Hilbert Modular Threefolds of Arithmetic Genus One

In 1981, Weisser proved that there are exactly four Galois cubic number fields with Hilbert modular threefolds of arithmetic genus one. In this paper, we extend Weisser's work to cover all cubic number fields. Our main result is that there are exactly 33 fields with Hilbert modular threefolds of arithmetic genus one. These fields are enumerated explicitly.     

A random point field related to Bose-Einstein condensation

The random point fields which describe the position distributions of the systems of ideal boson gas in states of Bose-Einstein condensations are obtained through the thermodynamic limits. The resulting point fields are given by convolutions of two kinds of independent point fields: the so-called boson processes whose generating functionals are represented by the inverses of the Fredholm determinants for operators related to the heat operator and the point fields whose generating functionals are represented by the resolvents of the operators. The construction of the latter point fields in an abstract formulation is also given.     

The genus fields of Kummer function fields

In this paper, we give a definition of genus field of function field with one variable over finite fields. And we explicitly describe the genus fields of Kummer function fields. For quadratic function fields case, our results are analogous to the genus fields of quadratic number fields.     

Invariant monotone vector fields on Riemannian manifolds

Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced. Some examples of invariant monotone vector fields are given. Several notions of invexities for functions on Riemannian manifolds are defined and their relations with invariant monotone vector fields are studied.     

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.     

SU(3)规范场的恰当形式(欧空间)

应用数学机械化方法讨论SU(3)规范场的规范化问题.首先提出一种具有明确几何意义的Yang-Mills方程,称其为恰当的Yang-Mills方程.然后构造了一类线性微分变换,称之为SU(3)规范场的示性变换,它具体给出联络和截面之间的微分关系.经由示性变换,将非线性的恰当的YM-方程变为一组线性Laplace方程,即实现了规范场YM-方程的线性化.从而证明了SU(3)规范场包括8个独立的Yang-Mills规范场.     

The structure of harmonizable isotropic random fields

The class of harmonizable processes and fields are a natural extension of the class of stationary processes and fields. Random fields admit an additional property called isotropy. The classical spectral and covariance representations for stationary isotropic random fields are extended to the harmonizable isotropic case. A classification of these fields is obtained based upon the smoothness properties of their covariances. In contrast to the stationary case, it is also shown that there exist non-trivial harmonizable isotropic fields which satisfy the Laplace operator in the L ²-sense     

Projective Vector Fields on Lorentzian Manifolds

Some relations between the causal character of projective vector fields and curvature on a Lorentzian manifold M are studied. As a consequence, obstructions to the existence of such vector fields are found. Affine, homothetic and Killing vector fields are considered specifically.     

Harmonicity of vector fields on the oscillator groups with neutral signature

In this paper, we mainly investigate curvature properties and harmonicity of invariant vector fields on the four-dimensional Oscillator groups endowed with three left-invariant pseudo-Riemannian metrics of signature (2,2). We determine all harmonic vector fields, vector fields which define harmonic maps and the vector fields which are critical points for the energy functional restricted to vector fields of the same length.     

Finslerian Fields in the Spacetime Tangent Bundle

Finslerian fields are investigated in the arena of the maximal-acceleration invariantspacetime tangent bundle. A variety of differential-geometric Finslerian fields are exposited. Thestructure of Finslerian quantum fields receives particular emphasis. Also, possible generalizedactions are proposed for Finslerian strings and p-branes. 1999 Elsevier Science Ltd.     

Generalized higher-order differentiation

Concepts of higher-order differentiation of functions and jet fields, of vector fields, and of covecter fields are introduced. These concepts, which generalize those of successive differentiation (ordinary or covariant), are shown to correspond to certain important types of derivative strings.     

SUBGROUPS OF CLASS GROUPS OF ALGEBRAIC QUADRATIC FUNCTION FIELDS

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

SU(2)规范场的恰当形式(欧空间)

应用数学机械化方法研究欧氏空间中SU(2)规范场的正规化问题.首先对Yang-Mills方程的表述进行了讨论,给出了一种具有物理和几何意义的YM-方程,称其为恰当的(exact)YM-方程.对于这种恰当的YM-方程,构造了一类线性微分变换,称之为SU(2)规范场的示性变换.经由示性变换,将非线性的恰当的YM-方程变为一组Laplace方程,实现了SU(2)规范场方程的线性化,即场方程的正规化.从而证明了SU(2)规范场存在3个独立的Yang-Mills规范场.     

Vector fields near a generic submanifold

We give a classification of generic vector fields near a generic submanifold. The normal forms are linear vector fields near the local model of the submanifold. Similar results are obtained for vector fields near a hypersurface with boundary and near a piecewise-smooth hypersurface.     

The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds

By using the conformal method, solutions of the Einstein-scalar field gravitational constraint equations are obtained. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. The proofs are constructive and allow for arbitrary dimension (> 2) as well as low regularity initial data.     

Algebraic complexities and algebraic curves over finite fields

Algebraic schemes of computation of bilinear forms over various rings of scalars are examined. The problem of minimal complexity of these schemes is considered for computation of polynomial multiplication and multiplication in commutative algebras, and finite extensions of fields. While for infinite fields minimal complexities are known (Winograd, Fiduccia, Strassen), for finite fields precise minimal complexities are not yet determined. We prove lower and upper bounds on minimal complexities. Both are linear in the number of inputs. These results are obtained using the relationship with linear coding theory and the theory of algebraic curves over finite fields.     

Harmonicity of vector fields on four-dimensional generalized symmetric spaces

Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.     

Models for Stationary Max-Stable Random Fields

Models for stationary max-stable random fields are revisited and illustrated by two-dimensional simulations. We introduce a new class of models, which are based on stationary Gaussian random fields, and whose realizations are not necessarily semi-continuous functions. The bivariate marginal distributions of these random fields can be calculated, and they form a new class of bivariate extreme value distributions.     

Thermodynamics and statistical analysis of Gaussian random fields

Summary Gaussian fields are considered as Gibbsian fields. Thermodynamic functions are calculated for them and the variational principle is proved. As an application we get an approximation of log likelihood and an information theoretic interpretation of the asymptotic behaviour of the maximum likelihood estimator for Gaussian Markov fields.     

泛权网场结合的逻辑守恒性及其在人工神经网络中的应用

给出了泛权网场复合的几个定义,证明了泛权网场复合的一组有关逻辑守恒性的定理。结合均场模型,探讨了泛权网场在人工神经网络中的应用前景。