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61.
The Gegenbauer reconstruction method was first proposed in 1992, but in early studies no attempts were made to optimize the relevant parameters of this method. These parameters were allowed to grow proportionally with the number of nodes which, in many cases, resulted in exponential convergence for a selected range of the proportionality constants. Early studies also made clear that very large error bounds could be expected if these key parameters were not chosen carefully. Subsequent studies then pointed out that, although unrelated to the method’s analytically predictable domains of poor accuracy, round-off errors could also sabotage the method’s accuracy. The challenge of successfully implementing a Gegenbauer reconstruction then rests on understanding the performance trade-offs we can expect when choosing the key parameters in accordance with different objectives.In this study, we propose a new strategy for choosing optimal parameters in the Chebyshev-Gegenbauer reconstruction method, specifically to achieve numerical stability. This strategy is based on asymptotic analysis as well as minimization problems in one and two dimensions. The effectiveness of our approach, which could also be applied to a wider selection of polynomials is then illustrated with results from numerical experiments. 相似文献
62.
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008 相似文献
63.
Michael Bildhauer Martin Fuchs 《Calculus of Variations and Partial Differential Equations》2005,24(3):309-340
We establish several smoothness results for local minimizers of non-autonomous variational integrals with anisotropic growth
conditions.
Mathematics Subject Classification (2000) 49N60, 49N99 相似文献
64.
Scott A. Sarra 《Numerical Algorithms》2006,41(1):17-33
Digital total variation filtering is analyzed as a fast, robust, post-processing method for accelerating the convergence of
pseudospectral approximations that have been contaminated by Gibbs oscillations. The method, which originated in image processing,
can be combined with spectral filters to quickly post-process large data sets with sharp resolution of discontinuities and
with exponential accuracy away from the discontinuities. 相似文献
65.
Gaetan?KerschenEmail author Alexander?F.?Vakakis Young?S.?Lee D.?Michael?Mcfarland Jeffrey?J.?Kowtko Lawrence?A.?Bergman 《Nonlinear dynamics》2005,42(3):283-303
The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator
weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are
encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in
terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic
orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly
and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that
this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric
study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink.
Finally, the results of experimental measurements supporting the theoretical developments are discussed.
This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at
the University of Illinois at Urbana-Champaign. 相似文献
66.
In this paper, a time‐fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0<α ?1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time‐fractional diffusion equation presents quenching solution that is not globally well‐defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
67.
About a decade after its foundation, the most advanced ballistics laboratory in Germany at the time, the Kruppsche Schiessplatz, was utilized by Ernst Mach in 1888. His intent was to validate his pioneering shock wave research using military shells as supersonic vehicles. The 125th anniversary of the Schiessplatz was celebrated in 2002. Along with Machs research, it served to initiate the field of supersonic transportation technology. The specific subject of this paper is the application of point-source spark shadowgraphy at the same laboratory in the 1970s to visualize gas flow over aeroballistic projectiles. However, different from Machs original interest, the new purpose of spark photography at that time in the ballistic ranges of the German Bundeswehr was to find technical solutions to aeroballistic problems when field-testing gave incomplete answers. Both a qualitative and a quantitative understanding of the principles of aeroballistics were sought in this research.Received: 3 February 2003, Accepted: 30 June 2003, Published online: 2 September 2003An abridged version of this paper was presented at the 13th American Physical Society Topical Conference on Shock Compression of Condensed Matter at Portland, Oregon, from July 20 to 25, 2003 相似文献
68.
Rapid detection of trace level anabolic steroids in urine is highly desirable to monitor the consumption of performance enhancing anabolic steroids by athletes. The present article describes a novel strategy for identifying the trace anabolic steroids in urine using Leidenfrost phenomenon assisted thermal desorption (LPTD) coupled to dielectric barrier discharge (DBD) ionization mass spectrometry. Using this method the steroid molecules are enriched within a liquid droplet during the thermal desorption process and desorbed all-together at the last moment of droplet evaporation in a short time domain. The desorbed molecules were ionized using a dielectric barrier discharge ion-source in front of the mass spectrometer inlet at open atmosphere. This process facilitates the sensitivity enhancement with several orders of magnitude compared to the thermal desorption at a lower temperature. The limits of detection (LODs) of various steroid molecules were found to be in the range of 0.05–0.1 ng mL−1 for standard solutions and around two orders of magnitude higher for synthetic urine samples. The detection limits of urinary anabolic steroids could be lowered by using a simple and rapid dichloromethane extraction technique. The analytical figures of merit of this technique were evaluated at open atmosphere using suitable internal standards. The technique is simple and rapid for high sensitivity and high throughput screening of anabolic steroids in urine. 相似文献
69.
Hong Zhou 《数学物理学报(B辑英文版)》2011,31(6):2289-2304
We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b*(6.7314863965), the only equilibrium state is isotropic and it is stable; when b*< b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state. 相似文献
70.