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161.
Kullback-Leibler divergence and the Neyman-Pearson lemma are two fundamental concepts in statistics. Both are about likelihood ratios: Kullback-Leibler divergence is the expected log-likelihood ratio, and the Neyman-Pearson lemma is about error rates of likelihood ratio tests. Exploring this connection gives another statistical interpretation of the Kullback-Leibler divergence in terms of the loss of power of the likelihood ratio test when the wrong distribution is used for one of the hypotheses. In this interpretation, the standard non-negativity property of the Kullback-Leibler divergence is essentially a restatement of the optimal property of likelihood ratios established by the Neyman-Pearson lemma. The asymmetry of Kullback-Leibler divergence is overviewed in information geometry. 相似文献
162.
163.
A. John Peter 《中国物理快报》2006,23(4):946-949
We present a simple demonstration of the nonfeasibility of metal-insulator transition in an exactly two-dimensional (2D) system. The Hartree-Fock potential in the 3D system is suitably modified and presented for the 2D case. The many body effects are included in the screening function, and binding energies of a donor are obtained as a function of impurity concentration so as to find out the possible way leading metal-insulator transition in the 2D system. While solving for the binding energy for a shallow donor in an isolated well of a GaAs/Ga1-x Als As superlattice system within the effective mass approximation, it leads to unphysical results for higher concentrations. It shows that the phase transition, the bound electron entering into the conduction band whereby (H)min=0, is not possible beyond this concentration. The results suggest thai a phase transition is impossible in 213 systems, supporting the scaling theory of localization. The results are compared with the existing data available and discussed in the light of existing literature. 相似文献
164.
John L. Johnson 《Foundations of Physics》1996,26(11):1529-1557
A four-dimensional operator is shown to contain the operator-generators for rotation, scale, reflections, and boosts. The hypothesis is advanced that a physical system changes under this operator by at most a complex phase factor due to invariance against the choice of menial frame. A canonical transform gives a simple relation between space-time and energy-momentum. The basic conserved quantity is a four-dimensional angular momentum and/or coupling constant. The differential of this function contains a second-order differential product which is constrained as a power series in the independent variable. The analysis explores the consequences of the model and shows its degree of correspondence to the standard models. 相似文献
165.
Applied Biochemistry and Biotechnology - It is generally recognized that the front-end (pretreatment, fractionation, enzymatic hydrolysis) steps of a lignocellulose-to-ethanol process are both... 相似文献
166.
167.
The germ of an analytic varietyX at a pointxX is said to bequadratic if it is bi-analytically isomorphic to the germ of a cone defined by a system of homogeneous quadratic equations at the origin. Arms, Marsden and Moncrief show in [2] that under certain conditions the analytic germ of a level set of a momentum mapping is quadratic. We discuss related ideas in a more algebraic context by associating to an affine Hamiltonian action a differential graded Lie algebra, which in the presence of an invariant positive complex structure, is formal in the sence of [5].Dedicated to the memory of Bruce Reinhart 相似文献
168.
Kamil John 《Mathematische Annalen》1990,287(1):509-514
169.
John Todd 《Numerische Mathematik》1990,57(1):737-746
Theorem.Let the sequences {e
i
(n)
},i=1, 2, 3,n=0, 1, 2, ...be defined by
where the e
(0)
s satisfy
and where all square roots are taken positive. Then
where the convergence is quadratic and monotone and where
The discussions of convergence are entirely elementary. However, although the determination of the limits can be made in an elementary way, an acquaintance with elliptic objects is desirable for real understanding. 相似文献
170.
Local nondeterminism and local times for stable processes 总被引:1,自引:0,他引:1
John P. Nolan 《Probability Theory and Related Fields》1989,82(3):387-410
Summary Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the L
p
representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to locally approximately independent increments. Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs. 相似文献