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101.
An ordinary subgroup of a group G is (1) a subset of G, (2) closed under the group operation. In a fuzzy subgroup it is precisely these two notions that lose their deterministic character. A fuzzy subgroup μ of a group (G,·) associates with each group element a number, the larger the number the more certainly that element belongs to the fuzzy subgroup. The closure property is captured by the inequality μ(x · y)?T(μ(x), μ(y)). In A. Rosenfeld's original definition, T was the function ‘minimum’. However, any t-norm T provides a meaningful generalization of the closure property. Two classes of fuzzy subgroups are investigated. The fuzzy subgroups in one class are subgroup generated, those in the other are function generated. Each fuzzy subgroup in these classes satisfies the above inequality with T given by T(a, b) = max(a + b ?1, 0). While the two classes look different, each fuzzy subgroup in either is isomorphic to one in the other. It is shown that a fuzzy subgroup satisfies the above inequality with if and only if it is subgroup generated of a very special type. Finally, these notions are applied to some abstract pattern recognition problems. 相似文献
102.
设$\mathcal{F}$是一个群类. 群$G$的子群$H$称为在$G$中$\mathcal{F}$-S-可补的,如果存在$G$的一个子群$K$,使得$G=HK$且$K/K\cap{H_G}\in\mathcal{F}$, 其中$H_G=\bigcap_{g\in G}H^g$是包含在$H$中的$G$的最大正规子群.本文利用子群的$\mathcal{F}$-S-可补性, 给出了有限群的可解性, 超可解性和幂零性的一些新的刻画. 应用这些结果, 我们可以得到一系列推论, 其中包括有关已知的著名结果. 相似文献
103.
Gerhard RÖhrle 《Geometriae Dedicata》1997,66(1):51-64
The principal aim of this paper is to show that every maximal parabolic subgroup P of a classical reductive algebraic group G operates with a finite number of orbits on its unipotent radical. This is a consequence of the fact that each parabolic subgroup of a group of type A
n
whose unipotent radical is of nilpotent class at most two has this finiteness property. 相似文献
104.
An anti-torus is a subgroup 〈a,b 〉 in the fundamental group of a compact non-positively curved space X, acting in a specific way on the universal covering space X such that a and b do not have any commuting nontrivial powers. We construct and investigate anti-tori in a class of commutative transitive fundamental groups of finite square complexes, in particular for the groups Γp,l originally studied by Mozes [Israel J. Math. 90(1–3) (1995), 253–294]. It turns out that anti-tori in Γp,l directly correspond to non commuting pairs of Hamilton quaternions. Moreover, free anti-tori in Γp,l are related to free groups generated by two integer quaternions, and also to free subgroups of
. As an application, we prove that the multiplicative group generated by the two quaternions 1+2i and 1+4k is not free. 相似文献
105.
P. Milnes 《Acta Mathematica Hungarica》2005,109(3):191-213
Summary For real connected nilpotent groups, 7 is the lowest dimension where there are infinitely many non-isomorphic groups, and
also where some groups (indeed, uncountably many) have no discrete cocompact subgroups. In [21] one infinite family <InlineEquation
ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\mathcal{G}$
of 7-dimensional groups was identified and classified. Discrete cocompact subgroups H were identified for some groups in $\mathcal{G}$
in [10], along with simple quotients of $C^{*}(\mathrm{H})$ and relevant flows $(\mathrm{H}_3,\mathbf{T}^3)$. In this paper,
such H and attributes are determined for more groups in $\mathcal{G}$; in particular, the members of $\mathcal{G}$ that admit
discrete cocompact subgroups are identified precisely. In achieving some of these results, we consider other known ways of
classifying the groups in $\mathcal{G}$, and also the classification of the analogous family of complex groups. 相似文献
106.
Nihal YILMAZ OZGUR 《数学学报(英文版)》2006,22(2):383-392
Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H(√q),q 〉 5 prime number. 相似文献
107.
In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated. 相似文献
108.
Fausto De Mari 《代数通讯》2018,46(4):1709-1715
In this paper (generalized) soluble groups for which the set of all non-modular subgroups satisfies some weak chain condition are described. Groups satisfying weak chain conditions on non-permutable subgroups are also considered. 相似文献
109.
110.
ZHANG JunQiang & LI XianHua School of Mathematical Sciences Soochow University Suzhou China 《中国科学 数学(英文版)》2010,(5)
Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich. 相似文献