有趣的摆动数列

巴克尔说：“先怀疑，其次是探求，然后就有了发现．”遇到数学问题，敢于提出猜想，提出疑问，并下功夫探究，就可能有新的发现，并因此增长数学才干，提升思维品质．以下是我在学习中遇到的一个题目，探究起来饶有趣味，此处与大家共享．     

(V_s,V_t)平面双流网络中的最小费用最大双流

本文利用（υ_ｓ，υ_ｔ）平面双流网络的平面性，找出并证明了该网络中最小费用双流的充要条件，最后给出了一个算法并估计了复杂性．     

三圆盘扭振系统主共振的理论与实验研究

本文应用非线性振动的平均法，分析了一个具有立方非线性并受简谐激励作用的三圆盘扭振系统的第二阶主共振，求得了稳态响应的分岔方程，并进行了奇异性分析，理论结果与实验结果相符·     

模糊数学在城市交通控制中的应用

本文将模糊数学方法应用到城市交通系统，对城市交通控制系统实施模糊控制，并改进了Ｐａｐｐｉｓ等人的控制方法，仿真结果表明模糊数学能成功地应用到交通控制系统，并比传统的控制方法有效．     

L-Fuzzy Domain及其相关性质

基于[5]提出的L-fuzzy拟序集，引入L-fuzzy集关于L-fuzzy偏序的并，当L是完全分配格时L-fuzzy拟序集上的L-fuzzy定向集等概念，在此基础上定义L-fuzzy domain，证明它是通常Domain的模糊推广，并得到若干相关性质。     

一个抛物型方程不适定问题的小波正则化方法

一维抛物型方程如下定解问题狌狋＋狌狓＝狌狓狓， ０≤狓＜ ∞，０≤狋＜ ∞，狌（１，狋）＝犵（狋）， ０≤狋＜ ∞，狌（狓，０）＝０， 狓≥０烅烄烆．是一个不适定问题．数据犵的微小变化可以引起解的巨大误差．该文通过构造一个在频域具紧支集的小波并在尺度空间上展开数据和解，滤除了高频分量，并结和Ｇａｌｅｒｋｉｎ方法，建立了一种逼近准确解的正则化方法，恢复了解对数据的连续依赖性，并建立了误差估计．     

Abelian范畴中的Jordan-H(o)lder定理

利用Abdian范畴中子对象的交与并的性质，将模范畴中的蝴蝶结引理推广到Abelian范畴中，并据此证明了Abelian范畴中的Jordan-Holder定理．     

不同情形下供应链优化决策模型的比较分析

本文提出三种不同情形（制造商与零售商追求各自利润最大化，并且没有价格折扣策略；制造商与零售商共同追求总利润最大化，不实施价格折扣策略；制造商与零售商共同追求总利润最大化，并实施价格折扣策略）下供应链价格和库存补充策略的优化决策模型，并通过具体数例进行比较分析，结果表明，供应链合作并实施价格折扣策略时的供应链总利润最高，而供应链双方利润分配系数的变化对基于供应链总利润最大化的供应链优化决策没有影响．     

一类带非单调搜索的SQP算法

本文给出了一个SQP新算法，其特点是使用了非单调搜索，并不再使用严格互补条件，使得算法在一定阶段后具有十分简洁的形式并保持整体收敛与超线性收敛性．     

基于因素空间理论的直觉模糊概念外延构建及其在决策中的应用

在因素空间理论基础上，提出直觉模糊概念，从原概念及其对立概念的表现外延出发，构造了直觉模糊概念外延的两种逼近，并在此基础上提出了基于反馈外延双层包络的DFE决策方法，最后，给出操作步骤并通过实例对上述理论方法进行了应用。     

不可压缩理想势流绕两平行平板间圆柱流动的新的近似解析解

文献[1]得到了不可压缩理想势流绕两平行平板间圆柱流动的近似分析解.本文指出,用М.Е.Швец法[2]亦可得到与文献[1]完全相同的结果.如果用本文作者新提出的改进了的М.Е.Швец法[2]则可得到比文献[1]更加精确的结果.有算例.     

Exact Solutions of Compressible Flow Equations with Spherical Symmetry

In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [ 1 ], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of motion and continuity without reference to adiabatic or isentropic relation. These solutions are quite general and can be applied to nonadiabatic motions, such as the motions of interstellar gas clouds that lose energy by radiation. All the solutions found by McVittie [ 1 ] have linear velocity profile with respect to distance. We introduce a nonlinear form of the velocity function containing an arbitrary function of the similarity variable. Adiabatic conditions lead to a second-order ODE, which we discuss in some detail. We relate our work to the earlier investigations of Taylor [ 2 ], McVittie [ 1 ], and Keller [ 3 ].     

Existence and multiplicity of solutions for elliptic problems with indefinite discontinuous nonlinearities

In this paper we study the critical points for a locally Lipschitz functional that in some sense will be solutions of an elliptic problem with indefinite discontinuous nonlinearities. We should mention that our results were inspired by the work of Ambrosetti-Badiale [3], Arcoya-Calahorrano [5], Alama-Tarantello [1] and Chang [8]. For the problem studied in [3] we introduce indefinite nonlinearities as in [1] and [6]. To obtain the existence and multiplicity of solutions we use the critical points theory developed by Chang. Applications for Plasma Physics are considered with nonlinearities that change sign. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [1] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [1]. More precisely, following Ni's method (Section 6 of [5]), we give an elliptic proof of this theorem.     

A remark on entire solutions of quasilinear elliptic equations

By applying a main comparison theorem of Pucci and Serrin (2007) [2] we cover, for general equations of p-Laplace type, the open cases of Theorems B, D, E of Farina and Serrin (submitted for publication) [1] as described in Problems 2 and 3 of Section 12 of Farina and Serrin (submitted for publication) [1]. Moreover, we provide significant improvements of Theorem C and Theorem 5 of Farina and Serrin (submitted for publication) [1], the latter in the context of mean curvature type operators, see Theorem 1.3 and Theorems 5.2-5.4 below.Finally, Theorem 1.1 provides a new Liouville theorem outside the context of work in Farina and Serrin (submitted for publication) [1].     

多中心牛顿定理及其应用

本文将论文［１］推广到离散型的多中心泰勒定理。即多中心牛顿定理．从而得到相应的论文［２］．即高阶差分的插值公式，并给出其应用。     

Transformations of linear connections,II

We elucidate [9] with two applications. In the first we view connections as differential systems. Specializing this to trivial bundles overS ¹ and applying the theory of Floquet, we obtain equivalent connections with constant Christoffel symbols. In the second application we prove that the canonical connections of parallelizable manifolds (in particular Lie groups) can be obtained from the canonical flat connection of appropriate trivial bundles. Thus, the formalisms of [1], [4], [5] and [6] fit in the general setting of [9].     

ON VARMA''s LACUNARY INTERPOLATION BY SPLINES OHEN TIANPING

In articles [1], [2], A. K. Varma investigated some lacunary interpolations by Spline. In this article we point out a mistake in the proof of Theorem 2 in [1] and give a new proof. Moreover, the results obtained in [1], [2] are improved.     

ON VARMA''s LACUNARY INTERPOLATION BY SPLINES OHEN TIANPING

In articles [1], [2], A. K. Varma investigated some lacunary interpolations by Spline. In this article we point out a mistake in the proof of Theorem 2 in [1] and give a new proof. Moreover, the results obtained in [1], [2] are improved.