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131.
M. Pereyaslavets I. Ogawa T. Idehara S. Mitsudo 《International Journal of Infrared and Millimeter Waves》1999,20(8):1453-1468
The excitation and transmission losses of a dielectric-lined waveguide have been calculated with real, experimentally measured output beams of a submillimeter wave gyrotron. It is shown that for not-so-long transmission lines the coupling losses far exceed the transmission losses in the waveguide. 相似文献
132.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
133.
Ju¨rg Hu¨sler 《Extremes》1999,2(1):59-70
Consider a triangular array of standard Gaussian random variables {n,i, i 0, n 1} such that {n,i, i 0} is a stationary normal sequence for each n 1. Let n,k = corr(n,i,n,i+k). If (1-n,k)log n k (0,) as n for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still the Gumbel distribution as in the stationary or i.i.d. case, but shifted by a parameter measuring the clustering. Triangular arrays of Gaussian sequences are used to approximate a continuous Gaussian process X(t), t 0. The cluster behavior of the random sequence refers to the behavior of the extremes values of the continuous process. The relation is analyzed. It reveals a new definition of the constants H
used for the limiting distribution of maxima of continuous Gaussian processes and provides further understanding of the limit result for these extremes. 相似文献
134.
Mikael Raab 《Extremes》1999,1(3):295-321
Consider a finite sequence of Gaussian random variables. Count the number of exceedances of some level a, i.e. the number of values exceeding the level. Let this level and the length of the sequence increase simultaneously so that the expected number of exceedances remains fixed. It is well-known that if the long-range dependence is not too strong, the number of exceeding points converges in distribution to a Poisson distribution. However, for sequences with some individual large correlations, the Poisson convergence is slow due to clumping. Using Steins method we show that, at least for m-dependent sequences, the rate of convergence is improved by using compound Poisson as approximating distribution. An explicit bound for the convergence rate is derived for the compound Poisson approximation, and also for a subclass of the compound Poisson distribution, where only clumps of size two are considered. Results from numerical calculations and simulations are also presented. 相似文献
135.
We show that if a bounded analytic semigroup on satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on , then generates a -regularized group on where . We obtain the estimate of () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.
136.
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.
137.
Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved. 相似文献
138.
J. A. Cuesta-Albertos C. Matrán-Bea A. Tuero-Diaz 《Journal of Theoretical Probability》1996,9(2):263-283
We provide two families of lower bounds for theL
2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02. 相似文献
139.
Numerical modelling of the Gaussian beam diffraction by a wire near the Fraunhofer limit is presented. Two cases are considered: the case of the wire being on the axis of the beam and the case of the wire being off-axis. For the case where the wire is on the axis, the displacements of the diffracted minima are calculated. For the off-axis case, the changes in the positions of the maxima and minima and the power density are calculated. The conditions are determined at which the measurements made using a Gaussian beam can be calculated using the formula for plane waves. This work arises in connection with research being performed into the Doppler spectrum of big particles. 相似文献
140.
Zbigniew J. Jurek 《Journal of multivariate analysis》1983,13(4):578-604
Let
= {Ut: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set
(X) of all probability measures on X. By
(Q;
) we denote the class of all limit measures of {Utn(μ1 * μ2*…*μn)*δxn}, where {μn}Q, {xn}X and measures Utnμj (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes Lm(
) as follows: L0(
)=
(
(X);
), Lm(
)=
(Lm−1(
);
) for m=1, 2,… and L∞(
)=m=0∞Lm(
). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from Lm(
), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators. 相似文献