Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

Estimation of power density in IMPATT using different materials

ABSTRACT

The RF output power dissipated per unit area is calculated using Runge-Kutta method for the high-moderate-moderate-high (n⁺-n-p-p⁺) doping profile of double drift region (DDR)-based impact avalanche transit time (IMPATT) diode by taking different substrate at Ka band. Those substrates are silicon, gallium arsenide, germanium, wurtzite gallium nitride, indium phosphide and 4H-silicon carbide. A comparative study regarding power dissipation ability by the IMPATT using different material is being presented thereby modelling the DDR IMPATT diode in a one-dimensional structure. The IMPATT based on 4H-SiC element has highest power density in the order of 10¹⁰ Wm^?2 and the Si-based counterpart has lowest power density of order 10⁶ Wm^?2 throughout the Ka band. So, 4H-SiC-based IMPATT should be preferable over others for the power density preference based application. This result will be helpful to estimate the power density of the IMPATT for any doping profile and to select the proper element for the optimum design of the IMPATT as far as power density is concerned in the Ka band. Also, we have focused on variation of power density with different junction temperatures and modelled the heat sink with analysis of thermal resistances.     

小波变换在金融数据分析中的应用

市场上的数据,从本质上讲都是一种时间序列。它和小波分析中的信号具有相同的特性。因此,完全可以将这些经济时间序列看成信号,应用小波变换进行分析和预测。     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

恒载超声雾化制取金属粉末的改进方法

本文提出一种改进的超声雾化制取金属粉末方法。克服了因变幅杆负载变化所引起的粉末产率的周期变化，给出装置的框图及有关的参数和实验结果。     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

A Construction of Optimal Constant Composition Codes

In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal constant composition codes meeting the upper bound given by [13].     

Time Consistent Dynamic Risk Measures

We introduce the time-consistency concept that is inspired by the so-called “principle of optimality” of dynamic programming and demonstrate – via an example – that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of the target-percentile risk measure which is time-consistent and hence more suitable in the multi-stage investment context. Finally, we also generalize the value-at-risk and CVaR to multi-stage risk measures based on the theory and structure of the target-percentile risk measure.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.     

Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response

We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results.