A method for double series summation

The method of summation by diagonals is shown to be a practical method for the summation of double series which can give good results. Where problems arise an elementary analysis can often be used which enables the sum to be calculated to a high degree of accuracy. The method can be extended in an obvious manner to higher dimensional series.     

沿虚轴无穷区问主值积分与逆傅里叶积分变换

在工程技术和科学研究的许多领域,傅里叶积分变换极为重要,但逆傅里叶积分变换手工计算比较困难,限制了傅里叶积分变换的应用范围。研究发现,逆傅里叶积分变换可以变换成沿复平面虚轴上的无穷区间主值积分,由此,导出一个逆傅里叶积分变换的计算公式,可用来快速完成逆傅里叶积分变换计算。     

第一类Dirichlet积分的公式解

利用三角降次公式及留数解决了第一类Dirichlet积分问题,即给出了第一类Dirichlet积分的公式解。利用所得结果,定义了Dirichlet数Dn,证明了其一般性质。     

地基附加应力和变形计算的Excel电子表格法

地基附加应力和变形计算是地基设计计算的重要内容,直接关系着结构设计的安全可靠程度.传统的计算方法是基于计算成果表的查表插值法.该方法手工计算工作量大且容易出现计算错误.基于弹性理论的地基应力计算原理,给出了地基附加应力计算的Excel电子表格法.对地基变形计算的假定前提进行了讨论,对地基变形计算的传统分层总和法和规范推荐方法进行了原理分析、计算分析和计算结果比较,给出了地基变形计算的Excel电子表格法的基本方法.提出了一个适于Excel电子表格法的新的e-p表达式.给出的地基附加应力及变形计算Excel电子表格法可极大提高相关内容的计算效率,避免出现计算差错.     

动态系统预测的一种统计方法

给出了动态系统预测的一种统计方法及其递推估计公式，该方法充分利用了新信息，提高了预测准确度，减少了计算量，预测效果优于普通最小二乘估计.     

Learning from examples with unspecified attribute values

A challenging problem within machine learning is how to make good inferences from data sets in which pieces of information are missing. While it is valuable to have algorithms that perform well for specific domains, to gain a fundamental understanding of the problem, one needs a “theory” about how to learn with incomplete data. The important contribution of such a theory is not so much the specific algorithmic results, but rather that it provides good ways of thinking about the problem formally. In this paper we introduce the unspecified attribute value (UAV) learning model as a first step towards a theoretical framework for studying the problem of learning from incomplete data in the exact learning framework.In the UAV learning model, an example x is classified positive (resp., negative) if all possible assignments for the unspecified attributes result in a positive (resp., negative) classification. Otherwise the classification given to x is “?” (for unknown). Given an example x in which some attributes are unspecified, the oracle UAV-MQ responds with the classification of x. Given a hypothesis h, the oracle UAV-EQ returns an example x (that could have unspecified attributes) for which h(x) is incorrect.We show that any class of functions learnable in Angluin’s exact model using the MQ and EQ oracles is also learnable in the UAV model using the MQ and UAV-EQ oracles as long as the counterexamples provided by the UAV-EQ oracle have a logarithmic number of unspecified attributes. We also show that any class learnable in the exact model using the MQ and EQ oracles is also learnable in the UAV model using the UAV-MQ and UAV-EQ oracles as well as an oracle to evaluate a given boolean formula on an example with unspecified attributes. (For some hypothesis classes such as decision trees and unate formulas the evaluation can be done in polynomial time without an oracle.) We also study the learnability of a universal class of decision trees under the UAV model and of DNF formulas under a representation-dependent variation of the UAV model.     

Recognition of Simple Enlarged Horn Formulas and Simple Extended Horn Formulas

The enlarged Horn formulas generalize the extended Horn formulas introduced by Chandru and Hooker (1991). Their satisfying truth assignments can be generated with polynomial delay. Unfortunately no polynomial algorithm is known for recognizing enlarged Horn formulas or extended Horn formulas. In this paper we define the class of simple enlarged Horn formulas, a subclass of the enlarged Horn formulas, that contains the simple extended Horn formulas introduced by Swaminathan and Wagner (1995). We present recognition algorithms for the simple enlarged Horn formulas and the simple extended Horn formulas whose complexity is bounded by the complexity of the arborescence-realization problem.     

计算机仿真方法在冷库电梯系统的应用研究

通过建立某电梯系统的动力学模型及状态方程，设计了一个具有普遍意义的仿真程序并利用此程序对电梯实例进行提速改造的模拟仿真，结果呈现低衰减率自由振动形态，有关参数均满足GB10058—1997和ISO2372等规定的要求；同时计算出系统固有频率的取值也在许可范围．从理论上论证了改造电梯是安全可靠的．     

Numerical inversion of multidimensional Laplace transforms by the Laguerre method

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional inversion is to calculate time-dependent performance measures of stochastic systems. Key features of our new algorithm are: (1) an efficient FFT-based extension of our previously developed variant of the Fourierseries method to calculate the coefficients of the multidimensional Laguerre generating function, and (2) systematic methods for scaling to accelerate convergence of infinite series, using Wynn's ε-algorithm and exploiting geometric decay rates of Laguerre coefficients. These features greatly speed up the algorithm while controlling errors. We illustrate the effectiveness of our algorithm through numerical examples. For many problems, hundreds of function evaluations can be computed in just a few seconds.     

Theory revision with queries: Horn, read-once, and parity formulas

A theory, in this context, is a Boolean formula; it is used to classify instances, or truth assignments. Theories can model real-world phenomena, and can do so more or less correctly. The theory revision, or concept revision, problem is to correct a given, roughly correct concept. This problem is considered here in the model of learning with equivalence and membership queries. A revision algorithm is considered efficient if the number of queries it makes is polynomial in the revision distance between the initial theory and the target theory, and polylogarithmic in the number of variables and the size of the initial theory. The revision distance is the minimal number of syntactic revision operations, such as the deletion or addition of literals, needed to obtain the target theory from the initial theory. Efficient revision algorithms are given for Horn formulas and read-once formulas, where revision operators are restricted to deletions of variables or clauses, and for parity formulas, where revision operators include both deletions and additions of variables. We also show that the query complexity of the read-once revision algorithm is near-optimal.