凸函数和凹函数的幂平均不等式

文 [1 ]获得了当 α≥ 1时的凸函数的幂平均不等式 (3)、(4 ) [1] .本文指出文 [1 ]中的一个错误 ,并且得到了 α≤ 1时的凹函数的幂平均不等式 .修正和充实了文 [1 ]的定理 .同时讨论了当 α取其它值时不等式的情况 .     

Smarandache函数的值分布性质

对于给定的自然数n,著名的Smarandache函数S(n)定义为S(n)=min{m: m∈N,n|m!|.本文主要目的是利用初等方法研究S(n)的值分布性质,并给出了一些有趣的渐近公式．     

常系数投资消费模型的一些优化性质

本文在有效易费的常系数投资消费模型下，讨论了折算函数和价值函数的一些基本性质，即给出了价值函数的凹性、连续性、正则性和变分不等式的粘性上解以及粘性解存在性等结果。     

Constructing the value function for an Integer Linear Programme over a Cone

The value function of an Integer Programme is the optimal objective value expressed as a function of the right-hand-side coefficients. For an Integer Programme over a Cone (ILPC) this takes the form of a Chvátal Function which is built up from the operations of taking non-negative linear combinations and integer round-up.A doubly recursive procedure for calculating such a value function is given. This is illustrated by a small numerical example.It is also shown how the optimal solution of an ILPC can be obtained as a function of the right-hand-side through this recursion. The connection with the Group optimization representation of an ILPC is also given together with a discussion of the difficulty of calculating the value function for a general Integer Programme.     

关于F.Smarandache LCM函数与除数函数的一个混合均值

利用初等及解析方法研究函数SL(n)与Dirichlet除数函数的加权均值问题,并获得一个有趣的渐近公式.     

多元函数中值定理中介值的渐近性

讨论了n元函数中值定理中介值的渐近性质.     

两个微分中值定理证明中辅助函数的多种作法

在数学分析中 ,三个微分中值定理极为重要 .在证明 Lagrange中值定理和 Cauchy中值定理时 ,都少不了作辅助函数 ,各种版本的《数学分析》或《高等数学》书本中 ,都只给出了一种形式的辅助函数 .为了扩展思路 ,给出了多种形式的辅助函数 ,并得出了一般形式 .     

考虑区间值的相对隶属函数与传统模糊分布函数的比较

通过分析比较,揭示了可变集理论中考虑区间值的相对隶属函数与传统的线性模糊分布函数之间的一些区别与联系,即传统的线性模糊分布函数是考虑区间值的相对隶属函数的一些特例,考虑区间值的相对隶属函数在描述模糊现象的模糊性时更具有普适性;同时指出了应用考虑区间值的相对隶属函数时应当注意的问题.     

时间序列中自相关与偏相关函数分析

相关函数表现出时间序列中任意两个值之间的相关性是如何随着时间间隔而改变的.自相关函数刻画了时间序列相邻变量之间的相关性,偏相关函数则是排除了其它中间变量的影响,真实地反映两个变量之间的相关性,并且二者紧密相连.同时两个相关图所反映的信息在时间序列分析各个方面发挥着关键作用.     

处处不连续又不可测的达布函数类的势

该文提出了一种构造处处不连续，而且在任何区间内取到任一函数值ｃ次的达布函数类的新方法，证明了该函数类的势为２＾ｃ（ｃ为连续统势）；还得到了处处不连续又不可测的达布函数类的势为２＾ｃ。     

代数体函数第二基本定理的一个推广

利用亚纯函数的Nevanlinna值分布理论,研究代数体函数第二基本定理的扩展形式,将该定理推广到两列互异且次数不超过d的多项式的情况,拓展了熊庆来、MillouX H等人的结果.     

Definition of the boundary in the local Charzynski-Tammi conjecture

According to the Charzynski-Tammi conjecture, the symmetrized Pick function is extremal in the problem on the estimate for the nth Taylor coefficient in the class of holomorphic univalent functions close to the identical one. In this paper we find the exact value of M ₄ such that the symmetrized Pick function is locally extremal in the problem on the estimate for the 4th Taylor coefficient in the class of holomorphic normalized univalent functions, whose module is bounded byM ₄.     

An algebroid function and its derivative

In this paper, we investigate the value distribution of an algebroid function and its derivative, and obtain two inequations between Nevanlinna characteristic function of an algebroid function and that of its derivative. We extend Chuang Chitai's theorem of meromorphic functions to algebroid functions.     

亚纯函数理论的一个基本不等式及其应用

本文首先证明了关于亚纯函数理论的一个基本不等式,进而用此不等式研究了与Hayman的一个结果密切相关的一类亚纯函数的值分布问题,得到如下结果:如果 f是一个超越亚纯函数,其所有零点的重数至少为k,则函数ff(k)取每一个有穷非零复数无穷多次,至多除去三个可能的例外正整数k=2,3,4．     

参数非线性规划中最优值函数的预不变凸凹性

本文给出了预拟不变单调函数的定义,提出了不变凸点到集映射、不变凹点到集映射的新概念,得到了不变凸点到集映射的一个充分必要条件,研究了参数非线性规划中最优值函数的预不变凸凹性。     

Generalization of the main equation of differential game theory

We consider feedback, two-person, zero-sum differential games. We obtain two inequalities for the directional derivatives of the nonsmooth value function. We show that these inequalities, together with the boundary conditions, constitute necessary and sufficient conditions which the value function must satisfy. In the region where the value function is differentiable, the inequalities become the well-known main equation of differential game theory (Isaacs-Bellman equation). The results obtained here may be useful in the approximation of the value function by piecewise smooth splines and also in the classification of singular surfaces.The author would like to thank Academician N. N. Krasovskii for his valuable advice and encouragement.     

区间数的绝对值与区间值函数的极限

研究了区间数的绝对值和区间值函数的极限问题.首先,讨论了区间数的H-差的性质,得到了H-差的两个运算法则;然后,给出了区间数的绝对值概念,并讨论了区间数绝对值的性质;最后,借助区间数的H-差和绝对值的概念,建立了区间值函数极限概念的一种新的表达方式,给出了极限存在的充分必要条件,证明了极限值的唯一性及对加法运算和数乘运算的封闭性.     

导数的性质及其应用

运用导数的思想来确定满足拉格朗日中值定理的一类函数,通过具体例子说明如何确定这些函数及由函数的n阶导数来判断函数的性质.     

关于k次加法补函数的因子函数的均值公式

对于任意正整数n,如果m n是完全k次方数,称最小非负整数m是n的k次加法补.为了研究m的性质及变化规律,这里运用初等数论和分析数论的方法,得到了d(n ak(n))的一个有趣的均值公式,从而得到了更一般的加法补函数的计算公式,完善了加法补函数在数论中的研究和应用.     

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.