关于有效点集的闭性和连通性

本文的主要结果是，假设Ａ是局部凸空间里的紧的Ｆ一集，则Ａ的有效点集Ｅ（Ａ｜Ｃ）是闭集。需要提及的是，此结果中关于Ａ并没有作任何凸性的假设，如果对它再附加某种凸性假设条件时，则本文进一步证明了有效点集Ｅ（Ａ｜Ｃ）不但是闭集，而且还是连通集。     

Hausdorff dimension of some kind of alternating Oppenheim series expansion

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.     

图的独立数的一个新下界

设α（Ｇ）表示简单图Ｇ＝（Ｖ，Ｅ）的独立数．本文给出了α（Ｇ）的一个新的下界：α（Ｇ）≥∑ｖ∈Ｖ（λｄ（ｖ）＋１）／（ｄ（ｖ）＋λｄ（ｖ）＋１），其中λｄ（ｖ）＝ｍａｘ｛０，βＮ（ｖ）－ｄ（ｖ）｝，ｄ（ｖ）＝｜Ｎ（ｖ）｜，Ｎ（ｖ）＝｛ｗ∈Ｖ｜（ｖ，ｗ）∈Ｅ｝，βＮ（ｖ）＝ｍｉｎｗ∈Ｎ（ｖ）ｄ（ｗ）．     

连续树映射的ω极限集与非游荡集

本文研究树上连续自映射f的ω极限集∧,非游荡集Ω的若干拓扑结构,主要证明了不在周期点集闭包中的ω极限点都有无限轨迹;Ω-     

连续树映射的ω极限集与非游荡集

本文研究树上连续自映射ｆ的ω极限集Λ,非游荡集Ω的若干拓扑结构,主要证明了：不在周期点集闭包中的ω极限点都有无限轨迹;Ω－Ｐ,Ω－Γ为可数集,Λ－Γ,Ｐ－Γ或为空集或可数无限,其中Γ为ｆ的γ极限集．     

填充Jnlia集与Mandelbrot集的面积与直径

本文用单叶函数中的面积定理及Ｇａｒａｂｅｄｉａｎ－Ｓｃｈｉｆｆｅｒ不等式的有关推论．给出了求多项式的填充Ｊｕｌｉａ集及Ｍａｎｄｅｌｂｒｏｔ集面积的方法及直径的上界估计，从而给Ａ．Ｄｏｕａｄｙ所提的有关问题一个回答．     

对称n筛计算式

本文引进一种筛法,由此给出从1,2,…,2a中经过n次两两互素的筛数筛减后的乘余数点个数的计算公式。     

扩张不变集相对非自治扰动的稳定性

本文研究了自映射的扩张不变集在Ｃ￣０非自治扰动和Ｃ￣１非自治扰动下的稳定性质。     

A Diller-Nahm-style functional interpretation of $\hbox{\sf KP} \omega$

The Dialectica-style functional interpretation of Kripke-Platek set theory with infinity () given in [1] uses a choice functional (which is not a definable set function of (). By means of a Diller-Nahm-style interpretation (cf. [4]) it is possible to eliminate the choice functional and give an interpretation by set functionals primitive recursive in . This yields the following characterization: The class of -definable set functions of coincides with the collection of set functionals of type 1 primitive recursive in . Received: 26 August 1998     

A Note on Some Link Polynomials

Hass and Wajnryb [2] have given a set of sufficient conditionsfor a recursive definition over crossing changes in link diagramsto provide a well-defined link invariant in a similar way to[3]. They also provide a number of examples satisfying theseconditions, including a number with non-linear recursive definitions.I here show that all of these examples are in fact special casesof the known invariant P(l, m) of [3, 1]. In particular, thereexists no linear recursive definition providing an invariantnot covered by P(l, m).     

