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71.
Matthias Neufang 《Proceedings of the American Mathematical Society》2008,136(5):1831-1839
Let be a locally compact, non-compact group (we make the non-compactness assumption, for the most part, simply to avoid trivialities). We show that under a very mild assumption on the weight function , the weighted group algebra is strongly Arens irregular in the sense of Dales and Lau; i.e., both topological centres of equal . Also, we show that the topological centre of the algebra equals the weighted measure algebra . Moreover, still in the same situation, we prove that every linear (left) -module map on is automatically bounded, and even --continuous, hence given by convolution with an element in . To this end, we derive a general factorization theorem for bounded families in the -module . Finally, using this result in the case where , we give a short proof of a theorem due to Protasov and Pym, stating that the topological centre of the semigroup is empty, where denotes the -compactification of . This sharpens an earlier result by Lau and Pym; moreover, our method of proof gives a partial answer to a problem raised by Lau and Pym in 1995.
72.
I. Naidoo 《Acta Mathematica Hungarica》2008,118(4):357-367
We introduce and study the concepts of connectedness and local connectedness in σ-frames. We also consider the local connectedness of the Stone-Čech compactification of a regular σ-frame.
相似文献
73.
This is a collection of open problems which touch on Neil Hindman's mathematics and were collected in conjunction with the Conference on Ramsey Theory and Topological Algebra in his honor. 相似文献
74.
75.
76.
For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 相似文献
77.
Jan J. Dijkstra 《Proceedings of the American Mathematical Society》2008,136(12):4461-4466
We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon.
78.
Scott A. Starks Olga Kosheleva Vladik Kreinovich 《International Journal of Theoretical Physics》2006,45(3):576-588
After the 1916 success of general relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂ g
ij
/∂ x
5 = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approach is that while the model itself is geometric, conditions like cylindricity are not geometric. This problem was partly solved by Einstein and Bergman who proposed, in their 1938 paper, that the 5th dimension is compactified into a small circle S
1 so that in the resulting cylindric 5D space-time R
4× S
1 the dependence on x
5 is not macroscopically noticeable. We show that if, in all definitions of vectors, tensors, etc., we replace R
4 with R
4× S
1, then conditions like cylindricity automatically follow – i.e., these conditions become fully geometric.
PACS: 11.10.Kk Field theories in dimensions other than four, 04.50.+h Gravity in more than four dimensions. 相似文献
79.
We define the gamma-compactification of an arbitrary measurable space and study its structure and properties in the general and topological cases. We introduce and study the notion of gamma-extension of a singleton in a topological space. We consider the procedure of extension of finitely additive measures from the original space to regular countably additive measures on the gamma-compactification of the space. 相似文献
80.
Mahmoud Filali 《Journal of Functional Analysis》2007,250(1):144-166
The paper proposes a unified approach to many key theorems proved in the last twenty years in different areas of abstract harmonic analysis. This approach is based on the so-called slowly oscillating functions which were introduced in coarse geometry. In addition to this method being the most natural and simple, it also leads to the generalisation of some of the results and to the achievement of some new results. Several of these results concern the topological centres of convolution algebras and semigroup compactifications. 相似文献