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1.
Michael Sturgeon 《Annals of the Institute of Statistical Mathematics》1996,48(4):675-686
f(x) is a univariate density in C
4 with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, –U, to any smooth unimodal symmetric kernel of order p=2 shifts expected estimator mass from regions where f(x)>0 to regions where f(x)<0. For large n, the mean automatic kernel adaptation induced by –U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of –U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f(x)|. 相似文献
2.
Frank J.S. Wang 《Stochastic Processes and their Applications》1977,5(2):173-193
Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density PA(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence PA(t) would converge to the solution P(t) of our integral equation in the sense that .In this paper, we obtain a “central limit theorem” for the random element √A(PA(t)?P(t)). We prove that under appropriate conditions √A(PA(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.) 相似文献
3.
In this paper, the authors study the integral operator
Sφf(z) = Z
C
φ(z, w)f(w)dλα(w)
induced by a kernel function φ(z, ·) ∈ F
∞α between Fock spaces. For 1 ≤ p ≤ ∞, they
prove that Sφ : F
1
α → F
p
α is bounded if and only if
sup
a∈C
kSφkakp,α < ∞, (?)
where ka is the normalized reproducing kernel of F
2
α; and, Sφ : F
1
α → F
p
α is compact if and
only if
lim
|a|→∞
kSφkakp,α = 0.
When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness
of Sφ : F
q
α → F
p
α .
In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F
2
α, for 1 ≤ q < p < ∞, they
show that Sφ : F
p
α → F
q
α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give
sufficient conditions for the boundedness or compactness of the operator Sφ : F
p
α → F
q
α. 相似文献
4.
5.
Li Jiayu 《偏微分方程(英文版)》1990,3(3)
Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue. 相似文献
6.
TangLin YangDachun 《分析论及其应用》2003,19(1):1-13
Let n≥2. In this paper, the author establishes the L^2 (R^n)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hypergeometric functions and congqucnt hypergeometric funtions. 相似文献
7.
Fuqing Gao 《Journal of Theoretical Probability》2003,16(2):401-418
Let f
n
be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random variables taking values in
d
. It is proved that if the kernel function is an integrable function with bounded variation, and the common density function f of the random variables is continuous and f(x) 0 as |x| , then the moderate deviation principle and large deviation principle for
hold. 相似文献
8.
In this paper, the authors obtain sharp upper and lower hounds for the heat kernel associated with Jacobi transform, and get some analogues of Hardy‘s Theorem for Jacobi transform by using the sharp estimate of the heat kernel. 相似文献
9.
We investigate infinite-dimensional differential inclusions. Sufficient conditions for nonemptiness of the viability kernels of such systems are obtained. 相似文献
10.
林正炎 《数学物理学报(B辑英文版)》2003,23(3)
Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions. 相似文献