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951.
Using a family of higher degree polynomials as a bridge, together with complex surgery techniques, we construct a homeomorphism
between any two limbs of the Mandelbrot set of equal denominator. Induced by these homeomorphisms and complex conjugation,
we obtain an involution between each limb and itself, whose fixed points form a topological arc. All these maps have counterparts
at the combinatorial level relating corresponding external arguments. Assuming local connectivity of the Mandelbrot set we
may conclude that the constructed homeomorphisms between limbs are compatible with the embeddings of the limbs in the plane.
As usual we plough in the dynamical planes and harvest in the parameter space. 相似文献
952.
Andrei E. Vityaev 《Journal of Geometric Analysis》1999,9(1):161-173
We study uniqueness of an H∞ optimization problem which is central to the worst case frequency domain system design. It was known that if the so-called
sublevel sets are strictly convex inC
N, then the uniqueness holds. On the other hand, there are examples of non-uniqueness if the sublevel sets are just strictly
pseudoconvex.
In this paper we prove that uniqueness holds for a type of convexity which is strictly in-between geometric and pseudoconvexity. 相似文献
953.
Given a compact, oriented Riemannian manifold M, without boundary, and a codimension-one homology class in H* (M, Z) (or, respectively, in H* (M, Zp) with p an odd prime), we consider the problem of finding a cycle of least area in the given class: this is known as the
homological Plateau’s problem.
We propose an elliptic regularization of this problem, by constructing suitable fiber bundles ξ (resp. ζ) on M, and one-parameter
families of functionals defined on the regular sections of ξ, (resp. ζ), depending on a small parameter ε.
As ε → 0, the minimizers of these functionals are shown to converge to some limiting section, whose discontinuity set is exactly
the minimal cycle desired. 相似文献
954.
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS
1×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra. 相似文献
955.
David Pollard 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):1039
The paper provides a recursive interpretation for the technique known as bracketing with adaptive truncation. By way of illustration, a simple bound is derived for the expected value of the supremum of an empirical process, thereby leading to a simpler derivation of a functional central limit theorem due to Ossiander. The recursive method is also abstracted into a framework that consists of only a small number of assumptions about processes and functionals indexed by sets of functions. In particular, the details of the underlying probability model are condensed into a single inequality involving finite sets of functions. A functional central limit theorem of Doukhan, Massart and Rio, for empirical processes defined by absolutely regular sequences, motivates the generalization. 相似文献
956.
Olaf Bröcker 《Journal of Geometry》2002,75(1-2):46-60
For M?bius planes Schaeffer [9] has proved that all seven
point degenerations of Miquel's Theorem characterize miquelian M?bius
planes. For Laguerre planes we have several degenerations of Miquel's
Theorem with eight and seven points. We prove that all except one of
these degenerations characterize miquelian Laguerre planes. The
remaining degeneration characterizes elation Laguerre planes.
Received 14 September 2001; revised 1 September 2002. 相似文献
957.
Loïc Colson 《BIT Numerical Mathematics》1992,32(1):5-9
We present a primitive recursive programinf_with_lists computing the minimum of two natural numbersn andp (written in unary notation) and using primitive recursion on lists. This program has at first sight the required property of visiting simultaneously its inputs, so it is a counterexample to a theorem showing that such a program cannot be written in the language of primitive recursion on natural numbers, in the more general framework of primitive recursion on term algebras. However, its complexity is at leastinf(n,p)2 so it does not implement the algorithm we have in mind to computeinf(n,p). 相似文献
958.
Cao An Wang 《BIT Numerical Mathematics》1991,31(2):230-236
An algorithm for finding a polygon with minimum number of edges nested in two simplen-sided polygons is presented. The algorithm solves the problem in at mostO(n logn) time, and improves the time complexity of two previousO(n
2) algorithms.The work was supported by NSERC grant OPG0041629. 相似文献
959.
Summary We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß-Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigridV-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes. 相似文献
960.
We consider the problem of constructing a graphG* from a collection of isomorphic copies of a graphG in such a way that for every two copies ofG, either no vertices or a section graph isomorphic to a graphH is identified. It is shown that ifG can be partitioned into vertex-disjoint copies ofH, thenG* can be made to have at most |H| orbits. A condition onG so thatG* can be vertextransitive is also included. 相似文献