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1.
Fortuné Massamba 《Mediterranean Journal of Mathematics》2009,6(1):27-46
We investigate lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field ξ and whose
screen distribution is integrable. We prove some results on parallel vector fields and on a leaf of the integrable distribution
of this class. A theorem on a geometrical configuration of the screen distribution is obtained. We show that any totally
contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface is an extrinsic sphere.
Received: February 22, 2008., Revised: June 18, 2008., Accepted: July 10, 2008. 相似文献
2.
For k an algebraic closure of the finite field , ℓ prime distinct from p and X a surface over k, we prove that the field of rational functions k(X) can be recovered from the maximal pro-ℓ-quotient of its absolute Galois group – in fact already from the second central descending series quotient of .
Submitted: July 2004, Revision: October 2005, Final revision: February 2008, Accepted: February 2008 相似文献
3.
G. Cortiñ as C. Haesemeyer C. Weibel 《Journal of the American Mathematical Society》2008,21(2):547-561
In this paper we prove that for an affine scheme essentially of finite type over a field and of dimension , -regularity implies regularity, assuming that the characteristic of is zero. This verifies a conjecture of Vorst.
4.
Wilhelm Plesken 《Archiv der Mathematik》2009,92(1):44-56
The paper introduces a new polynomial to count the solutions of a system of polynomial equations and inequations over an algebraically
closed field of characteristic zero based on the triangular decomposition algorithm by J. M. Thomas of the nineteen-thirties.
In the special case of projective varieties examples indicate that it is a finer invariant than the Hilbert polynomial.
Received: 8 March 2008; Revised: 12 August 2008 相似文献
5.
Nicolas Raymond 《Annales Henri Poincare》2009,10(1):95-122
The aim of this paper is to establish estimates of the lowest eigenvalue of the Neumann realization of on an open bounded subset with smooth boundary as B tends to infinity. We introduce a “magnetic” curvature mixing the curvature of ∂Ω and the normal derivative of the magnetic
field and obtain an estimate analogous with the one of constant case. Actually, we give a precise estimate of the lowest eigenvalue
in the case where the restriction of magnetic field to the boundary admits a unique minimum which is non degenerate. We also
give an estimate of the third critical field in Ginzburg–Landau theory in the variable magnetic field case.
Submitted: June 26, 2008., Accepted: November 28, 2008. 相似文献
6.
Using the recently introduced parametric representation of noncommutative quantum field theory, we implement here the dimensional
regularization and renormalization of the vulcanized model on the Moyal space.
Submitted: June 8, 2007. Accepted: December 11, 2007. 相似文献
7.
We study the three‐dimensional Ginzburg‐Landau model of superconductivity. Several “natural” definitions of the (third) critical field, H, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions as to when they coincide. An interesting part of the analysis is the study of the monotonicity of the ground state energy of the Laplacian with constant magnetic field and with Neumann (magnetic) boundary condition in a domain Ω. It is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields. As a consequence of our analysis, we give an affirmative answer to a conjecture by Pan. © 2008 Wiley Periodicals, Inc. 相似文献
8.
A -automorphism of the rational function field is called purely monomial if sends every variable to a monic Laurent monomial in the variables . Let be a finite subgroup of purely monomial -automorphisms of . The rationality problem of the -action is the problem of whether the -fixed field is -rational, i.e., purely transcendental over , or not. In 1994, M. Hajja and M. Kang gave a positive answer for the rationality problem of the three-dimensional purely monomial group actions except one case. We show that the remaining case is also affirmative.
9.
Christopher Svedberg 《Annales Henri Poincare》2011,12(5):849-917
Ringstr?m managed (in Invent Math 173(1):123–208, 2008) to prove future stability of solutions to Einstein’s field equations when matter consists of a scalar field with a potential
creating an accelerated expansion. This was done for a quite wide class of spatially homogeneous space–times. The methods
he used should be applicable also when other kinds of matter fields are added to the stress-energy tensor. This article addresses
the question whether we can obtain stability results similar to those Ringstr?m obtained if we add an electromagnetic field
to the matter content. Before this question can be addressed, more general properties concerning Einstein’s field equation
coupled to a scalar field and an electromagnetic field have to be settled. The most important of these questions are the existence
of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem. 相似文献
10.
Wilhelm Plesken 《Archiv der Mathematik》2009,92(2):111-118
Both the Gauss-Bruhat decomposition and the LU-decomposition of the general linear group over a field are examples of a Thomas
decomposition of systems of polynomial equations and inequations into disjoint triangular systems, a recently rediscovered
method of the nineteen-thirties, applied to the inequation det (A) ≠ 0 for an n × n-matrix of indeterminants. More specifically it is shown that the cells of the two decompositions can be described by determinantal
equations and inequations yielding simple systems in the sense of Thomas of a rather special type, which are called split
and allow counting solutions over any finite field.
