Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation

T. Wanner We investigate global dynamics of the equation where the parameters b,c, and f are nonnegative numbers with condition b + c > 0,f ≠ 0 and the initial conditions x_?1,x₀ are arbitrary nonnegative numbers such that x_?1+x₀>0. We obtain precise characterization of basins of attraction of all attractors of this equation and describe the dynamics in terms of bifurcations of period‐two solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparative studies of eye-safe intracavity and extracavity optical parametric oscillators with an unstable telescopic cavity

We have experimentally studied the lasing characteristics of an eye-safe optical parametric oscillator (OPO) with an unstable telescopic cavity when it is placed inside (intracavity OPO) and outside (extracavity OPO) the plane-parallel cavity of a pulsed, nearly single-mode KGW:Nd pump laser. We used a KTP crystal as the nonlinear medium for the OPO. We have shown that the intracavity OPO has the higher lasing efficiency. We have observed that the distribution of nonlinear losses introduced by the intracavity OPO, nonuniform over the cavity cross section, leads to an increase in the diameter and divergence of the radiation beam from the pump laser and a dependence of its temporal lasing dynamics on the transverse beam coordinate. We propose a physical model qualitatively explaining the spatial and temporal lasing dynamics of a radiation source with an intracavity OPO. Both OPO versions generate beams of radiation with about the same divergence. When the KGW:Nd laser has an electrical pumping energy of 7.3 J and a cavity length of 77 cm, the intracavity OPO and the extracavity OPO emit pulses with energies of 14.5 mJ and 12.0 mJ and duration 18 nsec and 13 nsec respectively. The divergence of the eye-safe radiation (λ = 1.578 μm) at 86.5% of the total pulse energy is no greater than 5.5 mrad for an OPO output beam diameter of = 2 mm. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 535–543, July–August, 2006.     

Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.     

Stability of command economies

We consider the impact of fluctuations in the technology matrix A on two command input- output models. In the first, resources and goals are fixed and the model is solved for industrial production. If the growth rate can be zero, expected values of fluctuations of industrial goods are infinite. In the second, produced goods are scaled down to fit resources. Here we derive a criterion that

$\text{2log n}\text{k}$

should be small, where k is the number of significant ingredients in a good efficiency of aggregated economies, with n replaced by n₁/2 where n₁ is the number of goods aggregated into one.     

COIL非稳腔实验的数值模拟

 在薄层增益近似与非均匀加宽饱和增益系数条件下,用C-7程序对COIL非稳腔实验进行了数值模拟,计算所得结果对分析实验结果有一定参考价值。     

Cr,Ca：YAG晶体中四价Cr^4＋中心的晶场特性

综合分析了铬钙离子共掺钇铝石榴石晶体可见光－近红外区的室温吸收光谱,其中四配位和六配位的四价Ｃｒ＾２＋离子光谱成分是共存的,拟合得到的晶场参数符合光谱学的理论和实验规律,并且这两类Ｃｒ＾４＋中心的晶声性质均受到晶体中二价补偿离子Ｃａ＾２＋的影响。     

不同皮秒非稳腔中的KTP晶体的腔内倍频效应

以ＫＴＰ晶体作为Ｎｄ：ＹＡＰ锁激光器的内腔倍频元件,在带非共振环（ＡＲＲ）的对撞脉冲锁模（ＣＰＭ）非稳腔虚共焦非稳腔中实现高效倍频转换,其倍频能量转换效率 ５３．４％和６０．２％,测定了两种腔型的基波脉宽分别为８ｐｓ和１８ｐｓ,二次谐波输出的最大能量起伏分别为１０．６％和１２．５％。理论分析了两种没腔型及其实验结果的特点。     

用AFM研究阳极氧化铝的不稳定生长

用原子力显微镜(AFM)研究了多孔阳极氧化铝(AAO)模板的不稳定生长. 结果表明:AAO模板的不稳定生长导致了纳米孔道结构有序度的降低.在H₃PO₄溶液中生长的AAO模板孔道结构稳定性较差;而在H₂C₂O₄溶液中生长的AAO模板稳定性依赖于氧化电压和电流密度,在低电压和电流密度下稳定性较好,高电压和电流密度下稳定性较差. 充分利用这种不稳定生长特性,通过控制AAO模板的阳极氧化条件,可得到具有分枝孔道结构的特殊模板,这为利用模板法制备各种Y形或T形纳米线、管提供了新的发展空间.     

Invariant manifolds near a minimizer

A classical result, studied, among others, by Carathéodory [C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989], states that, for second-order, scalar equations, nondegenerate periodic minimizers are hyperbolic. Consequently, the Stable/Unstable Manifold Theorem applies, and implies that, at least locally, the stable and unstable sets are regular curves intersecting transversally at the nondegenerate minimizer.For analytic equations, there is a version of this fact which holds for isolated, but possibly degenerate, minimizers.     

第八种统计分布、涨落及热力学平衡态的稳定性

由Jaynes最大信息熵原理及拉格朗日乘子法推导出第八种统计分布,通过引入非广延熵常数的方法解决了零系综的困难.理论验证表明:本文推导出的第八种分布(N-E-V分布)不仅适用于小系统,而且适用于大系统.由此分布计算的理想量子系统的热力学量与7种分布相同,但广延量相对涨落却是正比于1的.这不仅可以解释临界现象, 也说明热力学平衡态及近平衡定态并不总是稳定的.