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931.
It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949–1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called compatible if they satisfy the Morette–Van Hove formula and anti-compatible if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf–Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton–Jacobi equation has recently been enlarged. 相似文献
932.
The (3x+1)/2 problem is generalized into the n-furcation problem (l
i
x+m
i
)/n where i[0, 1, ..., n–1]. It is shown that, under some constraints on l
i
and m
i
, the main bijection property between the k less significant digits of the seed, written in base n, and the sequence of generalized parities of the k first iterates is preserved. This property is used to investigate a stochastic treatment of ensemble of large value seeds. The bijection property predicts stochasticity for a number of iterations equals to the number of significant digits of the seed. In fact, the stochastic approach is valid for much larger numbers, a property which is more easily shown by using increasing sequences than decreasing ones. Finally, we extend the stochastic approach to cases where the bijection theorem does not hold, introducing the matrix giving the probability that a j number (where j is the last significant digit of this number written in base n) gives a i number iterate. 相似文献
933.
Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques. 相似文献
934.
935.
Kristiansen PE Mitchell DJ Evans JN 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2002,157(2):253-266
A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz. 相似文献
936.
M. Vatasescu F. Masnou-Seeuws 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(2):191-204
The paper contains a time-dependent investigation of the tunneling effect observed in the photoassociation spectrum of Cs2 and attributed to the 0g
-(6s, 6p
3/2) double well. When by photoassociation of two cold cesium atoms a vibrational level of the outer well is populated, tunneling
is an efficient mechanism for transferring the population to the inner well (R < 15a
0), where spontaneous emission may lead to formation of cold molecules in low vibrational levels of the a
3Σ+
u(6s, 6s) electronic state. This tunneling effect is analyzed by wavepackets propagation, first considering the double well potential
alone, and following a packet made by a superposition of states initially located at large distances. Characteristic times
for the vibration dynamics, corresponding to a beating phenomenon between the two wells, to partial “revival” at large distances,
and to maxima in the population localized in the inner well are reported and discussed. Second, we simulate the two-channels
a
3Σ+
u(6s, 6s)↦0g
-(6s, 6p
3/2) photoassociation at detunings around 2.9 cm-1: the inner well can be populated either by the excitation of a vibrational level of the external well (resonant excitation),
or by tuning the photoassociation laser at the energy of the inner well level which displays tunneling (“off-resonance excitation”).
In the first case the photoassociation is efficient, while the tunneling probability is small; in the second, the tunneling
probability is large, so that despite the poor efficiency of the photoassociation process, more population can be transferred
to the inner well. This second choice is shown to be very sensitive to the laser intensity, which could be used to control
the population of the inner well and hence the formation of ultracold molecules in low vibrational levels.
Received 19 April 2002 Published online 1st October 2002
RID="a"
ID="a"e-mail: francoise.masnou@lac.u-psud.fr 相似文献
937.
Zhang J. Z. Deng N. Y. Chen L. H. 《Journal of Optimization Theory and Applications》1999,102(1):147-167
In unconstrained optimization, the usual quasi-Newton equation is B
k+1
s
k=y
k, where y
k is the difference of the gradients at the last two iterates. In this paper, we propose a new quasi-Newton equation,
, in which
is based on both the function values and gradients at the last two iterates. The new equation is superior to the old equation in the sense that
better approximates 2
f(x
k+1)s
k than y
k. Modified quasi-Newton methods based on the new quasi-Newton equation are locally and superlinearly convergent. Extensive numerical experiments have been conducted which show that the new quasi-Newton methods are encouraging. 相似文献
938.
We present an algorithm for variational inequalities VI(
, Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping
is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one. 相似文献
939.
Susanne C. Brenner. 《Mathematics of Computation》1999,68(225):25-53
We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.
940.
After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.