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41.
Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature.
In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives
for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested
consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition
graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives
with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the
orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for
the prismane (D
3h
) and adamantane (T
d
) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the
D
3h
group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T
d
point symmetry group.
This work is based on the text of the lecture presented by the authors at the 5th All-Russia Conference on Molecular Modeling
(Moscow, April 2007). The paper deals with the methodology and detailed treatment of applied aspects related to solution of
enumeration problems for substituted derivatives with prescribed symmetry groups. Unlike the known methods of symmetry specified
enumeration, the technique suggested is simple enough and may be regarded as generalization of the Pólya methodology, which
is widely used by chemists.
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–245, February, 2008. 相似文献
42.
Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%... 相似文献
43.
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L
V
the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ
v
associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering
groups are Sunada pairs. 相似文献
44.
A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
45.
M. I. Dykman D. G. Luchinsky R. Mannella P. V. E. McClintock N. D. Stein N. G. Stocks 《Il Nuovo Cimento D》1995,17(7-8):661-683
Summary We outline the historical development of stochastic resonance (SR), a phenomenon in which the signal and/or the signal-to-noise
ratio in a nonlinear system increase with increasing intensity of noise. We discuss basic theoretical ideas explaining and
describing SR, and we review some revealing experimental data that place SR within the wider context of statistical physics.
We emphasize the close relationship of SR to some effects that are well known in condensed-matter physics.
Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing
and Related Phenomena?, Elba, 5–10 June 1994. 相似文献
46.
47.
A laser micro-chopper has been designed to respond fast to a molecular beam. A method of spectral structure measurement is established to analyse the responding signals. In experiments, the minimum detectable signals correspond to an air molecular-beam intensity of 5 × 108/s 相似文献
48.
The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint
operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class.
The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose
imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the
trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding
the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications
of the spectral shift function have been discussed. 相似文献
49.
Ummadisetty Subramanyam Swaminathan Sivaram 《Journal of polymer science. Part A, Polymer chemistry》2007,45(2):191-210
Homopolymerization of octadecene‐1 at different reaction conditions has been studied. Significant chain running can be seen at higher polymerization temperatures. Interestingly, insertion of octadecene‐1 into a sterically hindered nickel‐cation/carbon (secondary) bond is observed. The microstructure of the polymer was established using NMR spectroscopy. The effects of chain running on polymer melting, crystallization behavior, and dynamic mechanical thermal properties were studied using DSC and DMTA. The extent of chain running (i.e., 2,ω‐, 1,ω‐enchainments) decreases with an increase in the carbon number of α‐olefins. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 191–210, 2007 相似文献
50.
John A. Mikroyannidis Larysa Fenenko Masayuki Yahiro Chihaya Adachi 《Journal of polymer science. Part A, Polymer chemistry》2007,45(20):4661-4670
Three new copolymers, namely poly(fluorenevinylene‐alt‐naphthalenevinylene) ( N ), poly(fluorenevinylene‐alt‐anthracenevinylene) ( A ) and poly(fluorenevinylene‐alt‐pyrenevinylene) ( P ), were synthesized by Heck coupling of 9,9‐dihexyl‐2, 7‐divinylfluorene with a polynuclear aromatic dibromide. The 9,10‐disubstituted anthracene was obtained exclusively for A while N and P were obtained as a mixture of two isomers with predominant the 1,4‐disubstituted naphthalene and 1,8‐disubstituted pyrene, respectively. The polymers were soluble in common organic solvents and decomposed above 370 °C. Their glass transition temperature increased from 58 to 110 °C by increasing the number of the phenyl rings of the polynuclear aromatic moiety. Rather high‐efficiency blue and blue‐greenish photoluminescence (PL) of these copolymers in solution was largely decreased in their films, indicating the presence of concentration quenching in the solid state. The OLED using these polymers demonstrated green EL in the case of copolymers N and A , and red EL in the P derivative with ηEL = 0.26–0.31%. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4661–4670, 2007 相似文献