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We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with
general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions
for tractability and strong tractability of multivariate integration in such weighted function spaces are found. These conditions
are also necessary if the weights are such that the reproducing kernel of the weighted Korobov space is pointwise non-negative.
The existence of a lattice rule which achieves the nearly optimal convergence order is proven. A component-by-component (CBC)
algorithm that constructs good lattice rules is presented. The resulting lattice rules achieve tractability or strong tractability
error bounds and achieve nearly optimal convergence order for suitably decaying weights. We also study special weights such
as finite-order and order-dependent weights. For these special weights, the cost of the CBC algorithm is polynomial. Numerical
computations show that the lattice rules constructed by the CBC algorithm give much smaller worst-case errors than the mean
worst-case errors over all quasi-Monte Carlo rules or over all lattice rules, and generally smaller worst-case errors than
the best Korobov lattice rules in dimensions up to hundreds. Numerical results are provided to illustrate the efficiency of
CBC lattice rules and Korobov lattice rules (with suitably chosen weights), in particular for high-dimensional finance problems. 相似文献
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Polytetrafluoroethylene (PTFE) is an important engineering material with a low coefficient of friction but a high rate of wear. As a semi‐crystalline polymer, its wear resistance is related to its micro‐morphology. Friction and wear properties of semi‐crystalline non‐spherulitic PTFE have been widely studied, but no investigation is reported about tribological properties of spherulitic PTFE due to difficulties in finding such properties. In this paper, friction and wear properties of PTFE with spherulitic micro‐morphology are studied for the first time. The results show that, first, under the same experimental condition, when two kinds of PTFE are rubbed against the steel disc, the number and size of debris of spherulitic PTFE are much less and smaller than that of debris of PTFE without spherulitic crystals. This means that the wear resistance of spherulitic PTFE is better than that of semi‐crystalline PTFE without spherulitic micro‐morphology. Second, the friction property of spherulitic PTFE is also different from that of PTFE without spherulitic crystals. Finally, the friction and wear mechanisms of spherulitic PTFE and non‐spherulitic PTFE are compared. 相似文献
14.
Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system 总被引:1,自引:0,他引:1
Damei Li Xiaoqun Wu Guanrong Chen 《Journal of Mathematical Analysis and Applications》2006,323(2):844-853
To estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general. In this paper, we attempt to investigate the ultimate bound and positively invariant set for two specific systems, the Lorenz system and a unified chaotic system. We derive an ellipsoidal estimate of the ultimate bound and positively invariant set for the Lorenz system, for all the positive values of its parameters a, b and c, and obtain the minimum value of volume for the ellipsoid. Comparing with the best results in the current literature [D. Li, J. Lu, X. Wu, G. Chen, Estimating the bounds for the Lorenz family of chaotic systems, Chaos Solitons Fractals 23 (2005) 529-534; X. Liao, On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization, Sci. China Ser. E 34 (2004) 1404-1419], our new results fill up the gap of the estimate for the cases of 0<a<1 and 0<b<2 [X. Liao, On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization, Sci. China Ser. E 34 (2004) 1404-1419]. Furthermore, the estimation derived here contains the results given in [D. Li, J. Lu, X. Wu, G. Chen, Estimating the bounds for the Lorenz family of chaotic systems, Chaos Solitons Fractals 23 (2005) 529-534] and [X. Liao, On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization, Sci. China Ser. E 34 (2004) 1404-1419] as special cases. Along the same line, we also provide estimates of cylindrical and ellipsoidal bounds for a unified chaotic system, for its parameter range , and obtain the minimum value of volume for the ellipsoid. The estimate is more accurate than and also extends the result of [D. Li, J. Lu, X. Wu, G. Chen, Estimating the bounds for the Lorenz family of chaotic systems, Chaos Solitons Fractals 23 (2005) 529-534] and [X. Liao, On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization, Sci. China Ser. E 34 (2004) 1404-1419]. 相似文献
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We report the passive mode-locking at harmonics of the free spectral range (FSR) of the intracavity multi-channel filter in a fiber ring laser. The laser uses a sampled fiber Bragg grating (SFBG) with a free spectral range (FSR) of 0.8 nm, or 99 GHz at 1555 nm, and a length of highly nonlinear photonic crystal fiber with low and flat dispersion. Stable picosecond soliton pulse trains with twofold to sevenfold enhancement in the repetition rate, relative to the FSR of the SFBG, have been achieved. The passive mode-locking mechanism that is at play in this laser relies on a dissipative four-wave mixing process and switching of repetition rate is realized simply by adjustment of the intracavity polarization controllers. 相似文献
20.
Stability enhancement on the basis of four-wave mixing (FWM) is proposed and proved for the first time to our knowledge. This technique is applied to dual-wavelength erbium-doped fiber lasers. Significant uniformity and stability of the novel fiber lasers are demonstrated experimentally. 相似文献