经济弹性函数的几何解释

弹性函数是研究当自变量有微弱变化时 ,函数的相对变化率 .本文构造一条初始弹性直线 ,弹性函数就是函数的切线斜率与初始弹性直线斜率之比 ;也是函数在弹性支点的微分与初始弹性直线在弹性支点的增量之比 .     

需求弹性与供给弹性的几何特征

常见的通过需求曲线(D)或供给曲线(S)的陡峭或平缓程度来研究需求弹性或供给弹性的大小,是不确切的、不全面的.为了更好地掌握弹性的大小变化,本文引进等弹性曲线簇的概念与图形,讨论需求弹性与供给弹性的几何特征,并通过实例分析更确切全面地比较需求弹性或供给弹性的大小.     

关于需求价格弹性的探讨

需求价格弹性是管理经济学中的一个重要概念,是指导市场行为的重要指标,如何理解需求价格弹性概念,掌握弹性的计算方法就显得格外重要.本文探讨需求价格弹性的概念及计算方法.     

半空间的热弹性问题——弹性通解方法的应用

本文基于弹性力学的通解,求解了半空间的热弹性问题.这种解法对于轴对称问题及半平面问题特别有效.应用这种解法我们对几种典型的热弹性半空间问题进行了求解.     

商品的总收益弹性与需求弹性守恒定理及其应用

本文介绍和证明了同一商品的总收益弹性与需求弹性守恒定理［１］及其推论，获得了一个重要公式，即ＥＲ±Ｅｄ＝１（ＥＲ即商品的总收益弹性，Ｅｄ即需求弹性）并以市场上常见的商品为例，列举了这一公式在经济预测决策方面的种种应用。     

非均匀法向荷载下半空间的二阶弹性效应问题

本文提供各向同性弹性半空间，在非均匀分布法向荷载下，二阶弹性效应的一个封闭形式解，运用积分变换方法，讨论了按Ｈｅｒｔｚ规律分布的荷载情形；导出了不可压缩各向同性弹性材料的极限解；算出了上述二阶弹性材料问题在ｚ方向的位移和法向应力数值。我们发现，与线弹性情形相比较，在二阶弹性材料中相应位移增大而法向应力减小。     

参考价格效应下报童模型的定价和库存联合策略研究

考虑带有消费者参考价格效应的具有乘项需求的价格报童模型,未满足的需求全部损失.基于平均销售的库存因子弹性定义了一类新的因子弹性-带有参考价格效应的平均销售库存因子弹性,借助此因子弹性和需求价格弹性分别分析了参考价格以及需求随机性对最优价格、订货量、最优利润以及最优服务水平的影响.最后,通过数值试验验证了结论的正确性.     

弹性电介质复合材料的多极材料力学

本文根据物质材料的多极概念研究了弹性电介质复合材料的宏观力学和电的性质.特别是:运用多极物质材料的统计连续体理论,可以得到不均匀颗粒间的电弹性相互作用和微结构(尺寸、形状、取向…)对复合材料的宏观性质的影响.本文首先给出了在某一无限的弹性电介质体中具有电极化的椭球的弹性不均匀性的基本解,这个解是由于电弹性相互作用而对Eshelby的经典弹性解的修正.其次,本文导出了电弹性相互作用的弹性电介质复合材料的宏观本构关系和宏观材料参量,最后对稀释的复合材料的具有统计的异向性的、形状效应的、以及电弹相互作用的一些问题进行了定量计算.     

电磁场中变厚度载流圆板的非线问题

本文建立了在非定常电磁场和机械场作用下变厚度载流弹性圆板在非线性变形状态下的磁弹性二维关系方程和运动方程，给出了弹性圆板在轴对称条件下的数值解．     

随机需求弹性及在经济分析中的应用

引入随机弹性的概念及随机弹性的相关性质，进而给出随机需求弹性．利用随机需求弹性分析了当消费群体的收入为随机变量时，其收入对需求量的变化和影响．给出了当收入服从某种分布时，需求量的弹性分布．     

Bidding under price uncertainty in multi-unit pay-as-bid procurement auctions for power systems reserve

In this paper a methodology for profit maximized bidding under price uncertainty in a day-ahead, multi-unit and pay-as-bid procurement auction for power systems reserve is proposed. Within this novel methodology a bidder is considered to follow a Bayes-strategy. Thereby, one bidder is assumed to behave strategically and the behavior of the remaining is summarized in a probability distribution of the market price and a reaction function to price dumping by the strategic bidder. With this approach two problems arise: First, as a pay-as-bid auction is considered, no uniform price and therefore no single probability distribution of the market price is readily available. Second, if historic bidding data of all participants are used to estimate such a distribution and market power is a relevant factor, the bid of the strategically behaving bidder is likely to influence the distribution. Within this paper for both of the problems solutions are presented. It is shown that by estimating a probability of acceptance the optimal bidding price with respect to a given capacity can be calculated by maximizing a stochastic non-linear objective function of expected profit. Taking the characteristics of recently established markets in Germany into account, the methodology is applied using exemplary data. It is shown that the methodology helps to manage existing price uncertainties and hence supports the trading decisions of a bidder. It is inferred that the developed methodology may also be used for bidding on other auction markets with a similar market design.     

