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971.
A. I. Parfenov 《Siberian Advances in Mathematics》2008,18(4):258-274
Let a piece of the boundary of a Lipschitz domain be parameterized conventionally and let the traces of functions in the Sobolev space W p 2 be written out through this parameter. In this space, we propose a discrete (diadic) norm generalizing A. Kamont’s norm in the plane case. We study the conditions when the space of traces coincides with the corresponding space for the plane boundary. 相似文献
972.
Matthias Neufang 《Proceedings of the American Mathematical Society》2008,136(5):1831-1839
Let be a locally compact, non-compact group (we make the non-compactness assumption, for the most part, simply to avoid trivialities). We show that under a very mild assumption on the weight function , the weighted group algebra is strongly Arens irregular in the sense of Dales and Lau; i.e., both topological centres of equal . Also, we show that the topological centre of the algebra equals the weighted measure algebra . Moreover, still in the same situation, we prove that every linear (left) -module map on is automatically bounded, and even --continuous, hence given by convolution with an element in . To this end, we derive a general factorization theorem for bounded families in the -module . Finally, using this result in the case where , we give a short proof of a theorem due to Protasov and Pym, stating that the topological centre of the semigroup is empty, where denotes the -compactification of . This sharpens an earlier result by Lau and Pym; moreover, our method of proof gives a partial answer to a problem raised by Lau and Pym in 1995.
973.
S. V. Astashkin 《Functional Analysis and Its Applications》2005,39(2):131-134
Let (X
0, X
1) be a Banach couple such that X
0 ∩ X
1 is dense in X
0 and X
1. By (X
0, X
1)θ,q
, 0 < θ < 1, 1 ⩽ q < ∞, we denote the spaces of the real interpolation method. Let ψ be a nonzero linear functional defined on some linear space M ⊂ X
0 + X
1 and such that ψ ∈ (X
0 ∩ X
1)*, and let N = Ker ψ. We examine conditions under which the natural formula
is valid. In particular, the results obtained here imply those due to Ivanov and Kalton on the comparison of the interpolation spaces (X
0, X
1)θ,q
and (N
0, X
1)θ,q
, where ψ ∈ X
0
*
and N
0 = Ker ψ. By way of application, we consider a problem, posed by Krugljak, Maligranda, and Persson, on the interpolation of intersections generated by an integral functional defined on weighted L
p
-spaces.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 61–64, 2005Original Russian Text Copyright © by S. V. Astashkin 相似文献
974.
In this paper, we first give a result which links any global Krylov method for solving linear systems with several right-hand
sides to the corresponding classical Krylov method. Then, we propose a general framework for matrix Krylov subspace methods
for linear systems with multiple right-hand sides. Our approach use global projection techniques, it is based on the Global
Generalized Hessenberg Process (GGHP) – which use the Frobenius scalar product and construct a basis of a matrix Krylov subspace
– and on the use of a Galerkin or a minimizing norm condition. To accelerate the convergence of global methods, we will introduce
weighted global methods. In these methods, the GGHP uses a different scalar product at each restart. Experimental results
are presented to show the good performances of the weighted global methods.
AMS subject classification 65F10 相似文献
975.
This paper describes an intriguing use of two relatively new statistical procedures, the bootstrap and non-stationary Markov modelling, to obtain confidence intervals for the design low-flow parameter, of great interest to hydrologists. The procedure described is applied to the stream-flow data gathered over more than 50 years from six gauging sites in Georgia, and is found to yield confidence intervals which are typically shorter than those given by traditional methods. 相似文献
976.
André Adler Andrew Rosalsky Andrej I. Volodin 《Journal of Theoretical Probability》1997,10(3):605-623
For a sequence of constants {a
n,n1}, an array of rowwise independent and stochastically dominated random elements { V
nj, j1, n1} in a real separable Rademacher type p (1p2) Banach space, and a sequence of positive integer-valued random variables {T
n, n1}, a general weak law of large numbers of the form
is established where {c
nj, j1, n1},
n , b
n are suitable sequences. Some related results are also presented. No assumption is made concerning the existence of expected values or absolute moments of the {V
nj, j1, n1}. Illustrative examples include one wherein the strong law of large numbers fails. 相似文献
977.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind
and
where
is a singular Volterra operator,
is continuous and positive on ]a, b],
is a norm in R
n, and [u]+ and [u]– are respectively the positive and the negative part of the vector u R
n. 相似文献
978.
979.
在"求解加权线性最小二乘问题的一类预处理GAOR方法"一文中,作者提出了求解加权线性最小二乘问题等价$2\times 2$块线性系统的一类预处理GAOR方法,并给出了几个比较定理来说明新提出预处理GAOR方法的优越性.本文我们将指出该文中几个比较定理的不完善之处和证明的错误之处,并给出正确的证明. 相似文献
980.
Christian Léger Joseph P. Romano 《Annals of the Institute of Statistical Mathematics》1990,42(4):709-735
Consider the problem of estimating θ=θ(P) based on datax
n
from an unknown distributionP. Given a family of estimatorsT
n, β
of θ(P), the goal is to choose β among β∈I so that the resulting estimator is as good as possible. Typically, β can be regarded as a tuning or smoothing parameter,
and proper choice of β is essential for good performance ofT
n, β
. In this paper, we discuss the theory of β being chosen by the bootstrap. Specifically, the bootstrap estimate of β,
, is chosen to minimize an empirical bootstrap estimate of risk. A general theory is presented to establish the consistency
and weak convergence properties of these estimators. Confidence intervals for θ(P) based on
, are also asymptotically valid. Several applications of the theory are presented, including optimal choice of trimming proportion,
bandwidth selection in density estimation and optimal combinations of estimates. 相似文献