CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM

In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time.

Effects of drive current rise-time and initial load density distribution on Z-pinch characteristics

A two-dimensional, three-temperature radiation magneto-hydrodynamics model is applied to the investigation of evolutional trends in x-ray radiation power, energy, peak plasma temperature and density as functions of drive current rise-time and initial load density distribution by using the typical experimental parameters of tungsten wire-array Z- pinch on the Qiangguang-I generator. The numerical results show that as the drive current rise-time is shortened, x-ray radiation peak power, energy, peak plasma density and peak ion temperature increase approximately linearly, but among them the x-ray radiation peak power increases more quickly. As the initial plasma density distribution in the radial direction becomes gradually flattened, the peak radiation power and the peak ion-temperature almost exponentially increase, while the radiation energy and the peak plasma density change only a little. The main effect of shortening drive current rise-time is to enhance compression of plasma, and the effect of flattening initial load density distribution in the radial direction is to raise the plasma temperature. Both of the approaches elevate the x-ray peak radiation power

Distribution and characteristics of initial PSA and PSA velocity in men younger than 50 years without prostate cancer

Objective To explore the distribution and characteristics of initial PSA and PSA velocity in men younger than years without prostate cancer. Methods PSA in men younger than 50 years without prostate cancer from January 2001 to November 2009 were retrieved retrospec-

MILP formulations for highway petrol station replenishment in initiative distribution mode

To investigate highway petrol station replenishment in initiative distribution mode,this paper develops a mixed-integer linear programming(MILP)model with minimal operational costs that includes loading costs,unloading costs,transport costs and the costs caused by unpunctual distribution.Based on discrete representation,the working day is divided into equal time intervals,and the truck distribution process is decomposed into a pair of tasks including driving,standby,rest,loading and unloading.Each truck must execute one task during a single interval,and the currently executing task is closely related to the preceding and subsequent tasks.By accounting for predictive time-varying sales at petrol stations,real-time road congestion and a series of operational constraints,the proposed model produces the optimal truck dispatch,namely,a detailed task assignment for all trucks during each time interval.The model is tested on a real-world case of a replenishment system comprising eight highway petrol stations,one depot,one garage and eight trucks to demonstrate its applicability and accuracy.

A Theory for the Initial Allocating of Real Time Tasks in Distributed Systems

Referring to a set of real time tasks with arriving time,executing time and deadline,this paperdiscusses the problem of polynomial time initial-allocating approximation algorithms in a distributedsystem and five new results are gained which provide a theory for the designing of initial-allocating algorithmsof real time tasks.