Questions of quality

Depending on your view, the Internet, and more particularly the World Wide Web, is either the best thing since Prosper Eckert screwed his first valve into ENIAC or the final, back‐breaking straw in a desert where oases of real information are few and far between and information technology rules the sands, OK?     

Your Questions Answered

Question: Many organizations are introducing culture change programmes. In your experience, what practical factors have to be taken into account in the introduction of such programmes?     

Necessary conditions for infinite-dimensional control problems

We consider infinite-dimensional nonlinear programming problems which consist of minimizing a functionf ₀(u) under a target set constraint. We obtain necessary conditions for minima that reduce to the Kuhn-Tucker conditions in the finite-dimensional case. Among other applications of these necessary conditions and related results, we derive Pontryagin’s maximum principle for a class of control systems described by semilinear equations in Hilbert space and study convergence properties of sequences of near-optimal controls for these systems. The work of this author was supported in part by the National Science Foundation under Grant DMS-8701877.     

Necessary optimality conditions for switched systems

A dynamic system that models the operation of a switching device (switch) is considered. During the operation, the system changes its state a finite number of times. The change of state (switching) is described by a recurrent inclusion, which corresponds to the representation of the switch by a dynamic finite state machine with memory; instantaneous multiple switchings are admitted. The instants of time at which switchings are made and the number of switchings are not given in advance. They are found by optimizing a functional in which the number of switchings and the cost of each of them are taken into account. Necessary optimality conditions for such systems are proved. Different versions of the optimality conditions for different types of constraints are given. In particular, under additional convexity conditions, conditions that are similar to the maximum principle for discrete systems are obtained. The application of the optimality conditions is illustrated by examples.     

Windows操作题自动阅卷系统的实现

分析了Windows操作题的类型,试题库的设计及给出了基于VB的Windows操作题考试环境的创设、自动阅卷实现的方法.     

More Questions than Answers

Abstract

In this commentary on ‘Time to Change Drivers for Science Literacy’ by Peter Fensham I address two issues raised by Fensham. First, Why is reforming the science curriculum so hard? I suggest that the reason that science curriculum reform is difficult to achieve is that the practice of science teaching has been shaped by the culture in which it is embedded. Second, What are the potential possibilities of and problems with Fensham's reform proposal? The content of the curriculum that Fensham proposes would be largely dependent on how the societal experts are chosen and on what media sources are examined. Finally, we need to recognize that whatever we agree upon today as the most appropriate content for the science curriculum must be continually negotiated and revised.     

Necessary stability conditions for linear delay systems

We present necessary conditions for the exponential stability of linear systems with multiple delays. They are expressed in terms of the delay Lyapunov matrix of the Lyapunov–Krasovskii functionals of complete type approach. New properties of independent interest, that establish connections of the system fundamental matrix with its Lyapunov matrix, are crucial elements of our proof. We illustrate our work with a number of examples.     

Necessary conditions for Schur-stability of interval polynomials

New bounds on the coefficient diameter of real Schur-stable interval polynomials are given using techniques from complex analysis. They can be used to unmask interval polynomials at low computational cost as being non-Schur-stable.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

图同构的一个充分必要条件

图同构的判定性问题是图论理论中的一个难问题,至今没有得到彻底解决。Ulam曾经提出过一个判定图同构的猜想,也称为图的重构猜想。提出了一个新的判定图同构的充分必要条件,即在子图同构的前提下,根据新增顶点及相应关联边的关系,判断母图同构的充分必要条件。基于具有同构关系的对应点无限衍生技术,采用数学归纳法证明了这个充分必要条件的成立。     

A Necessary Condition for Learning from Positive Examples

We present a simple combinatorial criterion for determining concept classes that cannot be learned in the sense of Valiant from a polynomial number of positive-only examples. The criterion is applied to several types of Boolean formulae in conjunctive and disjunctive normal form, to the majority function, to graphs with large connected components, and to a neural network with a single threshold unit. All are shown to be nonlearnable from positive-only examples.     

Necessary conditions for Hadamard factorizations of Hurwitz polynomials

A property of Hurwitz polynomials is related with the Hadamard product. Garloff and Wagner proved that Hadamard products of Hurwitz polynomials are Hurwitz polynomials, and Garloff and Shrinivasan shown that there are Hurwitz polynomials of degree 4 which do not have a Hadamard factorization into two Hurwitz polynomials of the same degree 4. In this paper, we give necessary conditions for an even-degree Hurwitz polynomial to have a Hadamard factorization into two even-degree Hurwitz polynomials; such conditions are given in terms of the coefficients of the given polynomial alone. Furthermore, we show that if an odd-degree Hurwitz polynomial has a Hadamard factorization then a system of nonlinear inequalities has at least one solution.     

Necessary and sufficient conditions for consistent global snapshots

Consistent global snapshots are important in many distributed applications. We prove the exact conditions for an arbitrary checkpoint, or a set of checkpoints, to belong to a consistent global snapshot, a previously open problem. To describe the conditions, we introduce a generalization of Lamport's (1978) happened-before relation called a zigzag path