Apollonius tenth problem via radius adjustment and Möbius transformations

The Apollonius Tenth Problem, as defined by Apollonius of Perga circa 200 B.C., has been useful for various applications in addition to its theoretical interest. Even though particular cases have been handled previously, a general framework for the problem has never been reported. Presented in this paper is a theory to handle the Apollonius Tenth Problem by characterizing the spatial relationship among given circles and the desired Apollonius circles. Hence, the given three circles in this paper do not make any assumption regarding on the sizes of circles and the intersection/inclusion relationship among them. The observations made provide an easy-to-code algorithm to compute any desired Apollonius circle which is computationally efficient and robust.     

Complete mobile email management

Years have lapsed since the inauguration of the first Wireless Application Protocol (WAP) application. One of the main reasons for the lukewarm response so far may be attributed to the lack of a “Killer” application. Many companies and developers have attempted to replicate email services (an Internet Killer appplication) within the WAP realm, but till now, no significant success has been reported. This paper will first discuss on the key functions which are lacking in the present WAP-email service, and which are arguably necessary if a much larger user base is to be attracted to these services. A new system will be proposed which can enable the user to send files residing in a remote personal computer (PC) as attachments to his emails using WAP-enabled mobile devices. The implementation of the system will be presented in details. Issue relating to the connection to various types of email servers and the security of the system will also be addressed in the paper.     

Adaptive boundary control for unstable parabolic PDEs—Part II: Estimation-based designs

The certainty equivalence approach to adaptive control is commonly used with two types of identifiers: passivity-based identifiers and swapping identifiers. The “passive” (also known as “observer-based”) approach is the prevalent identification technique in existing results on adaptive control for PDEs but has so far not been used in boundary control problems. The swapping approach, prevalent in finite-dimensional adaptive control is employed here for the first time in adaptive control of PDEs. For a class of unstable parabolic PDEs we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers. The result is applicable in any dimension. For physical reasons we restrict our attention to dimensions no higher than three. The results of the paper are illustrated by simulations.     

Interaction bounds in multivariable control systems

Time-domain limitations due to right half-plane zeros and poles in linear multivariable control systems are studied. Lower bounds on the interaction are derived. They show not only how the location of zeros and poles are critical in multivariable systems, but also how the zero and pole directions influence the performance. The results are illustrated on the quadruple-tank process, which is a new multivariable laboratory process.     

Hardware and software architecture for power quality analysis

This paper presents a novel concept for power quality hardware and software architecture. Software tools related to detection, classification and characterization of power quality events can be integrated into a Distribution Control Center in which the interconnection between different subsystems is being carried out through the Internet allowing flexibility to the system. This system is implemented using wavelet analysis applied in all proposed algorithms. Different power quality events are taken as examples to illustrate the capabilities of the proposed method. The obtained results reveal that the proposed architecture is feasible to be implemented as an integral part of a control center system.The proposed system has the property of fast and accurate detection and classification of any power quality disturbance event and introduces a new PQ index determination that allows characterizing any type of disturbance including the non-periodic signals.     

Extensions of LDA by PCA mixture model and class-wise features

Linear discriminant analysis (LDA) is a data discrimination technique that seeks transformation to maximize the ratio of the between-class scatter and the within-class scatter. While it has been successfully applied to several applications, it has two limitations, both concerning the underfitting problem. First, it fails to discriminate data with complex distributions since all data in each class are assumed to be distributed in the Gaussian manner. Second, it can lose class-wise information, since it produces only one transformation over the entire range of classes. We propose three extensions of LDA to overcome the above problems. The first extension overcomes the first problem by modelling the within-class scatter using a PCA mixture model that can represent more complex distribution. The second extension overcomes the second problem by taking different transformation for each class in order to provide class-wise features. The third extension combines these two modifications by representing each class in terms of the PCA mixture model and taking different transformation for each mixture component. It is shown that all our proposed extensions of LDA outperform LDA concerning classification errors for synthetic data classification, hand-written digit recognition, and alphabet recognition.     

A tolerant approach to reconstruct topology from unorganized trimmed surfaces

Presented in this paper is a topology reconstruction algorithm from a set of unorganized trimmed surfaces. Error-prone small geometric elements are handled to give proper topological information. It gives complete topology to topologically complete models, and it is also tolerant to incomplete models. The proposed algorithm is vertex-based in that clues for topological information are searched from the set of vertices first, not from that of edges.     

Data fitting with a spline using a real-coded genetic algorithm

To obtain a good approximation for data fitting with a spline, frequently we have to deal with knots as variables. The problem to be solved then becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain the global optimum. In this paper, we propose a method for solving this problem by using a real-coded genetic algorithm. Our method can treat not only data with a smooth underlying function, but also data with an underlying function having discontinuous points and/or cusps. We search for the best model among candidate models by using the Bayes Information Criterion (BIC). With this, we can appropriately determine the number and locations of knots automatically and simultaneously. Five examples of data fitting are given to show the performance of our method.