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81.
Mbekhta's subspaces and a spectral theory of compact operators 总被引:4,自引:0,他引:4
Let be an operator on an infinite-dimensional complex Banach space. By means of Mbekhta's subspaces and , we give a spectral theory of compact operators. The main results are: Let be compact. . The following assertions are all equivalent: (1) 0 is an isolated point in the spectrum of (2) is closed; (3) is of finite dimension; (4) is closed; (5) is of finite dimension; . sufficient conditions for to be an isolated point in ; . sufficient and necessary conditions for to be a pole of the resolvent of .
82.
A. Laurinčikas 《Acta Appl Math》2003,78(1-3):251-271
The first part of the paper contains a survey on the universality of zeta-functions. Zeta-functions with Euler's product as well as zeta-functions without Euler's product are discussed. Also, the joint universality theorems are considered. In the second part of the paper the universality of zeta-functions of finite Abelian groups of rank 3 is proved. 相似文献
83.
Einar Steingrímsson 《Journal of Algebraic Combinatorics》2001,14(1):73-84
Let G be a simple graph on d vertices. We define a monomial ideal K in the Stanley-Reisner ring A of the order complex of the Boolean algebra on d atoms. The monomials in K are in one-to-one correspondence with the proper colorings of G. In particular, the Hilbert polynomial of K equals the chromatic polynomial of G.The ideal K is generated by square-free monomials, so A/K is the Stanley-Reisner ring of a simplicial complex C. The h-vector of C is a certain transformation of the tail
T(n) = n
d – (n) of the chromatic polynomial of G. The combinatorial structure of the complex C is described explicitly and it is shown that the Euler characteristic of C equals the number of acyclic orientations of G. 相似文献
84.
We consider the existence of steady incompressible fluids (solutions to the Euler equations) on Riemannian manifolds of dimensions three and higher. We demonstrate that, as in the case of the ABC fields in dimension three, there exist chaotic Beltrami fields – nonsingular eigenfields of the curl operator – in higher dimensions. We give an explicit set of analytic examples on a non-Euclidean five-torus T
5. We also detail a plug construction for inserting chaotic vortices into a Beltrami field. These constructions employ contact-topological techniques. 相似文献
85.
Shamita Dutta Gupta Xiaotie She 《Proceedings of the American Mathematical Society》2000,128(8):2203-2212
In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form on the double cover of . Zagier's idea of Rankin-Selberg method is used to define the convolution of and the -function.
86.
We obtain Chern-Osserman's inequality of a complete properly immersed minimal surface in hyperbolic -space, provided the -norm of the second fundamental form of the surface is finite.
87.
This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the structural complexity of disordered surfaces (and interfaces) observed and/or simulated in nano, micro and ordinary scales. 相似文献
88.
Three-dimensional linearised Euler model simulations of sound propagation in idealised urban situations with wind effects 总被引:1,自引:0,他引:1
Dietrich Heimann 《Applied Acoustics》2007,68(2):217-237
A three-dimensional numerical time-domain model based on the linearised Euler equation is applied to idealised urban situations with elongated, isolated buildings beside a straight street with sound emissions. The paper aims at the investigation of principle relationships between the source-receiver geometry (street and building facades) and sound propagation under the consideration of ground and wind. By applying cyclic lateral boundary conditions for either one or both horizontal co-ordinates, two different idealised urban environments were considered: a single street and parallel streets. Numerical experiments were performed to elaborate the effects of different roof types, ground properties, wind flow, and turbulence in both urban environments with the focus on the back facades (‘quiet’ sides) of the buildings. As a result it was found that the back facades of flat-roof buildings are quieter than those of hip roof buildings despite equal cross-cut areas. The wind effect (resulting in quieter upwind and louder downwind facades) is more pronounced for hip-roof buildings. In the case of parallel streets upwind facades are slightly louder than downwind facades because they are simultaneously exposed to downwind propagating sound from the next parallel street. 相似文献
89.
We derive a representation formula for the solutions of the navier-Stokes flow in three dimensions in absence of boundary in terms of stochastic current lines. This pictures generalizes an analogous one given in two dimensions and on the other hand the classical Lafrangian picture for the Euler flow. We prove a Vanishing viscosity limit for the whole structure 相似文献
90.
Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献