Functional asymptotic confidence intervals for the slope in linear error-in-variables models

Modified least squares processes (MLSP’s) and self-randomized MLSP’s are introduced in D[0, 1] for the slope in linear structural and functional error-in-variables models (EIVM’s). Sup-norm approximations in probability and, as a consequence, functional central limit theorems (CLT’s) are established for the data-based self-normalized versions of these MLSP’s and self-randomized MLSP’s. The MLSP’s are believed to be new types of objects of study, and the invariance principles for them constitute new asymptotics, in EIVM’s. Moreover, the obtained data-based functional CLT’s for the MLSP’s open up new possibilities for constructing various asymptotic confidence intervals (CI’s) for the slope that are named functional asymptotic CI’s here. Three special examples of such CI’s are given.     

A weak variant of Hindman’s Theorem stronger than Hilbert’s Theorem

Hirst investigated a natural restriction of Hindman’s Finite Sums Theorem—called Hilbert’s Theorem—and proved it equivalent over \(\mathbf {RCA}_0\) to the Infinite Pigeonhole Principle for all colors. This gave the first example of a natural restriction of Hindman’s Theorem provably much weaker than Hindman’s Theorem itself. We here introduce another natural restriction of Hindman’s Theorem—which we name the Adjacent Hindman’s Theorem with apartness—and prove it to be provable from Ramsey’s Theorem for pairs and strictly stronger than Hirst’s Hilbert’s Theorem. The lower bound is obtained by a direct combinatorial implication from the Adjacent Hindman’s Theorem with apartness to the Increasing Polarized Ramsey’s Theorem for pairs introduced by Dzhafarov and Hirst. In the Adjacent Hindman’s Theorem homogeneity is required only for finite sums of adjacent elements.     

多元函数的L’Hospital法则及应用

将一元函数的L’Hospital法则推广到多元函数,为求多元函数极限提供了一个有效的方法,从而丰富了L’Hospital法则的内容,使应用范围更广泛.     

考虑长短期努力的过度自信代理人激励机制

以相对净收益为标准设计代理人薪酬契约,同时考虑代理人过度自信及长短期努力水平,并区分长短期努力的冲突性与非冲突性,分别建立非货币效用计量模型和代理人最优激励模型,探索各项因素对代理人努力水平及业绩分享比例的影响。研究发现如下几点主要结论:第一,垄断行业代理人努力水平远远低于竞争性行业,且行业垄断程度越高,代理人努力水平越低。第二,行业垄断盈余比例与业绩分享比例之间的关系受委托人与代理人过度自信程度影响,当代理人过度自信系数高于委托人时,行业垄断程度越高,业绩分享比例越大,反之结论相反。第三,代理人对有利状态过度自信程度越高,对不利状态过度自信程度越低,代理人努力水平与业绩分享比例越高;委托人对有利状态过度自信程度越高,对不利状态过度自信程度越低,代理人努力水平与业绩分享比例越低。第四,代理人努力水平与边际非货币收益正相关,与边际非货币成本呈负向变化关系。     

Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents

A fundamental result in the theory of minimal rational curves on projective manifolds is CartanFubini extension theorem proved by Hwang and Mok,which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents(VMRT),under a mild geometric assumption on the second fundamental forms of VMRT’s.Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold,under the assumptions that the map sends VMRT’s onto linear sections of VMRT’s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT’s.In the current paper,we give a generalization of Hong and Mok’s result,under the same condition on second fundamental forms,assuming only that the holomorphic immersions send VMRT’s to VMRT’s.Our argument is different from Hong and Mok’s and is based on the study of natural foliations on the total family of VMRT’s.This gives a substantially simpler proof than Hong and Mok’s argument.     

Brouwer and Euclid

We explore the relationship between Brouwer’s intuitionistic mathematics and Euclidean geometry. Brouwer wrote a paper in 1949 called The contradictority of elementary geometry. In that paper, he showed that a certain classical consequence of the parallel postulate implies Markov’s principle, which he found intuitionistically unacceptable. But Euclid’s geometry, having served as a beacon of clear and correct reasoning for two millennia, is not so easily discarded.Brouwer started from a “theorem” that is not in Euclid, and requires Markov’s principle for its proof. That means that Brouwer’s paper did not address the question whether Euclid’s Elements really requires Markov’s principle. In this paper we show that there is a coherent theory of “non-Markovian Euclidean geometry”. We show in some detail that our theory is an adequate formal rendering of (at least) Euclid’s Book I, and suffices to define geometric arithmetic, thus refining the author’s previous investigations (which include Markov’s principle as an axiom).Philosophically, Brouwer’s proof that his version of the parallel postulate implies Markov’s principle could be read just as well as geometric evidence for the truth of Markov’s principle, if one thinks the geometrical “intersection theorem” with which Brouwer started is geometrically evident.     

