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221.
222.
To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown meansμi's and unknown variancesσ2i's, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates ofμi's andσ2i's under the restriction and proposes an algorithm for obtaining the estimates. 相似文献
223.
J. C. Allwright 《Journal of Optimization Theory and Applications》1980,32(3):327-343
The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex
0. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx
0 and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations. 相似文献
224.
Nine methods for expressing a proper rational function in terms of partial fractions are presented for the case where the denominator polynomial has been reduced to linear factors. Only those methods which are amenable to computation algorithms are considered. To the extent possible, Newton's divided difference formula is used to provide a uniform derivational tool. Each method is illustrated numerically. The efficiency of the methods are compared on the basis of the number of multiplications and divisions required in the computation. 相似文献
225.
The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.Supported by National Science Foundation Grant ENG-7515882. 相似文献
226.
227.
We study the semidiscrete Galerkin approximation of a stochastic parabolic partial differential equation forced by an additive space-time noise. The discretization in space is done by a piecewise linear finite element method. The space-time noise is approximated by using the generalized L2 projection operator. Optimal strong convergence error estimates in the L2 and
norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The error estimates are applicable in the multi-dimensional case.
AMS subject classification (2000) 65M, 60H15, 65C30, 65M65.Received April 2004. Revised September 2004. Communicated by Anders Szepessy. 相似文献
228.
A. S. Mellit V. I. Rabanovich Yu. S. Samoilenko 《Functional Analysis and Its Applications》2004,38(2):157-160
We describe the set
of values of the parameter for which there exists a Hilbert space H and n partial reflections A
1,...,A
n
(self-adjoint operators such that A
k
3
=Ak or, which is the same, self-adjoint operators whose spectra belong to the set {-1,0,1}) whose sum is equal to the scalar operator I
H
. 相似文献
229.
Thilo?Meyer-BrandisEmail author Frank?ProskeEmail author 《Applied Mathematics and Optimization》2004,50(2):119-134
In this paper we explicitly solve a non-linear filtering problem
with mixed observations, modelled by a Brownian motion and a generalized Cox
process, whose jump intensity is given in terms of a Lévy measure.
Motivated by empirical observations of R. Cont and P. Tankov we propose a
model for financial assets, which captures the phenomenon of
time inhomogeneity of the jump size density. We apply the explicit formula
to obtain the optimal filter for the corresponding filtering problem. 相似文献
230.
An Implementation for the Algorithm of Janet bases of Linear Differential Ideals in the Maple System
Shan-qingZhang Zhi-binLi 《应用数学学报(英文版)》2004,20(4):605-616
In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division,Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package. 相似文献