Bootstrap of the offspring mean in the critical process with a non-stationary immigration

In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents α and β, respectively. We prove that 1+2α is the threshold for the validity of the bootstrap in this model. If β<1+2α, the standard bootstrap is valid and if β>1+2α it is invalid. In the case β=1+2α, the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages.     

A fuzzy shortest path with the highest reliability

This paper concentrates on a shortest path problem on a network where arc lengths (costs) are not deterministic numbers, but imprecise ones. Here, costs of the shortest path problem are fuzzy intervals with increasing membership functions, whereas the membership function of the total cost of the shortest path is a fuzzy interval with a decreasing linear membership function. By the max–min criterion suggested in [R.E. Bellman, L.A. Zade, Decision-making in a fuzzy environment, Management Science 17B (1970) 141–164], the fuzzy shortest path problem can be treated as a mixed integer nonlinear programming problem. We show that this problem can be simplified into a bi-level programming problem that is very solvable. Here, we propose an efficient algorithm, based on the parametric shortest path problem for solving the bi-level programming problem. An illustrative example is given to demonstrate our proposed algorithm.     

堆积脉冲光参量啁啾脉冲放大器

以自启动被动锁模掺镱光纤堆积脉冲激光器为种子源,采用非共线相位匹配的方法,进行了光参量啁啾脉冲放大器的实验研究,得到了两级放大总增益为1.1×107,单脉冲能量为11 mJ,能量稳定性小于2％ rms,8 nm的放大谱宽.实验结果表明,采用这种结构的光参量啁啾脉冲放大器,放大增益高,系统稳定、结构紧凑、便于调节,同时通过调节种子源中的堆积器,可以得到不同宽度的放大信号脉冲.     

Parametric methods in integer linear programming

In contrast to methods of parametric linear programming which were developed soon after the invention of the simplex algorithm and are easily included as an extension of that method, techniques for parametric analysis on integer programs are not well known and require considerable effort to append them to an integer programming solution algorithm.The paper reviews some of the theory employed in parametric integer programming, then discusses algorithmic work in this area over the last 15 years when integer programs are solved by different methods. A summary of applications is included and the article concludes that parametric integer programming is a valuable tool of analysis awaiting further popularization.     

非线性E-V回归模型中参数估计的渐近性质

本文讨论了非线性E-V回归模型中参数的估计问题,构造了未知参数β0的最小二乘估计β和误差方差σ2的估计σ2,证明了β具有渐近正态性,同时也证明了σ2依概率收敛于σ2的速度可达到n-1/2.     

Stochastic resonance in circadian rhythms

The effect of fluctuations in the two-variable discrete delay model proposed earlier by us [1] for the circadian rhythm of the fungal species Neurospora Crassa is studied. We have investigated the effect of parametric and additive noise in two different regimes namely, steady-state and Period-1 regimes. It is found that under the influence of noise coherent oscillations are generated in the steady-state. Oscillations are preserved and robust to a wide range of noise intensity in the Period-1 regime. The oscillations in both these regimes are always found to be close to the circadian period (21.5 h). Coherence resonance is observed when parametric or velocity additive noise is added near the Hopf bifurcation. Finally, the implications of fluctuations in circadian rhythms are discussed. This article is dedicated to Professor Karl Jug on the occassion of his sixtyfifth birthday.     

The capture into parametric autoresonance

In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Holder continuity of solutions to a parametric variational inequality

We prove a Hölder continuity property of the locally unique solution to a parametric variational inequality without assuming differentiability of the given data.This research was supported by the World Laboratory (Lausanne).     

Optimization with additional variables and constraints

Norton, Plotkin and Tardos proved that—loosely spoken, an LP problem is solvable in time O(Tq^k+1) if deleting k fixed columns or rows, we obtain a problem which can be solved by an algorithm that makes at most T steps and q comparisons. This paper improves this running time to O(Tq^k).