Upper Limitation of Kolmogorov Complexity and Universal P. Martin-Löf Tests

In this paper we study the Kolmogorov complexity of initial strings in infinite sequences (being inspired by [9]), and we relate it with the theory of P. Martin-Lof random sequences. Working with partial recursive functions instead of recursive functions we can localize on an apriori given recursive set the points where the complexity is small. The relation between Kolmogorov's complexity and P. Martin-Lof's universal tests enables us to show that the randomness theories for finite strings and infinite sequences are not compatible (e.g.because no universal test is sequential).We lay stress upon the fact that we work within the general framework of a non-necessarily binary alphabet.     

A multivariate QD-like algorithm

The problem of constructing a univariate rational interpolant or Padé approximant for given data can be solved in various equivalent ways: one can compute the explicit solution of the system of interpolation or approximation conditions, or one can start a recursive algorithm, or one can obtain the rational function as the convergent of an interpolating or corresponding continued fraction.In case of multivariate functions general order systems of interpolation conditions for a multivariate rational interpolant and general order systems of approximation conditions for a multivariate Padé approximant were respectively solved in [6] and [9]. Equivalent recursive computation schemes were given in [3] for the rational interpolation case and in [5] for the Padé approximation case. At that moment we stated that the next step was to write the general order rational interpolants and Padé approximants as the convergent of a multivariate continued fraction so that the univariate equivalence of the three main defining techniques was also established for the multivariate case: algebraic relations, recurrence relations, continued fractions. In this paper a multivariate qd-like algorithm is developed that serves this purpose.     

Solving a Hamilton–Jacobi–Bellman equation with constraints

Optimal investment strategies for an insurer with state-dependent constraints are computed via a recursive finite difference solution to the corresponding discretized Hamilton–Jacobi–Belman equation. Convergence is derived from viscosity solution arguments. For this, a comparison result is given which is similar to the result given by Azcue and Muler [Ann. Appl. Probab. 20 (2010), pp. 1253–1302].     

一类用迭代方法生成的分片线性谱序列

本文引入了空间L2[0,1]的一种具有指数形式的正交基,其中对应的指数序列称为谱序列.文章得出了一系列理论上的刻画,但主要贡献在于给出迭代解法以生成多节点分片线性谱序列,并且对分片常数谱序列进行了研究.另外,本文还给出在离散情形计算分解系数的快速算法,并估计了算法复杂度.     

最小能量控制与Lg样条函数

本文考察了一类带有泛函约束的线性系统的最小能量控制问题与Lg样条插值函数的对应关系.得到了求解最优控制——样条函数的递推算法;并建立了最优控制问题解法Ⅱ,指出文献[1]的解法可作为它的特例.     

Castor quadruplorum

The busy beaver problem of Rado [6] is reexamined for the case of Turing machines given by quadruples rather than quintuples. Moreover several printing symbols are allowed. Some values of the corresponding beaver function are given and it is shown that this function for a fixed number of states and varying number of symbols is nonrecursive for three or more states and recursive for two states. As a byproduct we get that the minimal number of states in a universal Turing machine (quadruples) is three.     

On Markovian decision programming with recursive reward functions

In this paper, the infinite horizon Markovian decision programming with recursive reward functions is discussed. We show that Bellman's optimal principle is applicable for our model. Then, a sufficient and necessary condition for a policy to be optimal is given. For the stationary case, an iteration algorithm for finding a stationary optimal policy is designed. The algorithm is a generalization of Howard's [7] and Iwamoto's [3] algorithms.This research was supported by the National Natural Science Foundation of China.     

The Ackermann function. a theoretical,computational, and formula manipulative study

Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is investigated.Results from tests with the Ackermann function of recursive procedure implementations in ALGOL-60, ALGOL W, PL/I and SIMULA-67 on IBM 360/75 and CD 6600 are given.A SYMBAL formula manipulating program, that automatically solves recurrence relations for the first members of the function class and for the number of calls needed in their straightforward computation, is given.The Ackermann rating of programming languages is discussed.