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1.
Djamel Meraghni Abdelhakim Necir 《Methodology and Computing in Applied Probability》2007,9(4):557-572
The characteristic exponent α of a Lévy-stable law S
α
(σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.
相似文献
2.
On the departure process of a leaky bucket system with long-range dependent input traffic 总被引:2,自引:0,他引:2
Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range
dependence, it is important to study the possible implications that such traffic may have for the design and performance of
these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature
after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control
in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket
system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time
is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable
with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite
variance, and a regularly varying tail, i.e., P(τ >К) ~ К-Lα
L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination.
We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it
too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and
lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range
dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
一类非经典扩散方程整体解的存在唯一性及长时间行为 总被引:5,自引:0,他引:5
本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为,建立了一系列新的结果,较好地改进许多已有的结论. 相似文献
4.
Serguei Foss Takis Konstantopoulos Stan Zachary 《Journal of Theoretical Probability》2007,20(3):581-612
We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural
conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the
process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make
full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs
are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks. 相似文献
5.
We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||1+
, where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion. 相似文献
6.
The results of variational solutions of the repeated ring and self-consistent repeated ring equations for the two-and three-dimensional overlapping Lorentz gas (LG), as formulated in a previous report, are presented. Calculations of the full velocity correlation function (VCF) for the 2D LG, including long-time tails, are compared with those from molecular dynamics. The trial functions chosen lead to predictions for the long-time tails that improve as the density of the scatterers is increased. At a value of 0.24 for* (=
2, where is the density and the radius of scatterers), the self-consistent amplitudes of the long-time tail are within 40% of the molecular dynamics. A limited number of 3D results for the short-time behavior of the repeated ring VCF are presented. The 3D solutions agree with the molecular dynamics to within 10%. 相似文献
7.
We prove that the integrated density of states () for a potentialW
=V
per +V
has Lifshitz tails where Vper is a periodic potential with reflection symmetry andV
is a random potential, e.g., of the formV
=q
i
()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833. 相似文献
8.
Let {X
t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew
–1(X
t), where {w(x):xd} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function
F(q,t)=E
0
(qd) is completely monotonic int (E
0 denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor
S(q, w)=2
0
cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|2, whereD is the diffusion constant. 相似文献
9.
We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 108 collisions of the diffusive particle. We find that (t) 1/t
fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)2 and x(t)4, and examine the behavior ofq
2
(t)=x(t)4/3x(t)22. We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM.
On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas. 相似文献
10.
Consider a simple random walk on
d
whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn
k
be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let
k
=E(n
k
)–q
–1. Our main result is a proof that (*) lim
k
k
d/2
k
= (1 –q)q
d/2 – 2(d/2)
d/2. Since it is known thatq
– 1
k
=E(n
1
n
k + 1 B) –E(n
1 B)E(n
k + 1 B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of
k
(1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of
k
for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of
k
cannot be faster than (*). 相似文献