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71.
G-protein coupled receptors (GPCRs) play a key role in different biological processes, such as regulation of growth, death and metabolism of cells. They are major therapeutic targets of numerous prescribed drugs. However, the ligand specificity of many receptors is unknown and there is little structural information available. Bioinformatics may offer one approach to bridge the gap between sequence data and functional knowledge of a receptor. In this paper, we use a bagging classification tree algorithm to predict the type of the receptor based on its amino acid composition. The prediction is performed for GPCR at the sub-family and sub-sub-family level. In a cross-validation test, we achieved an overall predictive accuracy of 91.1% for GPCR sub-family classification, and 82.4% for sub-sub-family classification. These results demonstrate the applicability of this relative simple method and its potential for improving prediction accuracy. 相似文献
72.
Farruh M Mukhamedov 《Indagationes Mathematicae》2004,15(1):85-99
We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ? p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ? p and p ≥ 3 (resp. q ? 22, p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ? p if p ≥ 3 and q ? 22 if p = 2. 相似文献
73.
Alexander Postnikov Boris Shapiro 《Transactions of the American Mathematical Society》2004,356(8):3109-3142
For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.
74.
In 1990, Gutman and Mizoguchi conjectured that all roots of the -polynomial (G,C,x) of a graph G are real. Since then, there has been some literature intending to solve this conjecture. However, in all existing literature, only classes of graphs were found to show that the conjecture is true; for example, monocyclic graphs, bicyclic graphs, graphs such that no two circuits share a common edge, graphs without 3-matchings, etc, supporting the conjecture in some sense. Yet, no complete solution has been given. In this paper, we show that the conjecture is true for all graphs, and therefore completely solve this conjecture. 相似文献
75.
V. I. Arnold 《Functional Analysis and Its Applications》2003,37(3):177-190
We study the graph each of whose edges connects an element of a given ring with the square of itself. For a finite commutative group (e.g., for the multiplicative group of coprime residue classes modulo a positive integer), we describe this graph explicitly: each of its connected components is an oriented attracting cycle equipped with identical
-vertex rooted trees of special form whose roots reside on the cycle. We also compute the graphs of permutation groups on not too many elements and of the subgroups of even permutations; the connected components of these graphs are also uniformly equipped cycles. 相似文献
76.
Let T be a homogeneous tree of homogeneity q+1. Let denote the boundary of T, consisting of all infinite geodesics b=[b
0,b
1,b
2,] beginning at the root, 0. For each b, 1, and a0 we define the approach region ,a
(b) to be the set of all vertices t such that, for some j, t is a descendant of b
j
and the geodesic distance of t to b
j
is at most (–1)j+a. If >1, we view these as tangential approach regions to b with degree of tangency . We consider potentials Gf on T for which the Riesz mass f satisfies the growth condition
T
f
p
(t)q
–|t|<, where p>1 and 0<<1, or p=1 and 0<1. For 11/, we show that Gf(s) has limit zero as s approaches a boundary point b within ,a
(b) except for a subset E of of -dimensional Hausdorff measure 0, where H
(E)=sup>0inf
i
q
–|t
i|:E a subset of the boundary points passing through t
i
for some i,|t
i
|>log
q
(1/). 相似文献
77.
Rein van der Hout 《Journal of Differential Equations》2003,192(1):188-201
Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time. 相似文献
78.
In this note, we consider a finite set X and maps
W from the set $ \mathcal{S}_{2|2} (X) $ of all 2, 2-
splits of X into $ \mathbb{R}_{\geq 0} $. We show that such a map
W is induced, in a canonical way, by a binary
X-tree for which a positive length $ \mathcal{l} (e) $ is
associated to every inner edge e if and only if (i) exactly
two of the three numbers W(ab|cd),W(ac|bd), and
W(ad|cb) vanish, for any four distinct elements
a, b, c, d in X,
(ii) $ a \neq d \quad\mathrm{and}\quad W (ab|xc) + W(ax|cd) = W(ab|cd) $ holds for all
a, b, c, d, x
in X with
#{a, b, c, x} = #{b, c, d, x} = 4
and $ W(ab|cx),W(ax|cd) $ > 0, and (iii) $ W (ab|uv) \geq \quad \mathrm{min} (W(ab|uw), W(ab|vw)) $
holds for any five distinct elements a, b, u, v, w in
X. Possible generalizations
regarding arbitrary $ \mathbb{R} $-trees and applications regarding tree-reconstruction algorithms
are indicated.AMS Subject Classification: 05C05, 92D15, 92B05. 相似文献
79.
Let T
n
be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1
n
as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T
n
as follows A(n;T)=|{S
T
n
: 1
n
∈S, S≅T}|, and B(n;T)=|{S
T
n
:1
n
∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim
n→∞[A(n;T)/B(n;T)]=2ℓ;−1−1, for any tree T with ℓ leaves.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
80.
Yuan-Qing Qiao Franklin D. Tall 《Proceedings of the American Mathematical Society》2003,131(12):3929-3936
In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", i.e., linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.