对积分型Lupas-Bézier算子收敛阶的估计

对函数f的积分型Lupas-Bézier算子在区间[0,∞)上的收敛阶进行估计.在Zeng等人关于积分型Lupas-Bézier算子的收敛阶研究的基础上,对其所给的估计结果作进一步的改进,得到更精确的系数估计.     

有界变差函数的Durrmeyer-Bézier算子收敛阶的估计

在Zeng等人对有界变差函数f的Durrmeyer-Bézier算子在区间(0,1)上收敛于(1/(α+1))f(x+)+(α/(α+1))f(x-)的收敛阶进行研究的基础上,利用基函数的概率性质等方法,对其所给的Durrmeyer-B啨zier算子收敛阶估计结果作进一步的改进,得到其收敛阶的精确估计.     

Fejér不等式加强形式的推广

通过建立积分恒等式,将一个关于4阶可微函数的Fejér不等式的加强形式推广到关于2n-1(n≥2)阶可微函数的Fejér型不等式.对此新推广的不等式还给出了若干误差估计.     

指数平均Bézier曲线族

利用指数平均族与Béier曲线结合定义了指数平均Bézier曲线族.首先研究了指数平均族,阐述了指数平均族的单调性和正规性,其次由Bernstein函数定义得到n次s阶指数平均Bernstein函数,讨论了它与函数f之间的关系,最后,研究指数平均Bézier曲线族的性质,讨论了它的升阶,de casteljan算法,分割定理等.     

带形状参数的T-Bézier曲线

给出了n阶带形状参数的三角多项式T-Bézier基函数.由带形状参数的三角多项式T-Bézier基组成的带形状参数的T-Bézier曲线,可通过改变形状参数的取值而调整曲线形状,随着形状参数的增加,带形状参数的T-Bézier曲线将接近于控制多边形,并且可以精确表示圆、螺旋线等曲线.阶数的升高,形状参数的取值范围将扩大.     

二次及三次Hermite-Padé逼近中的几个问题

给出了二次Hermite-Pad啨逼近的对偶性.证明了三次Hermite-Pad啨逼近的局部唯一性,并对其逼近阶进行估计.     

对于局部有界函数的积分型Szász-Bézier算子的逼近估计

引入一种积分型的 Szász- Bézier算子 ,并研究其逼近性质 ,得到了此类算子对局部有界函数的逼近阶估计公式     

函数分段有理二次Bézier插值与逼近

依据几何特征对函数进行合理分段,定义了函数的分段三角形凸包,给出了控制多边形的确定方案,详细地讨论了函数的分段有理二次Bézier插值算法.定义了一种便于计算的新型误差,在此误差意义之下,插值算法的精度高于已有的逼近算法.数值实验结果表明了算法的可行性和有效性.     

Lévy型算子所生成马氏过程的稳定性

利用Lévy型算子积分微分型表示形式和拟微分型表示形式,以寻求Lévy型算子生成的马氏过程各种稳定性的精确且可验证的充分条件.给出了由符号函数直接判定的Lévy型过程非爆炸的充分条件,这个条件包括了扩散过程非爆炸的线性增长条件;当Lévy型算子生成马氏过程对应半群的符号函数已知时,得到了由该符号函数直接表达的常返性充分条件,它推广了关于Lévy过程经典的Chun-Fuchs常返性准则.     

Bogdanov-Takens系统的一类三次扰动(Ⅰ)

通过计算高阶Mel'nikov函数,并引入新的Riccati方程,对Bogdanov-Takens系统的一类三次扰动进行了研究,得到了小扰动条件下环性阶数的估计,同时也给出了原点为中心的条件.     

后继函数法与 Bogdanov-Takens 系统的二次扰动

本文利用后继函数法和隐函数定理,并结合Mel’nikov函数的计算,对Bogdanov-Takens系统在二次扰动下从中心分岔出的极限环个数进行了估计．     

一类单中心Hamilton系统在三次扰动下的Poincare分岔

使用一阶Mel‘nikov函数讨论了一类具有以抛物线与直线为边界的周期环域的单中心二次Hamilton系统的三次扰动下的Poincare分岔,得到其Poincare分岔最多可以产生两个极限环。     

Limit cycles in the equation of whirling pendulum with autonomous perturbation

The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel'nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.     

