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111.
The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating 1-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (good groups) where the 1-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.Oblatum 20-II-1995 & 26-V-1995The first author is supported by the IHES, the Guggenheim foundation and the NSF.The second author is supported by the IHES and the Humboldt foundation. 相似文献
112.
Peter Hermann 《manuscripta mathematica》1995,88(1):1-24
The principal goal of this paper is to investigate the representation theory of double coset hypergroups. IfK=G//H is a double coset hypergroup, representations ofK can canonically be obtained from those ofG. However, not every representation ofK originates from this construction in general, i.e., extends to a representation ofG. Properties of this construction are discussed, and as the main result it turns out that extending representations ofK is compatible with the inducing process (as introduced in [7]). It follows that a representation weakly contained in the
left-regular representation ofK always admits an extension toG. Furthermore, we realize the Gelfand pair
(where
are a local field andR its ring of integers) as a polynomial hypergroup on ℕ0 and characterize the (proper) subset of its dual consisting of extensible representations. 相似文献
113.
E. G. Coffman Jr. Bjorn Poonen Peter Winkler 《Probability Theory and Related Fields》1995,102(1):105-121
Summary Letn random intervalsI
1, ...,I
n be chosen by selecting endpoints independently from the uniform distribution on [0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this best packing has wasted space
. It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case. 相似文献
114.
For all oddv 3 the complete graph onvK
v
vertices can be decomposed intov – 2 edge disjoint cycles whose lengths are 3, 3, 4, 5,...,v – 1. Also, for all oddv 7,K
v
can be decomposed intov – 3 edge disjoint cycles whose lengths are 3, 4,...,v – 4,v – 2,v – 1,v.
Research supported by Australian Research Council grant A49130102 相似文献
115.
116.
The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family 总被引:2,自引:0,他引:2
Dankmar Böhning Ekkehart Dietz Rainer Schaub Peter Schlattmann Bruce G. Lindsay 《Annals of the Institute of Statistical Mathematics》1994,46(2):373-388
We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log
n
, where
n
is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional
(2)
2
-distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio
n
are possible and the asymptotic distribution of 2 log
n
is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the 2-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log
n
are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of
(1)
2
. In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log
n
is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models. 相似文献
117.
Summary We start with a measurem on a measurable space (,A), decomposable with respect to an Archimedeant-conorm on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.The integral naturally leads to a -decomposable measurem on the space of all measurable functions from to [0, 1]. The main result of the present paper is the converse of this, namely that, under natural conditions, any -decomposable measurem on can be represented as an integral of a certain Markov-kernelK.
We extend this representation to measures
on which have values in a set of distribution functions.These results generalize the work done by the first author in the case of additive measures. 相似文献
118.
Peter Krauter 《Geometriae Dedicata》1994,51(3):287-303
We give a complete list of affine minimal surfaces inA
3 with Euclidean rotational symmetry, completing the treatise given in [1] and prove that these surfaces have maximal affine surface area within the class of all affine surfaces of rotation satisfying suitable boundary conditions. Besides we show that for rotationally symmetric locally strongly convex affine minimal hypersurfaces inA
n
,n4, the second variation of the affine surface area is negative definite under certain conditions on the meridian. 相似文献
119.
It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w
1 + ... + w
m
over , wherew
1,...,w
m
are given real numbers. In particular, if this dimension ism, i.e. ifw
1,...,w
m
are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade. 相似文献
120.
Mark A. Gallagher Kenneth W. Bauer Jr. Peter S. Maybeck 《Annals of Operations Research》1994,53(1):419-441
Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences. 相似文献