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91.
The classical functional delta method (FDM) provides a convenient tool for deriving the asymptotic distribution of statistical functionals from the weak convergence of the respective empirical processes. However, for many interesting functionals depending on the tails of the underlying distribution this FDM cannot be applied since the method typically relies on Hadamard differentiability w.r.t. the uniform sup-norm. In this article, we present a version of the FDM which is suitable also for nonuniform sup-norms, with the outcome that the range of application of the FDM enlarges essentially. On one hand, our FDM, which we shall call the modified FDM, works for functionals that are “differentiable” in a weaker sense than Hadamard differentiability. On the other hand, it requires weak convergence of the empirical process w.r.t. a nonuniform sup-norm. The latter is not problematic since there exist strong respective results on weighted empirical processes obtained by Shorack and Wellner (1986) [25], Shao and Yu (1996) [23], Wu (2008) [32], and others. We illustrate the gain of the modified FDM by deriving the asymptotic distribution of plug-in estimates of popular risk measures that cannot be treated with the classical FDM. 相似文献
92.
Jean-Paul Bezivin 《Aequationes Mathematicae》1988,36(1):112-124
Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta
i
,b
i
,(i = 1, , s), 2s nombres complexes, lesa
i
étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg
i
(x) = a
i
x + b
i
. On a alors le résultat suivant:
Théorème 1.Soient f, R
1, ,R
s
s + 1 fractions rationnelles de (x), régulières à l'origine, et ai, bi (i = 1,, s), 2s éléments de . On suppose que les ai sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle
相似文献
93.
94.
Karim Nour 《Mathematical Logic Quarterly》2002,48(3):357-366
In this paper, we present an extension of λμ‐calculus called λμ++‐calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel‐or. 相似文献
95.
Fumiyasu Komaki 《Journal of multivariate analysis》2009,100(10):2137-2154
Bayesian predictive densities for the 2-dimensional Wishart model are investigated. The performance of predictive densities is evaluated by using the Kullback–Leibler divergence. It is proved that a Bayesian predictive density based on a prior exactly dominates that based on the Jeffreys prior if the prior density satisfies some geometric conditions. An orthogonally invariant prior is introduced and it is shown that the Bayesian predictive density based on the prior is minimax and dominates that based on the right invariant prior with respect to the triangular group. 相似文献
96.
Nadine Hilgert J. Adolfo Minjárez-Sosa 《Mathematical Methods of Operations Research》2001,54(3):491-505
We consider a class of time-varying stochastic control systems, with Borel state and action spaces, and possibly unbounded
costs. The processes evolve according to a discrete-time equation x
n + 1=G
n (x
n , a
n , ξn), n=0, 1, … , where the ξn are i.i.d. ℜk-valued random vectors whose common density is unknown, and the G
n are given functions converging, in a restricted way, to some function G
∞ as n→∞. Assuming observability of ξn, we construct an adaptive policy which is asymptotically discounted cost optimal for the limiting control system
x
n+1=G
∞ (x
n , a
n , ξn). 相似文献
97.
In order to study copula families that have tail patterns and tail asymmetry different from multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Archimedean copula, we relate the tail heaviness of a positive random variable to the tail behavior of the Archimedean copula constructed from the Laplace transform of the random variable, and extend the results of Charpentier and Segers [7] [A. Charpentier, J. Segers, Tails of multivariate Archimedean copulas, Journal of Multivariate Analysis 100 (7) (2009) 1521–1537] for upper tails of Archimedean copulas. In addition, a new one-parameter Archimedean copula family based on the Laplace transform of the inverse Gamma distribution is proposed; it possesses patterns of upper and lower tails not seen in commonly used copula families. Finally, tail orders are studied for copulas constructed from mixtures of max-infinitely divisible copulas. 相似文献
98.
In this article, we propose a two‐level finite element method to analyze the approximate solutions of the stationary Navier‐Stokes equations based on a stabilized local projection. The local projection allows to circumvent the Babuska‐Brezzi condition by using equal‐order finite element pairs. The local projection can be used to stabilize high equal‐order finite element pairs. The proposed method combines the local projection stabilization method and the two‐level method under the assumption of the uniqueness condition. The two‐level method consists of solving a nonlinear equation on the coarse mesh and solving a linear equation on fine mesh. The nonlinear equation is solved by the one‐step Newtonian iteration method. In the rest of this article, we show the error analysis of the lowest equal‐order finite element pair and provide convergence rate of approximate solutions. Furthermore, the numerical illustrations coincide with the theoretical analysis expectations. From the view of computational time, the results show that the two‐level method is effective to solve the stationary Navier‐Stokes equations. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
99.
Recently, linear programming problems with special structures have assumed growing importance in mathematical programming.
It is well known that exploiting network structures within linear programs can lead to considerable improvement of the computational
solution of large-scale linear programming problems. A linear program is said to contain an embedded network structure provided
that some subset of its constraints can be interpreted as specifying conservation of flow. If a column of the constraint matrix
has at most two non-zeros, then it leads to embedded generalized network structure and if these non-zeros are unit elements
and of opposite signs, then it leads to embedded pure network structure.
In this paper, we are concerned with algorithms for detecting embedded pure network structures within linear programs. The
network extraction methods are presented in two groups. The first group covers deletion and addition based algorithms and
the second group covers GUB based algorithms. We have extended the GUB based algorithm appearing in the second group by introducing
Markowitz merit count approach for exploiting matrix non zeros. A set of well known test problems has been used to carry out
computational experiments which show that our extensions to the GUB based algorithms give better results than the algorithms
reported earlier. 相似文献
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