A Study on Abnormality in Variational and Optimal Control Problems

In this paper, a variational problem is considered with differential equality constraints over a variable interval. It is stressed that the abnormality is a local character of the admissible set; consequently, a definition of regularity related to the constraints characterizing the admissible set is given. Then, for the local minimum necessary conditions, a compact form equivalent to the well-known Euler equation and transversality condition is given. By exploiting this result and the previous definition of regularity, it is proved that nonregularity is a necessary and sufficient condition for an admissible solution to be an abnormal extremal. Then, a necessary and sufficient condition is given for an abnormal extremal to be weakly abnormal. The analysis of the abnormality is completed by considering the particular case of affine constraints over a fixed interval: in this case, the abnormality turns out to have a global character, so that it is possible to define an abnormal problem or a normal problem. The last section is devoted to the study of an optimal control problem characterized by differential constraints corresponding to the dynamics of a controlled process. The above general results are particularized to this problem, yielding a necessary and sufficient condition for an admissible solution to be an abnormal extremal. From this, a previously known result is recovered concerning the linearized system controllability as a sufficient condition to exclude the abnormality.     

A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games

In this paper, a scalar game is derived from a zero-sum multicriteria matrix game, and it is proved that the solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Pareto-optimal security strategy (POSS) for one of the players in the original game. This is done by proving that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.This work was done while the author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.The author wishes to express his gratefulness to Professor U. R. Prasad for helpful discussions and to two anonymous referees for suggestions which led to an improved presentation.     

A comparison of two sourcing tactics for a new component

We compare two sourcing tactics for a manufacturer to purchase a new component to be used in a one-time production run of a new product with uncertain and price-elastic demand. One alternative is to issue a request-for-quote (RFQ), which is where the manufacturer requests a price-quantity schedule from suppliers. The manufacturer uses this information to determine a production quantity and the number of components to purchase from each supplier. The other alternative is to post a bid specifying how the manufacturer’s purchase quantity will depend on the supplier’s component price. The suppliers use this information to compete on quantity.We find that relative to RFQ, which is more challenging for the manufacturer to characterize the supplier response due to the possibility of supplier interaction, the benefit to the manufacturer from posting a bid increases with the number of suppliers due to increased intensity of competition. If the new component is from an emerging industry where there is little mutual awareness among candidate suppliers, then regardless of number of suppliers, expected manufacturer profit is higher under RFQ. Posting a bid is more likely to benefit the manufacturer when the new component is from a more established industry with a high degree of awareness among candidate suppliers.     

Persistence Terrace for Topological Inference of Point Cloud Data

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online.     

Truncated Smoothing Newton Method for l_∞ Fitting Rotated Cones

In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use l∞ norm than l2 norm. l∞ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large...     

A Friedrichs–Maz'ya inequality for functions of bounded variation

The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that it is rather elementary, if the basic background in the theory of functions of bounded variation is assumed. Nevertheless, it allows to extend all the previously known versions of this fundamental inequality to a completely general version. In fact the inequality presented here is optimal in several respects. As already observed in previous proofs, the crucial step is to provide conditions under which a function of bounded variation on a bounded open set, extended to zero outside, has bounded variation on the whole space. We push such conditions to their limits. In fact, we give a sufficient and necessary condition if the open set has a boundary with σ‐finite surface measure and a sufficient condition if the open set is fully arbitrary. Via a counterexample we show that such a general sufficient condition is sharp.     

年龄点t0之后的NBU性的非参数检验方法

NBU＊t0寿命分布中新元件的寿命随机地大于旧的年龄不小于t0的元件的剩余寿命,这为更广泛地模拟元件的老化和劣化现象提供了丰富的内容。本文首先对那些t0年龄点之后剩余寿命随机等于新元件寿命的元件的结构加以刻画,然后建立了一个非参数检验方法以区分这种随机等价性和t0年龄点后的严格的NBU性,并给出了针对一个NBU＊t0但非NBU的寿命分布的例子的数值模拟结果。     

离散多时滞广义不确定系统的变结构控制

研究了线性离散多时滞广义不确定系统的变结构控制的综合与设计问题.首先引入了一种新的受限系统等价分解形式,把所给的系统分解成两个低维的子系统:一个是不带控制项的差分系统;一个是带有控制项的差分系统.其次,根据上面的分解形式及离散时滞广义系统鲁棒稳定性的有关结果,设计了带有差分补偿器的切换函数,使得系统在准切换流形上的运动渐近稳定.然后在不确定项有界的条件下,设计了离散变结构控制律,使得在此控制律的作用下,系统从状态空间中任意一点出发的解的轨迹,于有限步内或者到达准切换流形,此后在准切换流形上渐近滑向原点;或者进入准切换流形的一个小邻域内,并稳定于原点邻域内的一个小的抖振.最后给出了数值例子以说明该综合设计方法的可行性与简便性.     

Power-series approximations for the optimal feedback control of noisy nonlinear systems

Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms.