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21.
YAU Stephen S T 《中国科学A辑(英文版)》2006,(11)
Let V be a hypersurface with an isolated singularity at the origin in Cn 1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero. 相似文献
22.
Tomohiro Okuma 《Compositio Mathematica》1998,110(3):263-276
This paper studies the second pluri-genus of surface singularities. We give a formula for this invariant of a Gorenstein singularity, and several inequalities relating the invariant with the Milnor number, Tjurina number and the modality of a hypersurface singularity. 相似文献
23.
We introduce a generalized dot product and provide some embedding conditions under which the genus of a graph does not rise
under a dot product with the Petersen graph. Using these conditions, we disprove a conjecture of Tinsley and Watkins on the
genus of dot products of the Petersen graph and show that both Grünbaum’s Conjecture and the Berge-Fulkerson Conjecture hold
for certain infinite families of snarks. Additionally, we determine the orientable genus of four known snarks and two known
snark families, construct a new example of an infinite family of snarks on the torus, and construct ten new examples of infinite
families of snarks on the 2-holed torus; these last constructions allow us to show that there are genus-2 snarks of every
even order n ≥ 18. 相似文献
24.
The word theorem states that x can be denoted as a rotation inserting word of A if x is in the normal closure of A in F(X). As an application of the theorem, in this note a condition that guarantees reducing the genus of Heegaard splitting of 3-manifolds is given. This leads Poincare conjecture to a new formulation. 相似文献
25.
Aromatic components are important functional products during the wine fermentation process. In the current study, nine strains (Y10, Y5, Y21, Y2, Y19, Y16, Y3, Y13 and Y4) of non-Saccharomyces were isolated from Cabernet Sauvignon grape wine. Aromatic components from Cabernet sauvignon-fermented wine were determined the phylogenetic evolution status of different non-Saccharomyces based on 26S rDNA and D1/D2 sequence analysis and analysed by a gas chromatography–mass spectrometry analysis, and they were grouped into one category with four different yeast genus which were Meyerozyma guilliermondii, Brettanomyces naardenensis, Pichia guilliermondi and Candida fermentati. A total of 102 kinds of aroma components were detected, including 39 kinds of esters, 31 kinds of alcohols, 8 kinds of ketones, 10 kinds of alkanes, 15 kinds of acids and 4 kinds of other aroma substances. 相似文献
26.
Peter Šepitka 《Journal of Difference Equations and Applications》2017,23(4):657-698
In this paper we introduce the theory of dominant solutions at infinity for nonoscillatory discrete symplectic systems without any controllability assumption. Such solutions represent an opposite concept to recessive solutions at infinity, which were recently developed for such systems by the authors. Our main results include: (i) the existence of dominant solutions at infinity for all ranks in a given range depending on the order of abnormality of the system, (ii) construction of dominant solutions at infinity with eventually the same image, (iii) classification of dominant and recessive solutions at infinity with eventually the same image, (iv) limit characterization of recessive solutions at infinity in terms of dominant solutions at infinity and vice versa, and (v) Reid’s construction of the minimal recessive solution at infinity. These results are based on a new theory of genera of conjoined bases for symplectic systems developed for this purpose in this paper. 相似文献
27.
Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M0 in containing M such that . 相似文献
28.
Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1?K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1?K2)=t(K1)+t(K2)+1. 相似文献
29.
Two cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
相似文献
30.
In this paper, we show the following result: Let K
i
be a knot in a closed orientable 3-manifold M
i
such that (M
i
,K
i
) is not homeomorphic to (S
2 ×S
1, x
0 ×S
1), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K
i
) is less than the difference of one and twice of the tunnel number of K
i
. Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard
splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive. 相似文献
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