Prefix classes of krom formulae with identity

Two small classes of first order formulae without function symbols but with identity, in prenex conjunctive normal form with all disjunctions binary, are shown to have a recursively unsolvable decision problem, whereas for another such class an algorithm is developed which solves the decision problem of that class. This solves the prefix problem for such classes of formulae except for the Gödel-Kalmàr-Schütte case.     

Decision making under uncertainty comprising complete ignorance and probability

This paper investigates a model of decision making under uncertainty comprising opposite epistemic states of complete ignorance and probability. In the first part, a new utility theory under complete ignorance is developed that combines Hurwicz–Arrow's theory of decision under ignorance with Anscombe–Aumann's idea of reversibility and monotonicity used to characterize subjective probability. The main result is a representation theorem for preference under ignorance by a particular one-parameter function – the τ-anchor utility function. In the second part, we study decision making under uncertainty comprising an ignorant variable and a probabilistic variable. We show that even if the variables are independent, they are not reversible in Anscombe–Aumann's sense. This insight leads to the development of a new proposal for decision under uncertainty represented by a preference relation that satisfies the weak order and monotonicity assumptions but rejects the reversibility assumption. A distinctive feature of the new proposal is that the certainty equivalent of a mapping from the state space of uncertain variables to the prize space depends on the order in which the variables are revealed. Explicit modeling of the order of variables explains some of the puzzles in multiple-prior model and the models for decision making with Dempster–Shafer belief function.     

Sequences of closed sets of bounded variation converging in the deviation metric

From an arbitrary convergent sequence of sets of bounded variation we can select a subsequence such that there is convergence in almost every hyperplane.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 521–526, April, 1974.The author thanks A. G. Vitushkin and M. S. Mel'nikov for their constant interest in his work.     

ContributionsEdge colorings of graphs embeddable in a surface of low genus

In this paper, by using the Discharging Method, we show that any graph with maximum degree Δ 8 that is embeddable in a surface Σ of characteristic χ(Σ) 0 is class one and any graph with maximum degree Δ 9 that is embeddable in a surface Σ of characteristic χ(Σ) = − 1 is class one. For surfaces of characteristic 0 or −1, these results improve earlier results of Mel'nikov.     

The Poincaré-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I

On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered for a system on a plane.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1668–1681, December, 1993.     

Application of Fuzzy Linear Programming in Production Planning

In this paper, a new fuzzy linear programming based methodology using a specific membership function, named as modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility in taking up vagueness in parameters is established by an analytical approach. This membership function is tested for its useful performance through an illustrative example by employing fuzzy linear programming. The developed methodology of FLP has provided a confidence in applying to real life industrial production planning problem. This approach of solving industrial production planning problem can have feed back within the decision maker, the implementer and the analyst. In such case this approach can be called as IFLP (Interactive Fuzzy Linear Programming). There is a possibility to design the self organizing of fuzzy system for the mix products selection problem in order to find the satisfactory solution. The decision maker, the analyst and the implementer can incorporate their knowledge and experience to obtain the best outcome.     

Fuzzy linear programming with vague objective coefficients in an uncertain environment

In this paper, a new fuzzy linear programming (FLP)-based methodology using a specific membership function named modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility established by an analytical approach. This membership function is tested for its useful performance through an illustrative example by employing FLP. The developed methodology of FLP has provided confidence in applying to real-life industrial production planning problem. This approach of solving industrial production planning problem can provide feedback to the decision maker, implementer and analyst. In such cases, this approach can be called interactive FLP. There is a possibility to design the self-organizing of the fuzzy system for the product mix selection problem in order to find a satisfactory solution. The decision maker, analyst and implementer can incorporate their knowledge and experience to obtain the best outcome.