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61.
K. Lochmann A. Anikeenko A. Elsner N. Medvedev D. Stoyan 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(1):67-76
The performance of various structure characteristics in
the task of indicating structural peculiarities in packings of
hard spheres is investigated. Various characteristics based on
Voronoi polyhedra, spherical harmonics, and Delaunay simplices are
considered together with the pair correlation function and the
mean number of r-close triples. They are applied to a set of
hard sphere packings of density φ from 0.62 to 0.72. It turns
out that all used structure characteristics are able to indicate
changes of order from non-crystalline to crystalline packings.
However, not all of them are sensitive enough to indicate
different stages of structure transformation under densification.
The characteristics based on Delaunay simplices turn out to be the
most sensitive for this purpose.
For the models considered three principal structure classes are
found: packings of densities lower than the known critical value
0.64 showing a non-crystalline behavior; packings with
considerable crystalline regions for φ up to 0.66–0.67;
rather complete crystals although with numerous defects for φ
above 0.67. 相似文献
62.
The surface of amorphous solids cannot be usually represented by a regular lattice of adsorbing sites. One of the main characteristics of such surfaces is a variable connectivity for each site. A simple model consisting of a triangular lattice where a fraction of bonds (interactions) is suppressed at random is used here to find out, by using Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. Adsorption isotherm, differential heat of adsorption and adsorbed phase entropy calculations are carried out showing and interpreting the effects of the variable connectivity. In particular, it is found that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical mean connectivity. 相似文献
63.
64.
65.
Possible errors in the widely used 1972–1973 macroscopic original-electric-modulus formalism are identified, corrected, and their consequences considered. These errors include misidentification of the high-frequency-limiting dielectric constant arising entirely from mobile charges, εC1∞, and the failure to treat properly the high-frequency-limiting dielectric constant associated with bulk dipolar and vibrionic effects, εD∞. It is shown that the corrected modulus formalism, which describes dispersed mobile-charge effects, is isomorphic in form with the 1973 microscopic continuous-time random-walk hopping model of Scher and Lax after a minor but significant correction is made to the latter's response function. This firmly established correction, which nevertheless could not be determined by Kronig–Kramers transformation, involved inversion of synthetic frequency-response data to determine a distribution of relaxation times and led to extension of the real part of the Scher–Lax dielectric response to higher frequencies by the inclusion of a nonzero limiting value. This isomorphism, along with excellent data fitting using the corrected modulus formalism, suggests that since the Scher–Lax stochastic model involves no explicit Coulomb interactions, cation motion in glasses is dominated by short-range interactions. Finally, two very-high-frequency processes, which each lead to a limiting plateau value of the real part of the conductivity at sufficiently high frequencies, are discussed in detail. 相似文献
66.
本文给出了一般非线性控制系统的最小Hamiltonian实现的存在性条件和唯一性结果。 相似文献
67.
State space methods have proved to be powerful theoretical and computational tools in a number of areas of applications, in particular filtering and control theory. In this paper we advocate the use of state space methods for the study of discrete probability densities on the set {0,1,2,…}. The fundamental approach is to consider the class
of all discrete probability densities that can be represented as the impulse response/convolution kernel of a finite dimensional discrete time state space system. We show that all standard operations such as the calculation of moments, convolution, scaling, translation, product, etc. can be carried out using system representations. 相似文献
68.
Riccardo Zecchina 《Pramana》2005,64(6):1161-1173
The combinatorial problem of satisfying a given set of constraints that depend on N discrete variables is a fundamental one in optimization and coding theory. Even for instances of randomly generated problems, the question “does there exist an assignment to the variables that satisfies all constraints?” may become extraordinarily difficult to solve in some range of parameters where a glass phase sets in. We shall provide a brief review of the recent advances in the statistical mechanics approach to these satisfiability problems and show how the analytic results have helped to design a new class of message-passing algorithms — the survey propagation (SP) algorithms — that can efficiently solve some combinatorial problems considered intractable. As an application, we discuss how the packing properties of clusters of solutions in randomly generated satisfiability problems can be exploited in the design of simple lossy data compression algorithms. 相似文献
69.
Christof Külske 《Journal of statistical physics》2003,112(5-6):1079-1108
It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover non-trivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models. 相似文献
70.