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171.
Numerical evidence is presented which strongly suggests that ``Jacobi's last geometric statement"--that the conjugate locus from a point has exactly four cusps and the corresponding cut locus consists of only one topological segment--holds for compact real analytic Liouville surfaces diffeomorphic to if the Gaussian curvature is everywhere positive and has exactly six critical points, these being two saddles, two global minima, and two global maxima (as is the case for an ellipsoid). Our experiments suggest that this is a sufficient rather than a necessary condition. Furthermore, for compact real analytic Liouville surfaces diffeomorphic to upon which the Gaussian curvature can be negative but has exactly six critical points, these being two saddles, two global minima, and two global maxima, it appears that the cut locus is always a subarc of a line given by or , where are canonical coordinates with respect to which the metric has the form . In the case of an ellipsoid, these curves are lines of curvature.
172.
173.
K. G. Pruden K. Sinclair S. Beaudoin 《Journal of polymer science. Part A, Polymer chemistry》2003,41(10):1486-1496
Parylene‐N and parylene‐C are polymers of interest for microelectronic and medical coating applications. Modifications for improved surface properties could make them even more useful in such applications. Parylene‐N and parylene‐C films were exposed to ultraviolet light in the presence of oxygen and analyzed with Rutherford backscattering spectrometry, secondary‐ion mass spectroscopy, X‐ray photoelectron spectroscopy, and infrared spectroscopy. This study shows that such exposure results in the formation of aldehyde and carboxylic acid groups near the surface of the films. At the maximum exposure dose, the concentration of oxygen in both parylene‐N and parylene‐C is about 13% at the film surface, and it decreases exponentially with increasing depth. Further modeling and optimization of this process would allow it to be used to tailor the surface concentration of oxygenated species in parylene for the optimization of adhesion and wettability or for the chemical binding of other moieties. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1486–1496, 2003 相似文献
174.
175.
An ultracompact, actively Q -switched optical parametric oscillator (OPO) has been realized that is only 30 mm in length, based on a semimonolithic microchip laser, a quadrupole deflector, and a monolithic periodically poled lithium niobate crystal. The OPO threshold was 550 mW when Nd:YAG was used as the gain material and 590 mW for Nd:Y VO(4), giving signal pulses of as much as 8.7 muJ in energy with Nd:YAG at 1 kHz and 5.9-mu;J pulses with Nd:Y VO(4) at 5 kHz, for 1.2- and 2-W laser diode pumping, respectively. The output was single frequency and could be tuned over the range 1540-3440 nm. 相似文献
176.
Matrix methods are used to obtain better convergence of low-order lattice calculations. Strong-coupling expansions for the Hamiltonian matrix in a non-degenerate subspace of states are extrapolated to zero lattice spacing using matrix Padé approximants. The method is applied first to the massive Schwinger model and the continuum estimates from different fourth-order calculations compared. Then it is used to calculate the ratios of the π, ? and ω meson masses to the nucleon mass in a Hamiltonian lattice formulation of QCD. 相似文献
177.
This investigation treats the static response of a single elastic cable which is suspended between two points that are not necessarily at the same level. The cable is loaded by its self-weight and any number of concentrated vertical loads which may be arbitrarily placed along its length. The analysis presented uses a Lagrangian approach. For the strained cable profile, the tension and displacements are given as functions of a single Lagrangian co-ordinate. A specific application of the general analysis is made and compared with a simple experiment. 相似文献
178.
Anupam?Gupta?Email author Ilan?Newman Yuri?Rabinovich Alistair?Sinclair? 《Combinatorica》2004,24(2):233-269
Motivated by many recent algorithmic applications, this paper aims to promote a systematic study of the relationship between the topology of a graph and the metric distortion incurred when the graph is embedded into 1 space. The main results are:1. Explicit constant-distortion embeddings of all series-parallel graphs, and all graphs with bounded Euler number. These are the first natural families known to have constant distortion (strictly greater than 1). Using the above embeddings, algorithms are obtained which approximate the sparsest cut in such graphs to within a constant factor.2. A constant-distortion embedding of outerplanar graphs into the restricted class of 1-metrics known as dominating tree metrics. A lower bound of (log n) on the distortion for embeddings of series-parallel graphs into (distributions over) dominating tree metrics is also presented. This shows, surprisingly, that such metrics approximate distances very poorly even for families of graphs with low treewidth, and excludes the possibility of using them to explore the finer structure of 1-embeddability.* A preliminary version of this work appeared in Proceedings of the 40th Annual IEEE
Symposium on Foundations of Computer Science, 1999, pp. 399–408. This work was done while the author was at the University of California, Berkeley. Supported in part by NSF grants CCR-9505448 and CCR-9820951. 相似文献
179.
Fabio?MartinelliEmail author Alistair?Sinclair Dror?Weitz 《Communications in Mathematical Physics》2004,250(2):301-334
We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the so-called Bethe approximation. Specifically, we show that the spectral gap and the log-Sobolev constant of the Glauber dynamics for the Ising model on an n-vertex regular tree with (+)-boundary are bounded below by a constant independent of n at all temperatures and all external fields. This implies that the mixing time is O(logn) (in contrast to the free boundary case, where it is not bounded by any fixed polynomial at low temperatures). In addition, our methods yield simpler proofs and stronger results for the spectral gap and log-Sobolev constant in the regime where the mixing time is insensitive to the boundary condition. Our techniques also apply to a much wider class of models, including those with hard-core constraints like the antiferromagnetic Potts model at zero temperature (proper colorings) and the hard–core lattice gas (independent sets).An extended abstract of this paper appeared under the title The Ising model on trees: Boundary conditions and mixing time in Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, October 2003, pp. 628–639.This work was done while this author was visiting the Departments of EECS and Statistics, University of California, Berkeley, supported in part by a Miller Visiting Professorship.Supported in part by NSF Grant CCR-0121555 and DARPA cooperative agreement F30602-00-2-0601.Supported in part by NSF Grant CCR-0121555. 相似文献
180.
Jordan P Cooper J McNay G Docherty FT Smith WE Sinclair G Padgett MJ 《Optics letters》2004,29(21):2488-2490
We demonstrate three-dimensional trapping of micrometer-diameter silica particles, partially coated with silver, within conventional optical tweezers. Although metallic particles are usually repelled from the beam focus by the scattering force, we show that transparent spheres partially coated with silver can be trapped with efficiencies comparable with dielectric particles. The trapping characteristics of these particles are examined as a function of metallic coverage, and the application of these particles to surface-enhanced resonance Raman scattering is investigated. 相似文献