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991.
992.
D.J. Scott 《Stochastic Processes and their Applications》1978,6(3):241-252
A functional central limit theorem is obtained for martingales which are not uniformly asymptotically negligible but grow at a geometric rate. The function space is not the usual C[0,1] or D[0,1] but RN, the space of all real sequences and the metric used leads to a non-separable metric space.The main theorem is applied to a martingale obtained from a supercritical Galton-Watson branching process and as simple corollaries the already known central limit theorems for the Harris and Lotka-Nagaev estimators of the mean of the offspring distribution, are obtained. 相似文献
993.
Warren Dicks 《Journal of Pure and Applied Algebra》1983,27(1):15-28
Let λ be a finitary geometric theory and δ its classifying topos. We prove that δ is Boolean if and only if (1) every first-order formula in the language of λ is ?-provably equivalent to a geometric formula and (2) for any finite list of varibles, x, there are, up to ?-provable equivalence, only finitely many formulas, in the language of λ with free variables among x. We use this characterization to show that, when δ is Boolean, it is an atomic topos and can be viewed as a finite coproduct of topoi of continuous G-sets for topological groups G satisfying a certain finiteness condition. 相似文献
994.
Peter Hall 《Journal of multivariate analysis》1982,12(3):432-449
We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval—those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial estimators are superior in many respects. However, Legendre polynomial series can be more difficult to construct than trigonometric series, and to overcome this difficulty we show how to modify trigonometric series estimators to make them more competitive. 相似文献
995.
Let X(ω) be a random element taking values in a linear space endowed with the partial order ≤; let 0 be the class of nonnegative order-preserving functions on such that, for each g∈0, E[g(X)] is defined; and let 1?0 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf1E[g(X)]/g(x) ≤ inf1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability. 相似文献
996.
Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a1B + … + apBp) X(t) = [Πi=1p (I ? αiB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a1, a2,…, ap. In fact the number of possibilities is limited upwards by , there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned. 相似文献
997.
Some random environment population processes are considered. Using a coupling argument, a criticality condition is obtained. The criticality parameter governs whether the process dies out or fluctuates about a positive finite constant, which is explicitly computed. 相似文献
998.
Allan Gut 《Stochastic Processes and their Applications》1974,2(1):115-126
Let Sn,n = 1, 2, …, denote the partial sums of integrable random variables. No assumptions about independence are made. Conditions for the finiteness of the moments of the first passage times N(c) = min {n: Sn>ca(n)}, where c ≥ 0and a(y) is a positive continuous function on [0, ∞), such that a(y) = o(y)as y → ∞, are given. With the further assumption that a(y) = yP,0 ≤ p < 1, a law of large numbers and the asymptotic behaviour of the moments when c → ∞ are obtained. The corresponding stopped sums are also studied. 相似文献
999.
A completely regular space X is called nearly pseudocompact if υX?X is dense in βX?X, where βX is the Stone-?ech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X1, X2 such that Int X1 is locally compact, no points of X2 has a closed realcompact neighborhood, and . It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact. 相似文献
1000.
P. Le Gall 《Stochastic Processes and their Applications》1978,6(3):337-338
Let F be a univariate distribution with negative expectation, and let M denote the distribution of the positive maxima of a random walk generated by a sequence of independent observations from F. We consider the Laplace transforms of 1?F(x) and 1?M(x). A relation between the transforms yields some known results on the moments and the regularly varying properties of the two distributions. 相似文献