Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

Socially responsible merchant operations: Comparison of shutdown-averse CVaR and anticipated regret policies

Commodity and energy production assets are managed as real options on market uncertainties. Social impacts of plant shutdowns incentivize balancing asset value with shutdown probability. We propose new shutdown-averse policies based on the popular dynamic conditional value-at-risk (CVaR). We analytically and numerically compare these policies to known shutdown-averse policies based on anticipated regret (AR). Our findings support the use of AR over CVaR to embed shutdown-aversion and the consideration of hybrid policies that are asymptotically time-consistent but easily interpretable.     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.     

一类生物流体力学模型的稳定性

在研究颅内压集中参数模型的基础上，改进自适应的龙格-库塔法对一类生物流体力学模型进行数值模拟。通过合理控制计算量，得到了微分方程近似解的局部截断误差的估计。使用矩阵特征值分析微分方程的稳定性，在实际生理范围内变化模型参数，得到特征值随参数变化的关系，指出模型中存在实部为正的特征值。文章还讨论了控制矩阵特征值的变化对数值方法稳定步长的影响，并得到步长的取值范围。通过理论分析。得到控制方程的解随时间的发展和模型中生理参数的选取相关。分析了特征值变化的稳定性和参数的关系，并对模型进行改进，讨论其稳定性的情况。     

柔性壁面湍流边界层相干结构控制的实验研究

本文利用热膜测速技术对刚性壁面和柔性壁面湍流边界层的流向速度分量进行了实验测量,首先研究了柔性壁面对平均速度分布和湍流度分布的影响,结果表明:柔性壁面的边界层速度分布在对数律层向上有所平移,缓冲层加厚,具有一般的壁面减阻特征;而柔性壁的湍流度比刚性壁的湍流度要低,分布也更为平坦。然后综合运用自相关法和条件采样技术研究了湍流近壁区的相干结构,结果表明:刚性壁自相关曲线的第二峰值出现的时间比柔性壁的短,柔性壁的猝发频率比刚性壁的低许多。实验结果表明柔性壁面具有一定的减阻作用。     

用人工产生的拟湍流信号检验相干结构的检测方法

本文利用计算机产生拟湍流脉动信号，将数据进行频谱分析和能谱分析，发现湍流中相干结构不仅包合低频成分还包含一定数量高频成分，因而简单地认为湍流中低频部分是相干结构而高频部分是小尺度脉动，来确定相干结构能量在湍流中所占成分是不科学的；本文还将得到的数据用几种条件采样方法检测相干结构数量和位置，以此判断检测方法的优劣，发现就这类信号而言ＭＵ—ＬＥＶＥＬ法要比ＶＩＴＡ法准确性要高一些。     

吹吸扰动对壁湍流相干结构的影响

采用热线风速仪测量受吹吸扰动的壁湍流边界层的流向速度，用傅里叶变换和子波变换研究 吹吸扰动对壁湍流能谱的影响，结果显示施加的低频扰动使边界层内层大尺度结构的能量减 少，小尺度结构的能量有所增强，远离壁面时扰动强度逐步衰减直到在外层中消失；通过VITA 法和子波变换法检测猝发事件，表明该扰动降低了猝发强度，使猝发周期延长，条件平均速 度波形的幅值降低、持续时间变短，说明扰动明显抑制了相干结构的猝发过程. 利用子波变 换可以实现湍谱分析，能有效检测猝发中的湍流结构，是一种客观的分析工具.     

Resistance of a circular pipe with pulsatory variation of the flow rate

The results of an experimental investigation of the hydraulic resistance of a circular pipe for turbulent flow with periodic flow rate fluctuations are presented. The presence of resonance phenomena in the pipe is revealed. It is established that, for hydrodynamic nonstationarity, the pipe resistance is a nonmonotonous function of the frequency of the imposed flow rate fluctuations and differs from the pipe resistance in the stationary flow regime. Under the conditions considered, to find the pipe resistance it is necessary to take into account the variation of the flow kinetic energy with respect to the phase of the imposed flow rate fluctuations due to the deformation of the velocity profile.     

Minimum Divergence Estimators,Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).