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991.
We investigate a class of actions of real Lie groups on complex spaces. Using moment map techniques we establish the existence of a quotient and a version of Luna’s slice theorem as well as a version of the Hilbert–Mumford criterion. A global slice theorem is proved for proper actions. We give new proofs of results of Mostow on decompositions of groups and homogeneous spaces.First author partially supported by the Sonderforschungsbereich SFB/TR12 of the Deutsche Forschungsgemeinschaft and the DFG Schwerpunk program Globale Methoden in der komplexen Geometrie.Second author partially supported by NSA grant H98230–04–01–0070. 相似文献
992.
An American put option can be modelled as a variational inequality. With a penalization approximation to this variational
inequality, the convergence rate of the Binomial Tree Scheme is obtained in this paper. 相似文献
993.
We study the numerical approximation of the solutions of a class of nonlinear reaction–diffusion systems modelling predator–prey
interactions, where the local growth of prey is logistic and the predator displays the Holling type II functional response.
The fully discrete scheme results from a finite element discretisation in space (with lumped mass) and a semi-implicit discretisation
in time. We establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations.
Numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions.
The class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics,
expressed in nondimensional form. The theoretical techniques were adapted from a previous study of an idealised reaction–diffusion
system (Garvie and Blowey in Eur J Appl Math 16(5):621–646, 2005). 相似文献
994.
This work extends the classical F. and M. Riesz theorem to measures that are boundary values of holomorphic functions defined on wedges in
with edges that are in the class C
1,α.This work was supported in part by NSF INT-0203005, CNPq and FAPESP 相似文献
995.
Kenichiro Tamaki 《Journal of multivariate analysis》2007,98(3):638-659
We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-37]. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of . Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of . Numerical studies are given to confirm the theoretical results. 相似文献
996.
André Mas 《Journal of multivariate analysis》2007,98(6):1231-1261
The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This article aims at completing the theoretical study of the model by addressing the issue of weak convergence for estimates from the model. The main difficulties stem from an underlying inverse problem as well as from dependence between the data. Traditional facts about weak convergence in non-parametric models appear: the normalizing sequence is not an , a bias term appears. Several original features of the functional framework are pointed out. 相似文献
997.
The simplest condition characterizing quasi-finite CW complexes K is the implication XτhK⇒β(X)τK for all paracompact spaces X. Here are the main results of the paper:
Theorem 0.1.
If{Ks}s∈Sis a family of pointed quasi-finite complexes, then their wedge?s∈SKsis quasi-finite. 相似文献
998.
Arkadiusz Jadczyk 《Advances in Applied Clifford Algebras》2007,17(2):201-240
Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to
convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the
standard quantum theory. We study quantum jumps on n-dimensional spheres, jumps that are induced by symmetric configurations
of non-commuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (M?bius
transformations) and realize iterated function systems (IFS) with fractal attractors located on n-dimensional spheres. We
also extend the formalism to mixed states, represented by “density matrices” in the standard formalism, (the n-balls), but
such an extension does not lead to new results, as there is a natural mechanism of purification of states. As a numerical
illustration we study quantum fractals on the circle (one-dimensional sphere and pentagon), two–sphere (octahedron), and on
three-dimensional sphere (hypercubetesseract, 24 cell, 600 cell, and 120 cell). The attractor, and the invariant measure on
the attractor, are approximated by the powers of the Markov operator. In the appendices we calculate the Radon-Nikodym derivative
of the SO(n + 1) invariant measure on Sn under SO(1, n + 1) transformations and discuss the Hamilton’s “icossian calculus” as well as its application to quaternionic realization
of the binary icosahedral group that is at the basis of the 600 cell and its dual, the 120 cell.
As a by-product of this work we obtain several Clifford algebraic results, such as a characterization of positive elements
in a Clifford algebra
as generalized Lorentz “spin–boosts”, and their action as M?bius transformation on n-sphere, and a decomposition of any element
of Spin+(1, n + 1) into a spin–boost and a spin–rotation, including the explicit formula for the pullback of the SO(n + 1) invariant Riemannian metric with respect to the associated M?bius transformation. 相似文献
999.
We consider the Reynolds Averaged Navier–Stokes (RANS) model of order one (u,p,k) set in R3 which couples the Stokes Problem to the equation for the turbulent kinetic energy by k-dependent eddy viscosities in both equations and a quadratic term in the k -equation. We study the case where the velocity and the pressure satisfy periodic boundary conditions while the turbulent kinetic energy is defined on a cell with Dirichlet boundary conditions. The corresponding eddy viscosity in the fluid equation is extended to R3 by periodicity. Our contribution is to prove that this system has a solution when the eddy viscosities are nondecreasing, smooth, unbounded functions of k, and the eddy viscosity in the fluid equation is a concave function. 相似文献
1000.
Julianna S. Tymoczko 《Selecta Mathematica, New Series》2007,13(2):353-367
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology,
geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent
Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving
is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving
and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties
have no odd-dimensional homology.
相似文献