On periodic solutions of nonlinear integral equations modelling infectious disease on measure chain

The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case and the discrete case . The model is described by the integral equation

where x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples.     

PARALLEL DYNAMIC ITERATION METHODS FOR SOLVING NONLINEAR TIME—PERIODIC DIFFERENTIAL—ALGEBRAIC EQUATIONS

In this paper we presented a convergence condition of paralle dynamic iteration meth-ods for a nonlinear system of differential-algebraic equations with a periodic constraint.The convergence criterion is decided by the spectral expressjon of a linear operator derived form system partitions.Numerical experiments given here confirm the theoretical work of the paper.     

基于复合腔的波长可调谐连续橙红色激光器

设计并研制了一种基于复合腔结构的波长可调谐、瓦级连续输出的橙红色激光器.该激光器是由半导体激光侧泵Nd∶GdVO_4晶体产生p-偏振1 062.9nm基频光的谐振腔和使用周期性极化晶体MgO∶PPLN(三个极化周期为29.0μm、29.8μm和30.8μm)的单共振光学参量振荡器组成.在两个谐振腔的重叠区域,利用Ⅱ类临界相位匹配KTP晶体对s-偏振信号光与p-偏振1 062.9nm基频光进行腔内和频.通过对MgO∶PPLN晶体进行三个不同极化周期的调谐和30℃~200℃范围内的温度调谐,在三个波段(613.4~619.2nm@29.0μm、620.2~628.9nm@29.8μm和634.4~649.1nm@30.8μm)获得了波长可调谐的橙红色激光连续输出,并在相应波段(3 980.0~3 758.5nm@29.0μm、3 714.2~3 438.3nm@29.8μm和3 278.0~2 940.2nm@30.8μm)获得了波长可调谐的中红外闲频光的连续输出.在30℃最低调谐温度,通过改变晶体的极化周期,在613.4nm、620.2nm和634.4nm处测得最大连续输出功率分别为1.52 W、2.21 W和3.03 W,对应的三束闲频光最大连续输出功率分别为2.36 W@3 980.0nm、3.17 W@3 714.2nm和4.13 W@3 278.0nm.     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

一种采用脉冲串的自适应有源干扰抵消器

在许多应用中，周期性干扰是由旋转的机械设备所产生的。一个周期性信号可以与一个特殊形式的周期性的脉冲串完全相干。本文提出了一种采用脉冲串的自适应有源噪声抵消器(AANC)来抵消周期性干扰，这种抵消器产生一个与干扰信号相同步的周期性的单位脉冲串作为参考输入。将这种有源噪声抵消器和Delayed-X LMS算法相结合，可以大大地减小运算量，并且也可以保证良好的收敛特性。理论分析和计算机仿真验证了本文的结果。     

On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends

We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the observational records of various complex systems ranging from climate dynamics to physiology, network traffic, and finance. In monofractal records, we find that (i) additive white noise hardly results in spurious multifractality, but causes underestimated generalized Hurst exponents h(q) for all q values; (ii) short-range correlations lead to pronounced crossovers in the generalized fluctuation functions F_q(s) at positions that decrease with increasing moment q, thus causing significantly overestimated h(q) for small q and spurious multifractality; (iii) periodicities like seasonal trends (with standard deviations comparable with the one of the studied process) result in spurious “reversed” multifractality where h(q) increases with increasing q (except for very short time windows). We also show that in multifractal cascades moderate additions of noise, short-range memory, or periodic trends cause flawed results for h(q) with q<2, while h(q) with q>2 remains nearly unchanged.     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

Appearance of pseudo-band-gaps in a disordered quantum wire array

The density of states and the conductivity are calculated in lateral superlattices with disorder in the period within a self-consistent Born approximation. Although the potential loses its periodicity on average due to disorder, it leads to an opening up of a pseudo-band-gap and modifies the conductivity perpendicular to the superlattice even qualitatively, when the energy reaches the zone boundary.     

Digital volume gratings

An optical element constructed by stacking a set of binary-phase grating sheets can simulate the functions of optically recorded volume gratings. Our electromagnetic numerical study also shows that if one of the grating sheets is replaced by another one with different grating period, power spectrum of the diffracted wave changes completely with extra diffraction orders. This property will claim strong advantage in security document applications. Analysis of alignment error reveals interesting phenomena concerning to how misalignment affects diffraction efficiency.