排序方式: 共有139条查询结果,搜索用时 15 毫秒
111.
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also studied some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys–Tsallis divergence and the Jensen–Shannon–Tsallis divergence. 相似文献
112.
In this study which is the continuation of the first part (Pavlos et al. 2012) [1], the nonlinear analysis of the solar flares index is embedded in the non-extensive statistical theory of Tsallis (1988) [3]. The q-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using theq-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000) [25]. Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x), (ii) f(a) and D(q), and (iii) J(p) for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone. 相似文献
113.
In this study, nucleation and grain growth was studied by using 2-dimensional generalized Monte Carlo simulations and experiments. As an attempt to improve the JMAK model, we proposed a new differential equation to be able to model nucleation and growth phenomena using nonextensive thermostatistics. One of the reasons that we would like to perform generalized Monte Carlo simulations in studying of nucleation and grain growth phenomena is that the generalized Monte Carlo algorithm was shown to be more effective than the standard Monte Carlo algorithm and also than the standard Molecular Dynamic algorithm in locating the minimum energy configuration. Therefore, for a given temperature, the fact that a configuration of the system with lower energy could be obtained by using the generalized Monte Carlo simulation means that a different textural configuration of grain growth could be also expected. In this respect, it is possible to say that the nonextensive statistics might be an appropriate tool in studying of nucleation and growth phenomena. 相似文献
114.
Multiple Importance Sampling (MIS) combines the probability density functions (pdf) of several sampling techniques. The combination weights depend on the proportion of samples used for the particular techniques. Weights can be found by optimization of the variance, but this approach is costly and numerically unstable. We show in this paper that MIS can be represented as a divergence problem between the integrand and the pdf, which leads to simpler computations and more robust solutions. The proposed idea is validated with 1D numerical examples and with the illumination problem of computer graphics. 相似文献
115.
In this paper we recall, extend and compute some information measures for the concomitants of the generalized order statistics (GOS) from the Farlie–Gumbel–Morgenstern (FGM) family. We focus on two types of information measures: some related to Shannon entropy, and some related to Tsallis entropy. Among the information measures considered are residual and past entropies which are important in a reliability context. 相似文献
116.
We are concerned with the weighted Tsallis and Kaniadakis divergences between two measures. More precisely, we find inequalities between these divergences and Tsallis and Kaniadakis logarithms, prove that they are limited by similar bounds with those that limit Kullback–Leibler divergence and show that are pseudo-additive. 相似文献
117.
Motivated by studies onq-deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the
concept ofq-deformed nonlinear maps is introduced. As a specific example, aq-deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family ofq-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors — a phenomenon
rare in one-dimensional maps. 相似文献
118.
A.S. Parvan 《Physics letters. A》2006,350(5-6):331-338
The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution functions are derived by the thermodynamic method based upon the use of the fundamental equation of thermodynamics and the statistical definition of the functions of the state of the system. It is shown that if the entropic index ξ=1/(q−1) in the microcanonical ensemble is an extensive variable of the state of the system, then in the thermodynamic limit the principle of additivity and the zero law of thermodynamics are satisfied. In particular, the Tsallis entropy of the system is extensive and the temperature is intensive. Thus, the Tsallis statistics completely satisfies all the postulates of the equilibrium thermodynamics. Moreover, evaluation of the thermodynamic identities in the microcanonical ensemble is provided by the Euler theorem. The principle of additivity and the Euler theorem are explicitly proved by using the illustration of the classical microcanonical ideal gas in the thermodynamic limit. 相似文献
119.
The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here, we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999–31.10.2005 for the time lags ranging from 1min up to 1 h. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power law, as identified previously for majority of the mature markets. Within the time scales studied, a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single q-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter q was found to systematically decrease when increasing the time scales. The temporal correlations quantified here in terms of multifractality provide further arguments in favor of nonextensivity. 相似文献
120.
本文讨论了具有相同Tsallis熵或相同Tsallis相对熵的两个连续随机变量随机等价的一些条件,以及随机序与Tsallis熵序的一些关系. 相似文献