不动点理论与里卡提方程两个正周期解的存在性

利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.     

Extended crystal PDE’s stability,I: The general theory

This work, divided in two parts, follows some our previous works devoted to the algebraic topological characterization of PDE’s. In this first part, the stability of PDE’s is studied in some details in the framework of the geometric theory of PDE’s, and bordism groups theory of PDE’s. In particular we identify criteria to recognize PDE’s that are stable (in extended Ulam sense) and in their regular smooth solutions do not occur finite time unstabilities, (stable extended crystal PDE’s). Applications to some important PDE’s are carefully considered. (In the second part a stable extended crystal PDE, encoding anisotropic incompressible magnetohydrodynamics is obtained Ref. [A. Prástaro, Extended crystal PDE’s (submitted for publication)].)     

Optimal control approach to stability criteria on Hill’s equations

This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill's equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov's criterion, Neǐgauz and Lidskiǐ's criterion. Secondly, we present stability criteria on Hill's equations with sign-changing potential in which Brog's criterion and Krein's criterion are included.     

不同权力结构对制造商双渠道供应链的影响研究

在一个制造商和一个零售商组成的供应链中, 制造商拥有线下传统渠道及线上直销双渠道。首先根据消费者剩余理论, 构建了制造商双渠道需求函数;接着分别构建了两类Stackelberg博弈及Nash博弈三种权力结构下制造商和零售商的利润模型并对模型进行了求解;最后分析了三种不同权力结构对制造商双渠道供应链的影响。研究发现:制造商线上直销渠道价格不受三种博弈权力结构的影响;线下传统渠道零售价格、需求, 线上直销渠道需求及制造商双渠道供应链总利润不受两类Stackelberg博弈权力结构的影响;线下传统渠道零售价格及线上直销渠道需求在Nash博弈权力结构下最小, 而线下传统渠道需求及供应链总利润在Nash博弈权力结构下最大;制造商批发价格、利润及零售商利润对三种博弈权力结构较敏感, 随供应链成员自身博弈权力地位的下降而逐渐降低。     

Comparison of Some Trigonometric Integrals

Mathematical Notes - We show that Preiss–Thomson’s AS-integral is inconsistent with Burkill’s SCPintegral, James’ P2-integral, and Denjoy’s totalization T2s over the...     

考虑产品环境质量和消费者惯性的电动汽车供应链策略分析

按是否拥有传统汽车将潜在消费者分成两类,基于不同购买行为的消费者,根据消费者购买行为理论,针对每一类消费者分别建立效用模型,运用斯坦伯格博弈理论求解得到厂商的最优定价策略和政府的最优补贴策略,进而分析政府考虑包括厂商收益、消费者剩余、政府支出以及环境效益在内的社会福利最大化时电动汽车的环境质量、传统汽车原拥有比例以及消费者惯性三因素对电动汽车普及率、政府补贴以及生产商收益的影响。研究结果表明:当生产成本小于某阀值时,电动汽车的市场需求随电动汽车的环境质量的增加而增大,传统汽车的市场需求则随之减小,反之亦然。电动汽车的生产效率较高时,政府的最优补贴随产品环境质量的增加而增大,生产效率较低时,最优补贴随之减小,政府通过增大补贴的方式鼓励生产商提高生产效率。最后通过数值实验验证了以上结论,并分析得到以上三方面因素对生产商收益的影响。     

New modified optimal families of King’s and Traub-Ostrowski’s methods

Based on quadratically convergent Schröder’s method, we derive many new interesting families of fourth-order multipoint iterative methods without memory for obtaining simple roots of nonlinear equations by using the weight function approach. The classical King’s family of fourth-order methods and Traub-Ostrowski’s method are obtained as special cases. According to the Kung-Traub conjecture, these methods have the maximal efficiency index because only three functional values are needed per step. Therefore, the fourth-order family of King’s family and Traub-Ostrowski’smethod are the main findings of the present work. The performance of proposed multipoint methods is compared with their closest competitors, namely, King’s family, Traub-Ostrowski’s method, and Jarratt’s method in a series of numerical experiments. All the methods considered here are found to be effective and comparable to the similar robust methods available in the literature.     

