The Scaling Constant D in Item Response Theory

In item response theory (IRT), the scaling constant D = 1.7 is used to scale a discrimination coefficient a estimated with the logistic model to the normal metric. Empirical verification is provided that Savalei’s?[1] proposed a scaling constant of D = 1.749 based on Kullback-Leibler divergence appears to give the best empirical approximation. However, the understanding of this issue as one of the accuracy of the approximation is incorrect for two reasons. First, scaling does not affect the fit of the logistic model to the data. Second, the best scaling constant to the normal metric varies with item difficulty, and the constant D = 1.749 is best thought of as the average of scaling transformations across items. The reason why the traditional scaling with D = 1.7 is used is simply because it preserves historical interpretation of the metric of item discrimination parameters.

An Inventory Model of Production with Level Dependent Demand Allowing Few Defective Items

This paper considers a model regarding the products with finite life which allows defective items in reproduction and causes a small amount of decay. The market demand is assumed to be level dependent linear type. The model has also considered the constant production rate which stops after a desired level of inventories and that is the highest level of it. Due to the market demand, defective item and product’s decay, the inventory reduces to the zero level where again the production cycle starts. With a numerical search procedure, the proof of the proposed model has been shown. The objective of the proposed model is to find out the total optimum inventory cost, optimum ordering cost and optimum ordering cycle.

An Ordering Policy for Deteriorating Items with Time-Dependent Quadratic Demand and Salvage Value under Permissible Delay in Payment

The article deals with an economic order quantity (EOQ) inventory model for deteriorating items in which the supplier provides the purchaser a permissible delay in payment. This is so when deterioration of units in the inventory is subject to constant deterioration rate, demand rate is quadratic function of time and salvage value is associated with the deteriorated units. Shortages in the system are not allowed to occur. A mathematical formulation is developed when the supplier offers a permissible delay period to the customers under two circumstances: 1) when delay period is less than the cycle of time;and 2) when delay period is greater than the cycle of time. The method is suitable for the items like state-of-the-art aircrafts, super computers, laptops, android mobiles, seasonal items and machines and their spare parts. A solution procedure algorithm is given for finding the optimal order quantity which minimizes the total cost of an inventory system. The article includes numerical examples to support the effectiveness of the developed model. Finally, sensitivity analysis on some parameters on optimal solution is provided.

恒温加热台温度偏差的测量不确定度评定

恒温加热台主要用于提供一个温度可调节、均匀稳定的平面温场,广泛用于半导体器件焊接加工,以及材料理化分析及生物工程等领域。随着相应的校准规范的发布与实施,规范恒温加热台的校准工作迫在眉睫,测量不确定度的评定更能更加体现校准工作的严谨性,本文依据相应的校准规范,简述恒温加热台的校准条件、校准项目及方法,对恒温加热台温度偏差的测量不确定度进行评定。

带常利率和干扰项的负风险模型相关性质

为解决基本负风险模型与保险公司实际运营的偏差问题,在考虑了其他因素影响的前提下,建立了同时含有常利率和干扰项的负风险模型,使其更加贴近保险公司及经营性公司的实际情况.首先采用矩母函数的定义及相关性质推导了新模型的基本性质,介绍了调节系数的概念,然后利用切比雪夫不等式证明了新模型破产概率的表达式以及破产概率所满足的Lundberg上界,最后通过数值模拟,分别分析了两种因素对新模型破产概率上界的影响.结果表明:在干扰项不变的情况下,新模型的破产概率上界会随着利率的增加而减小;在利率不变的情况下,破产概率上界会随着随机因素的干扰而变大.该成果对保险公司的实际运营具有一定的指导意义.

基于误差方程常数项的选权稳健数据处理方法研究

相对稳健估计选权迭代法中基于观测值首次平差后的残差进行选权迭代,基于误差方程常数项的选权迭代方法将初权的设置于平差前进行,削弱了粗差观测值对其它正常观测值平差后残差的不利影响,提高了测绘数据处理的质量。

二阶常系数线性非齐次微分方程的一些解法

我们探讨了如何求二阶常系数线性齐次微分方程的解,利用通解的结构和自由项的形式来求解;利用通解公式来求解。

一种快速的定雅可比潮流算法

完美地组合了电流注入型潮流算法和保留二阶项的快速潮流算法的优点,弥补了二者的不足之处,提出了一种快速的定雅可比潮流算法。该算法修正方程式的雅可比矩阵是通过对电流注入型潮流算法PQ节点的雅可比矩阵进行改造而得来的,是一个对称的常数雅可比矩阵。修正方程式的常数项是在保留潮流方程式非线性项的基础上进行简化改进而获得的,是一个非常简单的修正公式,在迭代过程中完全不需要进行节点电压的修正和节点功率的计算。这些处理,既保证了算法的收敛性,又大大提高了计算速度。详细论述了该算法的原理及用法。最后将它与牛顿法、定雅可比牛顿算法、PQ分解法、快速解耦法(FDLF)等潮流算法在多个算例上进行了收敛性能和收敛速度的比较,结果证明该算法收敛速度远大于牛顿法和定雅可比牛顿算法,收敛能力与定雅可比牛顿算法相当,算法适用能力比PQ分解法和快速解耦法强。