一维无限深势阱中粒子动量测量问题的分析与讨论

对在一维无限深势阱中运动的粒子的动量测量问题进行了全面的分析和仔细的讨论,补充了量子力学教材中对这个问题的处理.     

用算子展开法求解 Fredholm 积分方程

提供了另一种求解积分方程的方法。利用 Hilbert 空间来研究 Fredholm 积分算子,并证明了可利用一组标准正交基将 Fredholn 积分算子展开,从而使积分方程得到简化。应用这一方法给出了一般第二类 Fredholm 积分方程的严格解析解。文中还对具体积分方程进行了求解并与严格解和其它方法所得的解进行了比较,结果吻合得很好。     

股价波动持续性与反转收益

动量效应和反转效应是资本市场的热点话题,学术界给出了诸多解释,但鲜有文献从风险时变性视角关注到波动持续性的影响。基于2005—2021年我国A股市场个股数据,利用GARCH族模型度量股价波动持续性,分别通过投资组合分析与混同横截面分析,实证检验了个股股价波动持续性与股票预期收益之间的关系。研究发现:股价波动持续性与预期收益之间存在显著的负相关关系;通过构建多空组合,在买入波动持续性小的股票的同时卖出波动持续性大的股票,能够获得显著的超额收益。同时,针对我国A股市场存在“反转效应”的特征事实,进一步检验了股价波动持续性对反转收益的影响。经验证据表明,股价波动持续性放大了反转收益。因此,投资者可以通过纳入刻画股价波动持续性与反转效应的因子改善投资组合的业绩;监管部门应加强对股价波动持续性的实时关注,并将其作为系统性风险预警的重点指标。      

Modelling activity times by hybrid synthetic method

Uncertain (manual) activity times impact a number of manufacturing system modules: plant and layout design, capacity analysis, operator assignment, process planning, scheduling and simulation. Direct observation cannot be used for non-existent production lines. A hybrid direct observation/synthetic method derived from Method Time Measurement available in industry is proposed. To determine accurate activity times required by heuristics and metaheuristics optimisation, manufacturing system modules are modelled by MILP and operator efficiency parameters are used for time standardisation. Among human factors considered are skill and ergonomics. Application to the sterilisation of reusable medical devices is extensively described. Experimental data taken from observation on the field and a worst-case date have shown the model direct applicability for professionals also to non-manufacturing cases.     

论各向同性谐振子能级的又一求解方法

在经典力学中的中心力场中,除了能量E和角动量L两个运动积分外,还存在着第三个运动积分,即Runge－Lenz矢量,该矢量可算符化。以各向同性谐振子为例,运用Runge－Lenz矢量简洁地求解出量子力学中另一类典型问题——谐振子的能级公式,与求解薛定谔方程的结果一致,从中可看出用Runge－Lenz矢量处理问题的简洁性。     

Bounds to Memory Loss

If we express our knowledge in sentences, we will find that these sentences are linked in complex patterns governed by our observations and our inferences from these observations. These inferences are to a large extent driven by logical rules. We ask whether the structure logic imposes on our knowledge restricts what we forget and what we remember. The model is a two period S5 logic. In this logic, we propose a memory loss operator: the agent forgets a sentence pif and only if he knows pat time 1 and he does not know pat time 2. Equipped with the operator, we prove theorems on the relation between knowledge and memory loss. The main results point to classes of formulas that an agent cannot forget, and classes of formulas he must forget. A desirable feature is that most results hold in the S4 logic. The results illustrate bounds to memory loss, and thus to bounded rationality. We apply the model to single-agent conventions: conventions made between an agent and himself.     

幂级数的求和公式

运用微积分算子和它们的运算性质,得出幂级数的求和公式。