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21.
22.
Let
n
be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean
n
and the Laplace transform
e-sn
is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results. 相似文献
23.
We prove some limiting results for a Lévy process X
t
as t0 or t, with a view to their ultimate application in boundary crossing problems for continuous time processes. In the present paper we are mostly concerned with ideas related to relative stability and attraction to the normal distribution on the one hand and divergence to large values of the Lévy process on the other. The aim is to find analytical conditions for these kinds of behaviour which are in terms of the characteristics of the process, rather than its distribution. Some surprising results occur, especially for the case t0; for example, we may have X
t
/t
P
+ (t0) (weak divergence to +), whereas X
t
/t a.s. (t0) is impossible (both are possible when t), and the former can occur when the negative Lévy spectral component dominates the positive, in a certain sense. Almost sure stability of X
t
, i.e., X
t
tending to a nonzero constant a.s. as t or as t0, after normalisation by a non-stochastic measurable function, reduces to the same type of convergence but with normalisation by t, thus is equivalent to strong law behaviour. Boundary crossing problems which are amenable to the methods we develop arise in areas such as sequential analysis and option pricing problems in finance. 相似文献
24.
We consider the asymptotic behavior of semi-stable Markov processes valued in ]0,[ when the starting point tends to 0. The entrance distribution is expressed in terms of the exponential functional of the underlying Lévy process which appears in Lamperti's representation of a semi-stable Markov process. 相似文献
25.
A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137. 相似文献
26.
Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total
reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first
derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by
channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and
reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It
becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width
and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial
for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling
only occurs in a finite range of ɛ. 相似文献
27.
We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is fed by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitors level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems Lévy-charged Ornstein–Uhlenbeck capacitors. Various random quantities associated with these systems are analyzed, including: the time-to- discharge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitors stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding standard Lévy-driven Ornstein–Uhlenbeck systems. 相似文献
28.
Thilo?Meyer-BrandisEmail author Frank?ProskeEmail author 《Applied Mathematics and Optimization》2004,50(2):119-134
In this paper we explicitly solve a non-linear filtering problem
with mixed observations, modelled by a Brownian motion and a generalized Cox
process, whose jump intensity is given in terms of a Lévy measure.
Motivated by empirical observations of R. Cont and P. Tankov we propose a
model for financial assets, which captures the phenomenon of
time inhomogeneity of the jump size density. We apply the explicit formula
to obtain the optimal filter for the corresponding filtering problem. 相似文献
29.
Wolfgang R.?BergmannEmail author Roberto?ContiEmail author 《Annali di Matematica Pura ed Applicata》2003,182(3):271-286
Let H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part H0 is the C*-inductive limit of B(Hr), we look for some family of representations on an inductive limit of Hr as r. When such construction is shaped according to the structure of H0, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of . 相似文献
30.
Robert Blackburn 《Journal of Theoretical Probability》2000,13(3):825-842
For X(t) a real-valued symmetric Lévy process, its characteristic function is E(e
iX(t))=exp(–t()). Assume that is regularly varying at infinity with index 1<2. Let L
x
t
denote the local time of X(t) and L*
t
=sup
xR
L
x
t
. Estimates are obtained for P(L
0
t
y) and P(L*
t
y) as y and t fixed. 相似文献