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31.
Michael E. Hoffman 《Journal of Algebraic Combinatorics》2000,11(1):49-68
Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be viewed as a generalization of the shuffle product III. We extend this commutative algebra structure to a Hopf algebra (U, *, ); in the case where A is the set of positive integers and the operation on A is addition, this gives the Hopf algebra of quasi-symmetric functions. If rational coefficients are allowed, the quasi-shuffle product is in fact no more general than the shuffle product; we give an isomorphism exp of the shuffle Hopf algebra (U, III, ) onto (U, *, ) the set L of Lyndon words on A and their images { exp(w) w L} freely generate the algebra (U, *). We also consider the graded dual of (U, *, ). We define a deformation *q of * that coincides with * when q = 1 and is isomorphic to the concatenation product when q is not a root of unity. Finally, we discuss various examples, particularly the algebra of quasi-symmetric functions (dual to the noncommutative symmetric functions) and the algebra of Euler sums. 相似文献
32.
Let(Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and HΨ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg and innerouter type factorization theorems of Hp(A) to this case. 相似文献
33.
该文在算子值非交换概率空间上引入半标准酉随机矩阵的概念, 证明了它是算子值Haar酉元的矩阵模型,并给出了半标准酉随机矩阵的渐近自由判定定理. 相似文献
34.
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the noncommutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the noncommutative zero curvature representations for these systems, based on the latter property. Quantum systems with their quantum zero curvature representations are particular cases of the general noncommutative ones. 相似文献
35.
This paper uses the background field method to calculate
one-loop divergent corrections to the gauge field propagators in
noncommutative U(1) gauge theory with scalar fields. It shows that
for a massless scalar field, the gauge field propagators are
renormalizable to θ2-order, but for a massive scalar field they
are renormalizable only to θ-order. 相似文献
36.
In order to further explore the effects of non-Gaussian smeared mass distribution on the thermodynamical properties of noncommutative black holes, we consider noncommutative black holes based on Maxwell-Boltzmann smeared mass distribution in (2+1)-dimensional spacetime. The thermodynamical properties of the black holes are investigated, including Hawking temperature, heat capacity, entropy and free energy. We find that multiple black holes with the same temperature do not exist, while there exists a possible decay of the noncommutative black hole based on Maxwell-Boltzmann smeared mass distribution into the rotating (commutative) BTZ black hole. 相似文献
37.
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent sheaves. The global category is very degenerate in general. Thus, we introduce a new notion of a semiformal deformation, a replacement in algebraic geometry of an actual deformation (versus a formal one). Deformed algebras obtained by semiformal deformations are Noetherian and have polynomial growth. We propose constructions of semiformal quantizations of projective and affine algebraic Poisson manifolds satisfying certain natural geometric conditions. Projective symplectic manifolds (e.g. K3 surfaces and Abelian varieties) do not satisfy our conditions, but projective spaces with quadratic Poisson brackets and Poisson–Lie groups can be semiformally quantized. 相似文献
38.
Andrzej Sitarz 《Letters in Mathematical Physics》1997,39(1):1-8
We build a q = –1 deformation of a plane on a product of two copies of algebras of functions on the plane. This algebra contains a subalgebra of functions on the plane. We present a general scheme (which could be also used to construct a quaternion from pairs of complex numbers) and we use it to derive differential structures and metrics, and discuss sample field-theoretical models.Mathematics Subject Classifications (1991):46L87, 81T13, 17B37. 相似文献
39.
M. A. Soloviev 《Theoretical and Mathematical Physics》2006,147(2):660-669
We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In
particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry
and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green’s functions
in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based
on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic
test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone
is replaced with that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics
theorems in this enlarged framework.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 257–269, May, 2006. 相似文献
40.
Stephen G. Low 《Foundations of Physics》2006,36(7):1036-1069
The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds2 = d t2. Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest frame by making velocities relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements and . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group. 相似文献