Received: 17 March 2008, Revised: 12 August 2008 相似文献
11.
Luis Arenas-Carmona 《Archiv der Mathematik》2008,91(6):486-491
It is known that classes of indefinite quadratic forms in a genus are classified by the Galois group of a spinor class field
[4]. Hsia has proved the existence of a representation field F with the property that a lattice in the genus represents a fixed given lattice if and only if the corresponding element of
the Galois group is trivial on F. Spinor class fields can also be used to classify conjugacy classes of maximal orders in a central simple algebra. In [1]
we left open the issue of whether for every fixed given non-maximal order in a central simple division algebra there exists a representation field L with the property that embeds into a given maximal order if and only if the corresponding element of the Galois group is trivial on L. In this work we give a negative answer to this question for central simple division algebras of dimension ≥ 32. The case of non-division algebras is also treated by replacing the phrase embeds into by is contained in a conjugate of. As a byproduct of the techniques used in this paper we compute the representation field of an Eichler order in a quaternion
algebra.
Received: 8 April 2008 相似文献
12.
Local Thermal Equilibrium States and Quantum Energy Inequalities 总被引:1,自引:0,他引:1
In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling
on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a quantum energy
inequality for these states, where the (lower) energy bounds depend only on the local temperature distribution and are local
and covariant (the dependence of the bounds other than on temperature is on parameters defining the quantum field model, and
on local quantities constructed from the spacetime metric). Moreover, we also establish the averaged null energy condition
(ANEC) for such locally thermal states, under growth conditions on their local temperature and under conditions on the free
parameters entering the definition of the renormalized stress-energy tensor. These results hold for a range of curvature couplings
including the cases of conformally coupled and minimally coupled scalar field.
Submitted: February 27, 2008. Accepted: May 5, 2008. 相似文献
13.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
14.
N. I. Dubrovin 《Journal of Mathematical Sciences》2008,149(3):1191-1223
The main result of this paper is the following theorem: the group ring of the universal covering
of the group SL(2, ℝ) is embeddable in a skew field
with valuation in the sense of Mathiak and the valuation ring is an exceptional chain order in the skew field
, i.e., there exists a prime ideal that is not completely prime. In this ring, every divisorial right fractional ideal is
principal, and the linearly ordered set of all divisorial fractional right ideals is isomorphic to the real line. This theorem
is a consequence of the fact that the universal covering group
satisfies sufficient conditions for the embeddability of the group ring of a left ordered group in a skew field.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 3, pp. 9–53, 2006. 相似文献
15.
Let be an algebraically closed field with trivial derivation and let denote the differential rational field , with , , , , differentially independent indeterminates over . We show that there is a Picard-Vessiot extension for a matrix equation , with differential Galois group , with the property that if is any differential field with field of constants , then there is a Picard-Vessiot extension with differential Galois group if and only if there are with well defined and the equation giving rise to the extension .
16.
O. V. Baburova V. Ch. Zhukovsky B. N. Frolov 《Theoretical and Mathematical Physics》2008,157(1):1420-1432
Based on the requirement that the gauge invariance principle for the Poincaré-Weyl group be satisfied for the space-time manifold,
we construct a model of space-time with the geometric structure of a Weyl-Cartan space. We show that three types of fields
must then be introduced as the gauge (“compensating”) fields: Lorentz, translational, and dilatational. Tetrad coefficients
then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general
equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation
current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the
spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincaré-Weyl group.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 64–78, October, 2008. 相似文献
17.
Dmitry Novikov 《Geometric And Functional Analysis》2009,18(5):1750-1773
We prove an existential finiteness result for integrals of rational 1-forms over the level curves of Darbouxian integrals.
Received: May 2007, Revision: March 2008, Accepted: March 2008 相似文献
18.
Andreas Fischer 《Proceedings of the American Mathematical Society》2008,136(7):2583-2587
Let be an -minimal expansion of the real exponential field which possesses smooth cell decomposition. We prove that for every definable open set, the definable indefinitely continuously differentiable functions are a dense subset of the definable continuous function with respect to the -minimal Whitney topology.
19.
Bernard Helffer Yuri A. Kordyukov 《Transactions of the American Mathematical Society》2008,360(3):1681-1694
We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold such that , equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries, has an arbitrarily large number of spectral gaps in the semi-classical limit.
20.
Jérémy Faupin 《Annales Henri Poincare》2008,9(4):743-773
We study a model describing a system of one dynamical nucleus and one electron confined by their center of mass and interacting
with the quantized electromagnetic field. We impose an ultraviolet cutoff and assume that the fine-structure constant is sufficiently
small. Using a renormalization group method (based on [3, 4]), we prove that the unperturbed eigenvalues turn into resonances
when the nucleus and the electron are coupled to the radiation field. This analysis is related to the Lamb–Dicke effect.
Submitted: October 19, 2007. Accepted: January 22, 2008. 相似文献