A Note of the Uniqueness Criterion for Single Birth Processes

This paper is devoted to studying the si ngle birth processes. The uniqueness criterion for the processes is presented.

Magnetization Reversal Process of Single Crystal a-Fe Containing a Nonmagnetic Particle

The magnetization reversal process and hysteresis loops in a single crystal α-iron with nonmagnetic particles are simulated in this work based on the Landau-Lifshitz-Gilbert equation. The evolutions of the magnetic domain morphology are studied, and our analyses show that the magnetization reversal process is affected by the interaction between the moving domain wall and the existing nonmagnetic particles. This interaction strongly depends on the size of the particles, and it is found that particles with a particular size contribute the most to magnetic hardening.

Fast time-division color electroholography using a multiple-graphics processing unit cluster system with a single spatial light modulator

We demonstrate fast time-division color etectroholography using a multiple-graphics-processing-unit （GPU） cluster system with a spatial light modulator and a controller to switch the color of the reconstructing light. The controller comprises a universal serial bus module to drive the liquid crystal optical shutters. By using the controller, the computer-generated hologram （CGH） display node of the multiple-GPU cluster system synchronizes the display of the CGH with the color switching of the reconstructing light. Fast time-division color electroholography at 20 fps is realized for a three-dimensional object comprising 21,000 points per color when 13 GPUs are used in a multiple-GPU cluster system.

OPTIMIZATIONOFTHECONTINUOUSAFFINITY－RECYCLEEXTRACTIONPROCESS

Single step and multi step CARE processes are optimized by computer simulations based on the mathematical model proposed previously. The product of purification factor and recovery yield is used as the objective function for optimizing a single step process. The objective function for the optimization of a multi step process is considered to obtain an anticipated product purity at a maximum recovery yield and a minimum number of CARE inividuals. Pairs of the operating conditions (eluant and affinity recycle flow rates) exist to give the maximums of above objective functions when membrane rejections to ligates and contaminants are equal in value. The optimum affinity recycle flow rate decreases with the increase of membrane rejections and equilibrium binding fractions of ligates. For a multi step process, when contaminants are rejected less than ligate, only one pair of the optimum eluant and affinity recycle flow rates exists.

Unified representation of formulas for single birth processes

Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented.

SINGLE BIRTH PROCESSES

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

Criteria on ergodicity and strong ergodicity of single death processes

Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.

Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes

We obtain sufficient criteria for central limit theorems （CLTs） for ergodic continuous-time Markov chains （CTMCs）. We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we present an explicit expression of the time average variance constant for a single birth process whenever a CLT exists. Several examples are given to illustrate these results.

Moments of integral-type downward functionals for single death processes

We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes.Meanwhile,main results are applied to more general integral-type downward functionals.

On Variation of Single Birth Processes

Suppose {X（t）; t≥ 0} is a single birth process with birth rate qii＋l （i 〉 0） and death rate qij （i 〉 j ≥ 0）. It is proved in this paper that （i） if there exists aconstant c≥ 0 such that b（i）-a（i）＋ci is nondecreasing with respect to i and a（i） ＋ u（i） - ci ≥ 0 （i≥ 0）, then VarX（t）-EX（t）≥-X（0）e^-2ct,t≥0,or （ii） if there exists a constant u（i） - c≥ 0 such that b（i）-a（i）＋ci is non-increasing with respect to i and a（i）＋u（i）-ci≤0（i≥0）,then VarX（t） - EX（t） ≤ -X（0）e^-2c,t ≥ 0 Hereb（i） = qii＋1, a（0） = 0, a（i） = ∑j=^ijqii-j （i≥ 1）, u（0） = u（1） =0 and u（i） = 1/2∑j=^ij（j - 1）qii-j （i ≥ 2） . This result covers the results for birth-death processes obtained in [7].

Fluctuation Limits of the Single Point Catalytic Super-stable Processes

We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.