基于电子优惠券的多渠道整合策略研究

在由制造商的网络直销渠道和混合零售商的实体渠道和网络渠道所构成的多渠道供应链中,考虑存在消费者无缺陷退货和消费者对购买渠道偏好的异质性,研究了混合零售商的基于电子优惠券的多渠道整合策略问题。探明了混合零售商愿意采用电子优惠券实现多渠道整合的临界条件,揭示了多渠道整合策略对市场均衡的影响,并且构建了基于零售商订货量和接受消费者退货量的转移支付机制来协调多渠道供应链。     

A dynamic programming model for effect of worker’s type on wage arrears

We analyze how wage arrears are affected by the worker’s type (in this paper, the worker’s type means the worker’s attitude to wage arrears). Wage arrears cause workers’ negative emotion which may lead to serious social problem and the government may intervene. In this paper, we model the process of wage arrears as a Markov decision process in which the firm is the decision maker. We develop an optimal solution approach under the assumption that the worker’s negative emotion threshold (The worker’s negative emotion increases monotonically with increasing back pay. Once the cumulative back pay exceeds a particular value, the worker will take legal actions and the government will intervene. We define the particular value as the worker’s negative emotion threshold.) is normally distributed and provide insights into how wage arrears vary with the worker’s type and the government intervention. We propose the optimal government intervention which stops wage arrears and does not disturb the normal order of the market economy. We show that the intervention depends on the worker’s type and the results imply that the government intervention should be adjusted dynamically according to different regions, industrial sectors and time periods.     

纵向研发合作中的敲竹杠问题与合同设计研究

考虑纵向研发合作中合同的不完全性,分析了里程碑支付合同中开发单位的敲竹杠行为,建立了防敲竹杠问题的投资激励模型,给出了不同信息结构下研究单位的投资决策和开发单位的合同设计。研究结果表明:均衡解存在的情况下,信息对称时,研究单位获得的预付款和里程碑支付分别为零和其外部选择收益;信息不对称时,开发单位为研究单位提供了一个高低两种质量类型下预付款和里程碑支付相互平衡的信息甄别合同。比较分析发现:信息不对称时研究单位的投资水平更高,且研究单位拥有信息优势时的投资激励作用随着创新的关系专用性程度和高质量创新出现的概率递减,但随着两种类型创新的质量的比值递增。     

A Bowley solution with limited ceded risk for a monopolistic reinsurer

Borch (1969) advocated that the study of optimal reinsurance design should take into consideration the conflicting interests of both an insurer and a reinsurer. Motivated by this and exploiting a Bowley solution (or Stackelberg equilibrium game), this paper proposes a two-step model that tackles an optimal risk transfer problem between the insurer and the reinsurer. From the insurer’s perspective, the first step of the model provisionally derives an optimal reinsurance policy for a given reinsurance premium while reflecting the reinsurer’s risk appetite. The reinsurer’s risk appetite is controlled by imposing upper limits on the first two moments of the coverage. Through a comparative analysis, the effect of the insurer’s initial wealth on the demand for reinsurance is then examined, when the insurer’s risk aversion and prudence are taken into account. Based on the insurer’s provisional strategy, the second step of the model determines the monopoly premium that maximizes the reinsurer’s expected profit while still satisfying the insurer’s incentive condition. Numerical examples are provided to illustrate our Bowley solution.     

Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal

This paper proposes a general multi-scrolls and multi-wings attractor systems while combining in one hand, Julia’s process with Lorenz’s attractor and in another hand Julia’s process with two coupled Lorenz systems. We have also studied the combination of Julia’s process with the chaotic attractor system proposed in [1].     

Generalizations of Sherman’s Inequality Via Fink’s Identity and Green’s Function

Ukrainian Mathematical Journal - New generalizations of Sherman’s inequality for n-convex functions are obtained with the help of Fink’s identity and Green’s function. By using...