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961.
962.
Milan Randić 《Theoretical chemistry accounts》1985,67(2):137-155
Isomerization mode defines the process of interconversion of one isomer into another. Several mechanisms are conceivable for degenerate rearrangements and, in general, lead to a distinctive network of relations between participating isomers. Here we consider selected modes which are complementary in the sense that if mode 1 transforms an isomer A into B, C, D etc., then mode 2 transforms the same isomer A into X, Y, Z, etc., which includes all isomers not comprised by the first mode. Physico-chemical complementarity can be translated into mathematical complementarity of associated chemical graphs. This allows us to use the tool of Graph Theory. One example of graph theoretical use is the theorem that graph G and its complement G have the same automorphism group (i.e., the same symmetry). We have shown that a close examination of a graph and its complement and their components allows us to recognize the automorphism group in some complex cases without resorting to canonical numbering or other involved procedures, and even allows us to determine isomorphism of different processes.Dedicated to Professor Kurt Mislow of Princeton UniversityOperated for the U.S. Department of Energy by Iowa State University under contract W-7405-Eng-82. Supported in part by the Office of the Director. 相似文献
963.
Gilles Caporossi Ivan Gutman Pierre Hansen Ljiljana Pavlovi 《Computational Biology and Chemistry》2003,27(1):85-90
Let G be a graph and dv the degree (=number of first neighbors) of its vertex v. The connectivity index of G is χ=∑ (dudv)−1/2, with the summation ranging over all pairs of adjacent vertices of G. In a previous paper (Comput. Chem. 23 (1999) 469), by applying a heuristic combinatorial optimization algorithm, the structure of chemical trees possessing extremal (maximum and minimum) values of χ was determined. It was demonstrated that the path Pn is the n-vertex tree with maximum χ-value. We now offer an alternative approach to finding (molecular) graphs with maximum χ, from which the extremality of Pn follows as a special case. By eliminating a flaw in the earlier proof, we demonstrate that there exist cases when χ does not provide a correct measure of branching: we find pairs of trees T, T′, such that T is more branched than T′, but χ(T)>χ(T′). The smallest such examples are trees with 36 vertices in which one vertex has degree 31. 相似文献
964.
A simple pictorial algorithm for factorisation of symmetric chemical graphs (weighted and unweighted) leading to simultaneous
determination of their eigenvalues and eigenvectors has been devised. The method does not require group-theoretical techniques
(viz. identification of the point group of the species under study, formation of symmetryadopted linear combinations using
character tables etc.). It requires consideration of only one symmetry element, e.g., a reflection plane and is based on elementary
row and column operations which keep the secular determinant of the adjacency matrix unchanged (except possibly for a multiplicative
constant). 相似文献
965.
Although there is an extensive literature on the linearization instability of the nonlinear system of partial differential
equations that governs an elastic material, there are very few results that prove that a second branch of solutions actually
bifurcates from a known solution branch when the known branch becomes unstable. In this paper the implicit function theorem
in a Banach space setting is used to prove that the quasistatic compression of a rectangular elastic rod between rigid frictionless
plates leads to the buckling of the rod as is observed in experiment and as first predicted by Euler.
This work was supported in part by the National Science Foundation under Grant No. DMS–8810653 and DMS–0405646. 相似文献
966.
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation 总被引:5,自引:0,他引:5
The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM, special functions are added to the finite element approximation using the framework of partition of unity. For crack modeling in isotropic linear elasticity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are used to account for the crack. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence quasi-static crack propagation simulations can be carried out without remeshing. In this paper, we discuss some of the key issues in the X-FEM and describe its implementation within a general-purpose finite element code. The finite element program Dynaflow™ is considered in this study and the implementation for modeling 2-d cracks in isotropic and bimaterial media is described. In particular, the array-allocation for enriched degrees of freedom, use of geometric-based queries for carrying out nodal enrichment and mesh partitioning, and the assembly procedure for the discrete equations are presented. We place particular emphasis on the design of a computer code to enable the modeling of discontinuous phenomena within a finite element framework. 相似文献
967.
968.
This paper deals with representations of groups by \"affine\" automorphisms of compact,convex spaces,with special focus on \"irreducible\" representations:equivalently \"minimal\" actions.When the group in question is PSL(2,R),the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations.This analysis shows that,surprisingly,all these representations are equivalent.In fact,it is found that all irreducible affine representations of this group are equivalent.The key to this is a property called \"linear Stone-Weierstrass\"for group actions on compact spaces.If it holds for the \"universal strongly proximal space\"of the group (to be defined),then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group. 相似文献
969.
三维荧光光谱结合PCA-SVM对几种浓香型白酒的鉴别 总被引:1,自引:0,他引:1
提出一种利用三维荧光光谱技术鉴别不同品牌浓香型白酒的方法。运用FLS920荧光光谱仪测量了七个不同品牌浓香型白酒的三维荧光光谱,不同品牌浓香型白酒的荧光光谱特征相似,仅凭荧光特征参数较难区分。采用求偏导和小波压缩相结合的数据预处理方法,求解光谱数据中每一激发波长下,荧光强度对发射波长的一阶和二阶偏导数,选取db7紧支撑正交小波对数据进行压缩,选择4尺度分解后的近似系数作为新的数据矩阵,然后做主成分分析(PCA)。将提取的主成分作为支持向量机(SVM)的输入,并利用K-fold交叉验证的方法寻找支持向量机的最优参数c和γ,建立不同品牌白酒的分类鉴别模型。从每个品牌白酒中随机选取14个样本,共98个样本组成训练集,其余的42个样本组成预测集。分别比较了数据不求偏导,对数据求一阶偏导和二阶偏导的预处理后对鉴别模型的影响。结果表明:三维荧光光谱经过二阶偏导的预处理后,结合主成分分析和支持向量机能很好地实现不同品牌浓香型白酒的分类鉴别,模型的准确率为98.98%,预测集的准确率为100%。该方法具有简单,快速,成本低的优点,可为中国白酒的检测和鉴别技术的发展提供帮助。 相似文献
970.
传统通信系统在强干扰环境下进行通信时,系统会出现性能下降甚至无法通信的问题。设计并实现了一种新的网络情报数据滤波通信系统,设计强干扰环境下网络情报数据滤波通信系统的整体结构;按照网络情报数据滤波通信系统的标准以及分析强干扰的特性,对瞬态电压抑制模块、瞬态保护模块、语音信号输入模块进行设计,采用电磁滤波去噪的方法对故障修复模块进行优化,实现网络情报数据滤波通信系统的设计。实验表明,改进的网络情报数据滤波通信系统较传统的通信系统具有较强的抗干扰能力,通信效果好等明显优势。 相似文献