分数次积分的多线性换位子(英文)

设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0<α<n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1<p<α/n,1/q=1/p-α/n.

贝叶斯优化模糊C均值的城市交通状态判别方法

准确的城市交通状态判别是实现城市智能交通诱导、管理、控制的基础和前提,对出行推荐和城市规划等具有重大的参考价值。通过分析浮动车GPS点位数据具备的位置、速度、方向等信息,可以实时获取交通参数,反映交通运行状态。针对交通状态的模糊性、不确定性等特性,以路段行驶速度和速度方差为指标,提出一种贝叶斯优化模糊C均值的聚类算法(BO-FCM)。BO-FCM用贝叶斯算法对FCM算法的初始化参数进行优化,避免FCM陷入局部最优解而导致聚类无法收敛到最优结果,降低交通状态判别的准确度。以深圳市主干道的实测数据为例,进行BO-FCM城市道路交通状态判别算法的实验分析,结果表明,BO-FCM算法较其他FCM算法,鲁棒性更高,聚类结果更准确。

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and -dimensional Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality (or the fractal dimensionality ). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.

Phase transition and critical phenomenon of AdS black holes in Einstein-Gauss-Bonnet gravity

Thermodynamics of phase transition for a black hole in 5D Einstein-Gauss-Bonnet gravity with a negative cosmological constant is studied.As the Bekenstein-Hawking entropy is adopted,we find the heat capacity,volume expansion coefficient and isothermal compressibility are divergent at the critical points,which implies the existence of phase transitions.The fact that the phase transitions are indeed second order is revealed by studying the Ehrenfest's equations and the Prigogine-Defay ratio.Furthermore near the critical points,we also explicitly calculate the critical exponents of the relevant thermodynamic quantities at fixed charge or fixed temperature.It is shown that the corresponding critical exponents satisfy the thermodynamic scaling law.The Generalized Homogeneous Function hypothesis is also checked by studying the Helmholtz free energy,which is shown to be consistent with the thermodynamic scaling law.

Area and Entropy Spectrum of Gauss-Bonnet Gravity in de Sitter Space-Times for Black Hole Event Horizon

In this paper, we use the modified Hod's treatment and the Kunstatter's method to study the horizon area spectrum and entropy spectrum in Gauss-Bonnet de-Sitter space-time, which is regarded as the natural generalization of Einstein gravity by including higher derivative correction terms to the original Einstein-Hilbert action. The horizon areas have some properties that are very different from the vacuum solutions obtained from the frame of Einstein gravity. With the new physical interpretation of quasinormal modes, the area/entropy spectrum for the event horizon for nearextremal Gauss-Bonnet de Sitter black holes are obtained. Meanwhile, we also extend the discussion of area/entropy quantization to the non-extremal black holes solutions.

New Generalizations of Migdal-Kadanoff Bond-Moving Recursion Procedures and Their Applications

Considering in symmetrical half-length bond operations,we present in this paper two types of newlydeveloped generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures.The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively.Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.