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491.
We show that for a graph G it is NP-hard to decide whether its independence number α(G) equals its clique partition number even when some minimum clique partition of G is given. This implies that any α(G)-upper bound provably better than is NP-hard to compute.To establish this result we use a reduction of the quasigroup completion problem (QCP, known to be NP-complete) to the maximum independent set problem. A QCP instance is satisfiable if and only if the independence number α(G) of the graph obtained within the reduction is equal to the number of holes h in the QCP instance. At the same time, the inequality always holds. Thus, QCP is satisfiable if and only if . Computing the Lovász number ?(G) we can detect QCP unsatisfiability at least when . In the other cases QCP reduces to gap recognition, with one minimum clique partition of G known. 相似文献
492.
Let K(a) be the so-called classical Kloosterman sum over . In this paper, we compute K(a) modulo 24 for even m, completing our previous results for odd m. We extensively study the links between K(a) and other exponential sums, especially the cubic sums. We point out (as we did for odd m) that the values K(a) are involved in the computation of the weight distributions of cosets of primitive narrow sense extended BCH codes of length 2m and minimum distance 8. We also complete some recent results on K(a)−1 modulo 3. 相似文献
493.
Vadim P. Sirkeli Dmitrii D. Nedeoglo Natalia D. Nedeoglo Ivan V. Radevici Raisa L. Sobolevskaia Konstantin D. Sushkevich Erkki Lähderanta Alexander V. Lashkul Reino Laiho Jens-Peter Biethan Oktay Yilmazoglu Dimitris Pavlidis Hans L. Hartnagel 《Physica B: Condensed Matter》2012,407(18):3802-3807
Magnetic and photoluminescent properties of manganese-doped ZnSe crystals with different impurity concentrations were investigated. The concentration of Mn2+ ions in ZnSe crystals has been varied from 0.01 to 0.3 at%. Magnetic and photoluminescent studies have confirmed the introduction of Mn in ZnSe crystals. It was established that Mn2+ ions are responsible for the emission bands with maximum at 616 nm and 633 nm, which correspond to 4T2→6A1 and 4T1→6A1 intracentre transitions of Mn2+ ions respectively. It was found that the concentration quenching of the photoluminescent bands is associated with Mn2+ ions, which are due to the formation of Mn–Mn clusters. Magnetic properties studies have shown that at high doping levels the manganese atoms form Mn–Mn clusters in ZnSe. From the temperature dependence of magnetic susceptibility of ZnSe:Mn crystals that follows the Curie–Weiss law, it was possible to estimate the Curie–Weiss temperature Θ(x) and the effective Mn–Mn antiferromagnetic exchange constant (J1). 相似文献
494.
Adrià Canós Valero Dmitrii Borovkov Aleksandr Kalganov Alexandra Dudnikova Mikhail Sidorenko Pavel Dergachev Egor Gurvitz Lei Gao Vjaceslavs Bobrovs Andrey Miroshnichenko Alexander S. Shalin 《Laser \u0026amp; Photonics Reviews》2024,18(4):2200740
Multipoles are paramount for describing electromagnetic fields in many areas of nanoscale optics, playing an essential role in the design of devices in plasmonics and all-dielectric nanophotonics. Challenging the traditional division into electric and magnetic moments, toroidal moments are proposed as a physically distinct family of multipoles with significant contributions to the properties of matter. However, the apparent impossibility of separately measuring their response sheds doubt on their true physical significance. Here, the possibility of selectively exciting toroidal moments is confirmed without any other multipole. A set of general conditions is developed that any current distribution must fulfill to be entirely described by toroidal moments and prove the results in an analytically solvable case. The new theory allows to design and verify experimentally an artificial structure supporting a pure broadband toroidal dipole response in the complete absence of the electric dipole and other “ordinary” multipole contributions. In addition, a structure capable of supporting a novel type of non-radiating source is proposed- a “toroidal anapole,” originating from the destructive interference of the toroidal dipole with the unconventional electromagnetic sources known as mean square radii. The results in this work provide conclusive evidence on the independent excitation of toroidal moments in electrodynamics. 相似文献
495.
Mark Krasnosel'Skii Reinhard Mennicken Dmitrii Rachinskii 《Mathematische Nachrichten》1999,207(1):133-155
We study quasilinear elliptic equations with strong nonlinear terms and systems of such equations. The methods developed by the authors in [1], [2] are used to prove the existence of solutions for boundary—value problems using some information on behavior of potential bounds for nonlinearities; the L–characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classical solutions of quasilinear second order elliptic equations. 相似文献
496.
Pascale Charpin Aimo Tietäväinen Victor Zinoviev 《Designs, Codes and Cryptography》1999,17(1-3):81-85
We deal with the minimum distances of q-ary cyclic codes of length q
m
- 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for the case that the minimum distance is two, show that the minimum distance is at most three if q > 3, and consider also the case q = 3. 相似文献
497.
498.
Dimitris K. Agrafiotis Dmitrii N. Rassokhin Victor S. Lobanov 《Journal of computational chemistry》2001,22(5):488-500
Multidimensional scaling (MDS) is a collection of statistical techniques that attempt to embed a set of patterns described by means of a dissimilarity matrix into a low‐dimensional display plane in a way that preserves their original pairwise interrelationships as closely as possible. Unfortunately, current MDS algorithms are notoriously slow, and their use is limited to small data sets. In this article, we present a family of algorithms that combine nonlinear mapping techniques with neural networks, and make possible the scaling of very large data sets that are intractable with conventional methodologies. The method employs a nonlinear mapping algorithm to project a small random sample, and then “learns” the underlying transform using one or more multilayer perceptrons. The distinct advantage of this approach is that it captures the nonlinear mapping relationship in an explicit function, and allows the scaling of additional patterns as they become available, without the need to reconstruct the entire map. A novel encoding scheme is described, allowing this methodology to be used with a wide variety of input data representations and similarity functions. The potential of the algorithm is illustrated in the analysis of two combinatorial libraries and an ensemble of molecular conformations. The method is particularly useful for extracting low‐dimensional Cartesian coordinate vectors from large binary spaces, such as those encountered in the analysis of large chemical data sets. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 488–500, 2001 相似文献
499.
V. A. Komornikov A. M. Grechikhina V. V. Grebenev I. S. Timakov O. B. Zajnullin V. G. Zinoviev 《Crystallography Reports》2018,63(5):806-811
Proton-conducting composites xCs4(HSO4)3(H2PO4) + (1–x)AlPO4 in the composition range x = 0.9–0.5 have been obtained. Their transport properties are studied by impedance spectroscopy. The dependences of the phase composition of the materials on the component ratio are investigated by X-ray diffraction analysis. The spatial phase distribution in the materials is analyzed using scanning electron microscopy. 相似文献