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61.
Yang–Baxter operators from algebra structures appeared for the first time in [11, 22, 23]. Later, Yang–Baxter systems from entwining structures were constructed in [8]. In fact, Yang–Baxter systems are equivalent with braid systems. In this paper we show that braidings and entwinings of various algebraic structures—in particular, algebra factorisations—can be constructed from a braid system, whence from a Yang–Baxter system as well. 相似文献
62.
Kanishka Perera 《Applicable analysis》2013,92(9):883-888
We obtain nontrivial solutions for a class of p-Laplacian problems that are p-superlinear at infinity and nonresonant at zero. The proof is based on showing that the associated variational function has a (generalized) local linking near the origin and makes use of a new sequence of min-max eigenvalues of the p-Laplacian defined using the Yang index. 相似文献
63.
ABSTRACT It is shown that a Yang–Baxter system can be constructed from any entwining structure. It is also shown that,conversely,Yang–Baxter systems of certain types lead to entwining structures. Examples of Yang–Baxter systems associated to entwining structures are given,and a Yang–Baxter operator of Hecke type is defined for any bijective entwining map. 相似文献
64.
65.
We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a ‘finite manifold structure’ on the set of vertices. We equip any graph with a canonical ‘Euclidean metric’ and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations. 相似文献
66.
R. Hofmann 《Annalen der Physik》2009,18(9):634-639
Based on SU(2) Yang‐Mills thermodynamics we interprete Aracde2's and the results of earlier radio‐surveys on low‐frequency cosmic microwave background (CMB) line temperatures as a phase‐boundary effect. We explain the excess at low frequencies by evanescent, nonthermal photon fields of the CMB whose intensity is nulled by that of Planck distributed calibrator photons. The CMB baseline temperature thus is identified with the critical temperature of the deconfining‐preconfining transition. 相似文献
67.
68.
Hugo?García-CompeánEmail author Pablo?Paniagua 《General Relativity and Gravitation》2005,37(4):723-731
Cohomological Yang–Mills theory is formulated on a noncommutative differentiable four manifold through the -deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the -deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley–Eilenberg homology of noncommutative spacetime and the Chevalley–Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons. 相似文献
69.
The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate.By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian four-manifolds. Compared with the more widely known L2 metric, the information metric better reflects the conformal invariance of the self-dual Yang–Mills equations, and seems to have better completeness properties. In the case of SU(2) instantons on S4 of charge one, g is known to be the hyperbolic metric on the five-ball. We show more generally that for charge-one SU(2) instantons over 1-connected, positive-definite manifolds, g is non-degenerate and complete in the collar region of M, and is asymptotically hyperbolic there; g vanishes at the cone points of M. We give explicit formulae for the metric on the space of instantons of charge one on CP2. 相似文献
70.
It is shown that the connection form (gauge field) related to the generalization of the Berry phase to mixed states proposed by Uhlmann satisfies the source-free Yang–Mills equation * D * D = 0, where the Hodge operator is taken with respect to the Bures metric on the space of finite-dimensional nondegenerate density matrices. 相似文献