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In this paper we consider proving to be the activity in search for a proof, whereby proof is the final product of this activity that meets certain criteria. Although there has been considerable research attention on the functions of proof (e.g., explanation), there has been less explicit attention in the literature on those same functions arising in the proving process. Our aim is to identify conditions for proving by mathematical induction to be explanatory for the prover. To identify such conditions, we analyze videos of undergraduate mathematics students working on specially designed problems. Specifically, we examine the role played by: the problem formulation, students’ experience with the utility of examples in proving, and students’ ability to recognize and apply mathematical induction as an appropriate method in their explorations. We conclude that particular combinations of these aspects make it more likely that proving by induction will be explanatory for the prover. 相似文献
154.
姜翠美 《数学的实践与认识》2016,(6):1-5
绿色大学评价是一个多指标,多属性且具有模糊性的评价过程,由模糊层次分析法确立了评价指标权重,建立了绿色大学的模糊综合评价模型.利用提出的评价模型对高等院校进行评价能够更客观,更科学地反映绿色大学的创建情况. 相似文献
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Ikehara K 《Chemical record (New York, N.Y.)》2005,5(2):107-118
Based on the fact that RNA has not only a genetic function but also a catalytic function, the RNA world theory on the origin of life was first proposed about 20 years ago. The theory assumes that RNA was amplified by self-replication to increase RNA diversity on the primitive earth. Since then, the theory has been widely accepted as the most likely explanation for the emergence of life. In contrast, we reached another hypothesis, the [GADV]-protein world hypothesis, which is based on pseudo-replication of [GADV]-proteins. We reached this hypothesis during studies on the origins of genes and the genetic code, where [G], [A], [D], and [V] refer to Gly, Ala, Asp, and Val, respectively. In this review, possible steps to the emergence of life are discussed from the standpoint of the [GADV]-protein world hypothesis, comparing it in parallel with the RNA world theory. It is also shown that [GADV]-peptides, which were produced by repeated dry-heating cycles and by solid phase peptide synthesis, have catalytic activities, hydrolyzing peptide bonds in a natural protein, bovine serum albumin. These experimental results support the [GADV]-protein world hypothesis for the origin of life. 相似文献
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** Email: aas96106{at}maths.strath.ac.uk Grindrod (2002. Phys. Rev. E, 66, 06670210667027) posedthe problem of reordering a range-dependent random graph andshowed that it is relevant to the analysis of data sets frombioinformatics. Reordering under a random graph hypothesis canbe regarded as an extension of clustering and fits into thegeneral area of data mining. Here, we consider a generalizationof Grindrod's model and show how an existing spectral reorderingalgorithm that has arisen in a number of areas may be interpretedfrom a maximum likelihood range-dependent random graph viewpoint.Looked at this way, the spectral algorithm, which uses eigenvectorinformation from the graph Laplacian, is found to be automaticallytuned to an exponential edge density. The connection is precisefor optimal reorderings, but is weaker when approximate reorderingsare computed via relaxation. We illustrate the performance ofthe spectral algorithm in the weighted random graph contextand give experimental evidence that it can be successful forother edge densities. We conclude by applying the algorithmto a data set from the biological literature that describescortical connectivity in the cat brain. 相似文献
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ZHAOXiao-Wei ZHOULi-Ming CHENTian-Lun 《理论物理通讯》2004,42(2):242-246
In this paper, we introduce a new modified evolution model on a small world network. In our model,the spatial and temporal correlations and the spatial-temporal evolve pattern of mutating nodes exhibit some particular behaviors different from those of the original BS evolution model. More importantly, these behaviors will change with φ, the density of short paths in our network. 相似文献
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CAI Rong-Gen ZHANG Hong-Sheng WANG An-Zhong 《理论物理通讯》2005,44(5):948-954
Recent type Ia supernovas data seemingly favor a dark energy model whose equation of state w(z) crosses -1 very recently, which is a much more amazing problem than the acceleration of the universe. In this paper we show that it is possible to realize such a crossing without introducing any phantom component in a Gauss-Bonnet brane worm with induced gravity, where a four-dimensional curvature scalar on the brahe and a five-dimensional Gauss-Bonnet term in the bu/k are present. In this realization, the Gauss-Bonnet term and the mass parameter in the bulk play a crucial role. 相似文献