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71.
We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex. 相似文献
72.
Jian-pingOu Fu-jiZhang 《应用数学学报(英文版)》2003,19(3):505-510
An m-restricted edge cut is an edge cut that separates a connected graph into a disconnected one with no components having order less than m. m-restrict edge connectivity λm is the cardinality of a minimum m-restricted edge cut. Let G be a connected k-regular graph of order at least 2m that contains m-restricted edge cuts and X be a subgraph of G. Let θ(X) denote the number of edges with one end in X and the other not in X and ξm=min{θ(X) ;X is a connected vertex-induced subgraph of order m}.It is proved in this paper that if G has girth at least m/2 2,then λm≤ξm.The upper bound of λm is sharp. 相似文献
73.
Let G be a graph, $ \{a, b, c\}\subseteq V(G) $, and
$ \{a', b', c'\}\subseteq V(G) $ such that $ \{a, b, c\}\neq \{a', b', c'\} $. We say that
$ (G, \{a, c\}, \{a', c'\}, (b, b')) $ is an obstruction if, for
any three vertex disjoint paths from {a, b, c} to
{a', b', c'} in G, one path is
from b to b'. In this paper
we characterize obstructions. As a consequence, we show that no obstruction can be 8-connected,
unless b = b' or {a, c} = {a', c'}.AMS Subject Classification: 05C38. 相似文献
74.
In this paper the question of what classes A of T
0-spaces should be paired with classes of domains in order that all function spaces [AB] for AA and B are -compact domains is considered. It is shown that core compact spaces are paired with bounded complete domains and a class of topological spaces called RW-spaces (with finitely many components) is paired with the class of -compact pointed L-domains (L-domains). 相似文献
75.
Gancho Tachev 《Journal of Computational Analysis and Applications》2001,3(4):361-381
A direct theorem for approximation by algebraic polynomials in two variables with different degrees in each variable in Lp-metric (1 p ) on rectangles is proved, and the dependence of the constants on various parameters is studied. 相似文献
76.
James H. Schmerl 《Transactions of the American Mathematical Society》2000,352(6):2479-2489
Fix an integer and consider real -dimensional . A partition of avoids the polynomial , where each is an -tuple of variables, if there is no set of the partition which contains distinct such that . The polynomial is avoidable if some countable partition avoids it. The avoidable polynomials are studied here. The polynomial is an especially interesting example of an avoidable one. We find (1) a countable partition which avoids every avoidable polynomial over , and (2) a characterization of the avoidable polynomials. An important feature is that both the ``master' partition in (1) and the characterization in (2) depend on the cardinality of .
77.
P. G. Walsh. 《Mathematics of Computation》2000,69(231):1183-1191
The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in , the ring of polynomials with coefficients from the field of Laurent series in with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complexity bound for the number of bit operations required to perform this irreducibility test is computed.
78.
F. Michelot M. Rey 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,44(3):467-495
Effective vibronic Hamiltonian models are built for E ⊗e Jahn-Teller systems and analytical solutions are
obtained through Lie algebraic methods. Although approximate, we show that these models allow in particular to recover the
possible ground state crossover when quadratic couplings are present. The equivalence of E ⊗e and G' ⊗e
vibronic systems in cubic symmetry is precisely established through a particular realization of the electronic operators for
an
orbital quadruplet. We show how this equivalence is broken by a rovibronic interaction which, for a G' ⊗e system, still
gives an exactly solvable model. 相似文献
79.
P. F. Landrum S. W. Fisher H. Hwang J. Hickey 《SAR and QSAR in environmental research》2013,24(5):423-450
Abstract Toxicities of ten organophosphorus (OP) insecticides were measured against midge larvae (Chironomus riparius) under varying temperature (11, 18, and 25°C) and pH (6, 7, and 8) conditions and with and without sediment. Toxicity usually increased with increasing temperature and was greater in the absence of sediment. No trend was found with varying pH. A series of unidimensional parameters and multidimensional models were used to describe the changes in toxicity. Log K ow was able to explain about 40–60% of the variability in response data for aqueous exposures while molecular volume and aqueous solubility were less predictive. Likewise, the linear solvation energy relationship (LSER) model only explained 40–70% of the response variability, suggesting that factors other than solubility were most important for producing the observed response. Molecular connectivity was the most useful for describing the variability in the response. In the absence of sediment, 1χ v and 3κ were best able to describe the variation in response among all compounds at each pH (70–90%). In the presence of sediment, even molecular connectivity could not describe the variability until the partitioning potential to sediment was accounted for by assuming equilibrium partitioning. After correcting for partitioning, the same molecular connectivity terms as in the aqueous exposures described most of the variability, 61–87%, except for the 11°C data where correlations were not significant. Molecular connectivity was a better tool than LSER or the unidimensional variables to explain the steric fitness of OP insecticides which was crucial to the toxicity. 相似文献
80.
Eon-Kyung Lee 《代数通讯》2013,41(3):1121-1139
In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups. 相似文献