Solvability of multi-point boundary value problem at resonance (III)
In this paper, we consider the following second order ordinary differential equation(1.1)x^'^'=f(t,x(t),x^'(t))+e(t),t@?(0,1),subject to one of the following boundary value conditions: (1.2)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),(1.3)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x^'(1)=@?"j"="1^n^-^2@b"jx^'(@h"j),(1.4)x^'(0)=@?"i"="1^m^-^2@a"ix^'(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),where @a"i(1=

title: A note on a nonlocal boundary value problems
abstract: A nonlocal boundary value problems for a second-order ordinary differential equation is considered in this note. An existence result is obtained by the help of the coincidence degree theory.

title: Note on third-order boundary value problem for differential equations with deviating arguments
abstract: A third-order boundary value problem for differential equations with deviating arguments is considered in this note. An existence result is obtained by the help of the well-known Leray-Schauder Alternative. Also, a uniqueness result is given.

title: Positive solutions of three-point boundary value problems for the one-dimensional p-laplacian with infinitely many singularities
abstract: We consider thesingular three-point boundary value problems 
(φp(y′))′ + a(t)f(y(t)) = 0, 0 < t < 1, y′(0) = 0, y(1) = βy(ƞ), 
where φp(s) = |s|p−2s, p ≥ 2, 0 < β < 1, 0 < η < 1, f ϵ C([0, + ∞), [0, + ∞)), a: [0,1] → [0, + ∞), andhas countably many singularities in [0, frsol|1/2). We show that there exist countably many positive solutions by using the fixed-point index theory.

title: A singular integral of the composite operator
abstract: We establish the Poincare-type inequalities for the composition of the homotopy operator and the projection operator. We also obtain some estimates for the integral of the composite operator with a singular density.

title: Conceptual design: issues and challenges
abstract: Decisions made during conceptual design have signi®cant in ̄uence on the cost, performance, reliability, safety and environmental impact of a product. It has been estimated that design decisions account for more than 75% of ®nal product costs. It is, therefore, vital that designers have access to the right tools to support such design activities. In the early 1980s, researchers began to realize the impact of design decisions on downstream activities. As a result, different methodologies such as design for assembly, design for manufacturing and concurrent engineering, have been proposed. Software tools that implement these methodologies have also been developed. However, most of these tools are only applicable in the detailed design phase. Yet, even the highest standard of detailed design cannot compensate for a poor design concept formulated at the conceptual design phase. In spite of this, few CAD tools have been developed to support conceptual design activities. This is because knowledge of the design requirements and constraints during this early phase of a product's life cycle is usually imprecise and incomplete, making it dif®cult to utilize computer-based systems or prototypes. However, recent advances in ®elds such as fuzzy logic, computational geometry, constraints programming and so on have now made it possible for researchers to tackle some of the challenging issues in dealing with conceptual design activities. In this special issue, we have gathered together discussions on various aspects of conceptual design phase: from the capturing of the designer's intent, to modelling design constraints and solving them in an ef®cient manner, to verifying the correctness of the design.  Qin et al. begin this issue with the article aFrom online sketching to 2D and 3D geometry: a fuzzy knowledge based systemo in which they look at the interesting research problem of capturing the user's sketching intentions and automatically generating the corresponding geometric primitives. The motivation of this work comes from the fact that most designers still prefer to express their creative design ideas through 2D sketches. It is therefore important for a computer-aided conceptual design system to allow sketched input. Qin et al. built a prototype system that allows 2D sketched input, interprets the input sketch into more geometrically exact 2D vision objects and, when needed, projects the 2D objects into 3D models. The system receives the sketched input data through a sequence of mouse button presses, mouse motions and mouse button release events. After that, the system attempts to identify each curve segments and generate a precise 2D primitive for the identi®ed segment. For each pair of 2D primitives identi®ed, a 2D relationship (connectivity, parallelism or perpendicularity) is inferred by the system. As the 2D geometry (primitives 1 relationships) slowly accumulates, the system continually checks to see whether it can recognize a 3D object or feature. Upon recognition, the 3D object/ feature will be placed in 3D space and new features can be built upon previous ones. Latif Al Hakim et al. approach the problem from the concurrent engineering perspective. Traditionally, design is a serial activity whereby reliability, manufacturability, maintainability, safety and other requirements are considered sequentially. In recent years, in an effort to increase competitiveness and reduce design life cycle, the concept of concurrent engineering is introduced. Instead of performing design-related activities in series, they are performed simultaneously. This approach greatly increases the complexity of the design process due to the highly interactive nature of the various design tasks. To support design activities adequately in such an environment, Latif Al Hakim et al. propose the incorporation of reliability with functional perspectives at the conceptual design stage. They use graph theory to represent a product and the relationships between its components. A product's components are represented as the vertices of a graph, while the edges of the graph represent the ̄ow of energy between components. With this representation, it is easy to visualize energy ̄ow between components and thus trace any loss of functionality. In addition, this representation allows one easily to take into consideration various constraints such as cost for further design re®nement. The third paper in this special issue points out the need for a suitable conceptual design representation scheme for smooth integration with downstream applications of the product development process. Brunnetti and Golob propose a feature-based representation scheme for capturing product semantics handled in the conceptual design phase. They believe that any computer-aided design system should accomplish two major goals. The ®rst is to support the ̄ow of information without loss along the product development process, and the second is to assist designers in Computer-Aided Design 32 (2000) 849±850 COMPUTER-AIDED DESIGN

title: A refinement approach to search and constraint satisfaction problem

title: Multi-level organization and summarization of the discovered rules
abstract: Many existing data mining techniques often p roduce a large number of rules, which make it very difficult for manual inspection o f the rules to identify those interesting ones. This problem represents a major gap between the results of data mining and the understanding and use of the mining results. In this paper, we a rgue that t he key problem is not with the large number of rules because if there are indeed many rules that exist in data, they should b e discovered. The main p roblem is with ou r inability to organize, summarize and present the rules in such a way that they can b e ea sily analyzed b y the user. In this paper, we propose a technique to intuitively organize a nd summarize the discovered rules. With this organization, the discovered rules can b e presented to the user in the way as we think and talk about knowledge in ou r daily lives. This organization also allows the user to view the discovered rules at different levels of details, and to focus his/her attention on those interesting aspects. This paper presents this technique a nd u ses it t o o rganize, summarize a nd present t he knowledge e mbedded in a decision tree, and a set of association rules. Experiment results and p ractical applications show that the technique is both intuitive and effective.

title: Boundary Constrained Manifold Unfolding

title: Classification by Association Rule Analysis
abstract: An interface between a dual mode mobile station and a piece of data terminal equipment supports both a logical digital interface and a logical analog interface, with the analog interface passing through a modem. At set-up of either a mobile originated or mobile terminated data/fax call, a supporting dual mode communications network determines whether a digital traffic channel is available on an air interface. If so, the channel is allocated to the mobile station, and data/fax communication with the data terminal equipment occurs using the logical digital interface. Otherwise, an analog voice channel is allocated, and the data/fax communication with the data terminal equipment occurs using the logical analog interface and modem. Within the supporting network, data/fax communications via the digital traffic channel are routed through an interworking functionality that terminates a radio link protocol utilized for communicating over the digital air interface. Analog voice channel data/fax communications are instead routed through a modem pool that terminates a selected modem protocol utilized by the modem for communicating over the analog air interface.