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91.
If X is a point random field on d then convergence in distribution of the renormalization Cλ|Xλ ? αλ| as λ → ∞ to generalized random fields is examined, where Cλ > 0, αλ are real numbers for λ > 0, and Xλ(f) = λ?dX(fλ) for . If such a scaling limit exists then Cλ = λθg(λ), where g is a slowly varying function, and the scaling limit is self-similar with exponent θ. The classical case occurs when and the limit process is a Gaussian white noise. Scaling limits of subordinated Poisson (doubly stochastic) point random fields are calculated in terms of the scaling limit of the environment (driving random field). If the exponent of the scaling limit is then the limit is an independent sum of the scaling limit of the environment and a Gaussian white noise. If the scaling limit coincides with that of the environment while if the limit is Gaussian white noise. Analogous results are derived for cluster processes as well. 相似文献
92.
A. A. Papin 《Journal of Applied Mechanics and Technical Physics》2008,49(4):527-536
A model problem of the motion of water and air in thawing snow is examined using the Masket-Leverett equations of two-phase
filtration. The theorem of existence of a self-similar solution is proved.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 13–23, July–August, 2008. 相似文献
93.
94.
Tian-You Hu 《Proceedings of the American Mathematical Society》2001,129(6):1713-1720
Let be a self-similar probability measure on satisfying where 0$"> and Let be the Fourier transform of A necessary and sufficient condition for to approach zero at infinity is given. In particular, if and for then 0$"> if and only if is a PV-number and is not a factor of . This generalizes the corresponding theorem of Erdös and Salem for the case
95.
Dilated Fractional Stable Motions 总被引:2,自引:0,他引:2
Dilated fractional stable motions are stable, self-similar, stationary increments random processes which are associated with dissipative flows. Self-similarity implies that their finite-dimensional distributions are invariant under scaling. In the Gaussian case, when the stability exponent equals 2, dilated fractional stable motions reduce to fractional Brownian motion. We suppose here that the stability exponent is less than 2. This implies that the dilated fractional stable motions have infinite variance and hence they cannot be characterised by a covariance function. These dilated fractional stable motions are defined through an integral representation involving a nonrandom kernel. This kernel plays a fundamental role. In this work, we study the space of kernels for which the dilated processes are well-defined, indicate connections to Sobolev spaces, discuss uniqueness questions and relate dilated fractional stable motions to other self-similar processes. We show that a number of processes that have been obtained in the literature, are in fact dilated fractional stable motions, for example, the telecom process obtained as limit of renewal reward processes, the Takenaka processes and the so-called random wavelet expansion processes. 相似文献
96.
Starting from a finitely ramified self-similar set X we can construct an unbounded set X
by blowing-up the initial set X. We consider random blow-ups and prove elementary properties of the spectrum of the natural Laplace operator on X
(and on the associated lattice). We prove that the spectral type of the operator is almost surely deterministic with the blow-up and that the spectrum coincides with the support of the density of states almost surely (actually, our result is more precise). We also prove that if the density of states is completely created by the so-called Neuman–Dirichlet eigenvalues, then almost surely the spectrum is pure point with compactly supported eigenfunctions. 相似文献
97.
Ethernet PON (ePON): Design and Analysis of an Optical Access Network 总被引:29,自引:0,他引:29
With the expansion of services offered over the Internet, the last mile bottleneck problems continue to exacerbate. A passive optical network (PON) is a technology viewed by many as an attractive solution to this problem. In this study, we propose the design and analysis of a PON architecture which has an excellent performance-to-cost ratio. This architecture uses the time-division multiplexing (TDM) approach to deliver data encapsulated in Ethernet packets from a collection of optical network units (ONUs) to a central optical line terminal (OLT) over the PON access network. The OLT, in turn, is connected to the rest of the Internet. A simulation model is used to analyze the systems performance such as bounds on packets delay and queue occupancy. Then, we discuss the possibility of improving the bandwidth utilization by means of timeslot size adjustment, and by packet scheduling. 相似文献
98.
We construct non-axially symmetric self-similar solutions to the porous medium equation by showing that the family of radial self-similar solutions found by Aronson and Graveleau (1993) undergoes a sequence of symmetry breaking bifurcations as the parameter decreases from to .
99.
We consider a constant coefficient coagulation equation with Becker–D?ring type interactions and power law input of monomers
J
1(t) = α t
ω, with α > 0 and . For this infinite dimensional system we prove solutions converge to similarity profiles as t and j converge to infinity in a similarity way, namely with either or constants, where is a function of t only. This work generalizes to the non-autonomous case a recent result of da Costa et al. (2004). Markov Processes Relat. Fields
12, 367–398. and provides a rigorous derivation of formal results obtained by Wattis J. Phys. A: Math. Gen. 37, 7823–7841. The main part of the approach is the analysis of a bidimensional non-autonomous system obtained through an appropriate
change of variables; this is achieved by the use of differential inequalities and qualitative theory methods. The results
about rate of convergence of solutions of the bidimensional system thus obtained are fed into an integral formula representation
for the solutions of the infinite dimensional system which is then estimated by an adaptation of methods used by da Costa
et al. (2004). Markov Processes Relat. Fields
12, 367–398.
相似文献
100.
对于自相似集合,已知开集条件与强开集条件是等价的,我们讨论了强开集条件的基些性质,并给出了自似测度局部维数研究的一个应用。 相似文献