly 3 ramified primes under the Extended Riemann Hypothesis (ERH). In addition, we give the list of all imaginary quadratic fields with Ono number 3.     

Generalized Gabidulin codes over fields of any characteristic

We generalize Gabidulin codes to a large family of fields, non necessarily finite, possibly with characteristic zero. We consider a general field extension and any automorphism in the Galois group of the extension. This setting enables one to give several definitions of metrics related to the rank-metric, yet potentially different. We provide sufficient conditions on the given automorphism to ensure that the associated rank metrics are indeed all equal and proper, in coherence with the usual definition from linearized polynomials over finite fields. Under these conditions, we generalize the notion of Gabidulin codes. We also present an algorithm for decoding errors and erasures, whose complexity is given in terms of arithmetic operations. Over infinite fields the notion of code alphabet is essential, and more issues appear that in the finite field case. We first focus on codes over integer rings and study their associated decoding problem. But even if the code alphabet is small, we have to deal with the growth of intermediate values. A classical solution to this problem is to perform the computations modulo a prime ideal. For this, we need study the reduction of generalized Gabidulin codes modulo an ideal. We show that the codes obtained by reduction are the classical Gabidulin codes over finite fields. As a consequence, under some conditions, decoding generalized Gabidulin codes over integer rings can be reduced to decoding Gabidulin codes over a finite field.     

Quadratic function fields with exponent two ideal class group

It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensions for future reference. In doing so we correct some errors in earlier published literature.     

On orders in number fields: Picard groups,ring class fields and applications

We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group.As an application, we give criteria of the integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.     

Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell

We show that the intrinsic equations of Koiter's model of a linearly elastic shell can be derived from the intrinsic formulation of the three-dimensional equations of a linearly elastic shell, by using an appropriate a priori assumption regarding the three-dimensional strain tensor fields appearing in these equations. To this end, we recast in particular the Dirichlet boundary conditions satisfied by any admissible displacement field as boundary conditions satisfied by the covariant components of the corresponding strain tensor field expressed in the natural curvilinear coordinates of the shell. Then we show that, when restricted to strain tensor fields satisfying a specific a priori assumption, these new boundary conditions reduce to those of the intrinsic equations of Koiter's model of a linearly elastic shell.     

Capitulation problem for global function fields

Let q be a power of an odd prime number p, k=\mathbbF_q(t){p, k=\mathbb{F}_{q}(t)} be the rational function field over the finite field \mathbbF_q.{\mathbb{F}_{q}.} In this paper, we construct infinitely many real (resp. imaginary) quadratic extensions K over k whose ideal class group capitulates in a proper subfield of the Hilbert class field of K. The proof of the infinity of such fields K relies on an estimation of certain character sum over finite fields.