产品多方面差异下双寡头定位定价模型

建立在同类产品存在多方面差异条件下双寡头企业两阶段动态定位定价博弈模型,在市场中存在不同类型消费者时,求出了使企业利润最大化的子博弈精炼纳什均衡,并深入分析了消费者对两家企业平均偏好效用差(ΔU)和企业的运输成本率(t)对企业定位定价策略的影响.     

广义Fibonacci数的一些恒等式

利用非数学归纳法,以及广义Fibonacci数的性质,得到了广义Fibonacci数的一些求和公式.     

Boundary normal pressure-based electrical conductivity reconstruction for magneto–acoustic tomography with magnetic induction

As a kind of multi-physics imaging approach integrating the advantages of electrical impedance tomography and ultrasound imaging with the improved spatial resolution and image contrast, magneto–acoustic tomography with magnetic induction(MAT-MI) is demonstrated to have the capability of electrical impedance contrast imaging for biological tissues with conductivity differences. By being detected with a strong directional transducer, abrupt pressure change is proved to be generated by the gradient of the induced Lorentz force along the force direction at conductivity boundary. A simplified boundary normal pressure(BNP)-based conductivity reconstruction algorithm is proposed and the formula for conductivity distribution inside the object with the clear physical meaning of pressure derivative, is derived. Numerical simulations of acoustic pressure and conductivity reconstruction are conducted based on a 2-layer eccentric cylindrical phantom model using Hilbert transform. The reconstructed two-dimensional conductivity images accord well with the model, thus successfully making up the deficiency of only imaging conductivity boundary in traditional MAT-MI. The proposed method is also demonstrated to have a spatial resolution of one wavelength. This study provides a new method of reconstructing accurate electrical conductivity and suggests the potential applications of MAT-MI in imaging biological tissues with conductivity difference.     

从数学解题看数学美

本论述了“教学好玩”(陈省身语)的五个方面；教学语言精确；教学发现(类比发现；归纳发现和直党发现)；教学解题思路；教学思想方法和数学应用都体现了教学关。     

三维拟线性波方程的小初值光滑解

对三维小初值拟线性波方程3∑(i,j=0)g~(ij)(u)■_(ij)u=0,H.Lindblad证明了它有整体光滑解.本文考虑如下带有小初值的拟线性波方程3∑(i,j=0)g~(ij)(u)■_(ij)u=(■u)~3,通过得到低阶导数的衰减估计和高阶导数的能量估计,由连续论证法证明了这个方程也存在整体光滑解.     

Extremal graphs for the k‐flower

The Turán number of a graph H, , is the maximum number of edges in any graph of order n that does not contain an H as a subgraph. A graph on vertices consisting of k triangles that intersect in exactly one common vertex is called a k‐fan, and a graph consisting of k cycles that intersect in exactly one common vertex is called a k‐flower. In this article, we determine the Turán number of any k‐flower containing at least one odd cycle and characterize all extremal graphs provided n is sufficiently large. Erdős, Füredi, Gould, and Gunderson determined the Turán number for the k‐fan. Our result is a generalization of their result. The addition aim of this article is to draw attention to a powerful tool, the so‐called progressive induction lemma of Simonovits.     

HCHO-(DL-苹果酸)-BrO-3-Mn2+-H2SO4体系化学振荡反应动力学研究

研究了HCHO参与下的(DL-苹果酸)-BrO-3-Mn2+-H2SO4化学振荡反应体系的非线性动力学行为,考察了该体系中各反应物的初始浓度范围及主要影响因素. 结果表明,在5.0×10-5～1.0×10-2 mol·L-1范围内, HCHO对振荡反应的诱导期和周期有较大影响,且HCHO浓度的对数lnc(HCHO)与诱导期倒数的对数ln(1/tin)及周期倒数的对数ln(1/tp)均存在线性关系. 诱导期和周期的表观活化参数分别为70.87,55.71 kJ·mol-1. 另外还对HCHO参与下的可能振荡反应机理进行了探讨.     

Extending the applicability of Secant methods and nondiscrete induction

We use nondiscrete mathematical induction to extend the applicability of the Secant methods for solving equations in a Banach setting. Our approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where our results apply but earlier ones fail to solve nonlinear equation as well as tighter error bounds are also provided in this study.     

Factorization in generalized power series

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.

     

Cost-optimal multistage sampling plans in statistical quality control

Multistage Bayesian decision procedures in statistical quality control are known from attribute sampling. In this paper they are introduced in a more general framework occuring in lot-control by using the theory of Bayesian sequentially planned decision procedures. We show that under sufficiency and transitivity assumptions and monotonicity properties concerning the distribution and cost set-up these Bayes-procedures have (z, c ^–,c ⁺)-structure which, on one hand, generalizes results of K.-H. Waldmann and, on the other hand, reduces computational effort significantly. Finally, examples taken from attribute sampling and life testing for an outgoing lot are presented.The theory presented in this paper is taken from [11].