Comments on "finite-time stability theorem of stochastic nonlinear systems" [Automatica 46 (2010) 2105-2108]

In this comment, we will point out some errors existing in Chen and Jiao (2010) from definitions to the proof of the main result, where the authors discussed the finite-time stability of stochastic nonlinear systems and proved a Lyapunov theorem on the finitetime stability.

A finite-time stability theorem of stochastic nonlinear systems and stabilization designs

This paper focuses on the finite-time stability and stabilization designs of stochastic nonlinear systems. We first present and discuss a definition on the finite-time stability in probability of stochastic nonlinear systems, then we introduce a stochastic Lyapunov theorem on the finite-time stability, which has been established by Yin et al. We also employ this theorem to design a continuous state feedback controller that makes a class of stochastic nonlinear systems to be stable in finite time. An example and a simulation are given to illustrate the theoretical analysis.

A characterization theorem for t-representable n-dimensional triangular norms

n-dimensional fuzzy sets are an extension of fuzzy sets that includes interval-valued fuzzy sets and interval-valued Atanassov intuitionistic fuzzy sets. The membership values of n-dimensional fuzzy sets are n-tuples of real numbers in the unit interval [0,1], called n-dimensional intervals, ordered in increasing order. The main idea in n-dimensional fuzzy sets is to consider several uncertainty levels in the memberships degrees. Triangular norms have played an important role in fuzzy sets theory, in the narrow as in the broad sense. So it is reasonable to extend this fundamental notion for n-dimensional intervals. In interval-valued fuzzy theory, interval-valued t-norms are related with t-norms via the notion of t-representability. A characterization of t-representable interval-valued t-norms is given in term of inclusion monotonicity. In this paper we generalize the notion of t-representability for n-dimensional t-norms and provide a characterization theorem for that class of n-dimensional t-norms. © 2011 Springer-Verlag Berlin Heidelberg.

Decompositions of finite projective planes

We consider decompositions of finite projective planes into copies of a particular structure. Our main theorem provides a connection between the existence of a proper projective subplane and the existence of a decomposition into sets of collinear points. Based on this result, we develop a connection between the existence of a projective subplane in a plane II and that of a hitting set in the dual of II.

Combinatorial aspects of jump codes

We develop an approach to jump codes concentrating on their combinatorial and symmetry properties. The main result is a generalization of a theorem previously proved in the context of isodual codes. We show that several previously constructed jump codes are instances of this theorem.

A scale-model room as a practical teaching experiment

A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham’s p-theorem.

Leontief paradox and the role of factor intensity measurement

In contrast with the prediction of the Heckscher-Ohlin (HO) theorem, Leontief (1953) found that the capital-labor ratio embodied in the US exports is smaller than the capital-labor ratio embodied in the US competitive import replacements. In Leontief's analysis, the measured factor content of US imports is computed based on the assumption that all countries are using the US factor intensity techniques. This paper relaxes all assumption of identical factor intensity techniques. It uses an inferring method to infer the factor intensity techniques of different countries based on international relative factor price differences. With the inferred differentiated factor intensity techniques , the Leontief paradox is re-investigated and is found to be either disappeared or eased.

Mining inconsistent secure messages toward analyzing security protocols

Traditional approaches such as theorem proving and model checking have been successfully used to analyze security protocols. Ideally, they assume the data communication is reliable and require the user to predetermine authentication goals. However, missing and inconsistent data have been greatly ignored, and the increasingly complicated security protocol makes it difficult to predefine such goals. This paper presents a novel approach to analyze security protocols using association rule mining. It is able to not only validate the reliability of transactions but also discover potential correlations between secure messages. The algorithm and experiment demonstrate that our approaches are useful and promising.

3D haptic needle insertion simulator utilising an agent based spherical voxel model

This paper describes a technique for the real-time modeling of deformable tissue. Specifically geared towards needle insertion simulation, the low computational requirements of the model enable highly accurate haptic feedback to a user without introducing noticeable time delay or buzzing generally associated with haptic surgery simulation. Using a spherical voxel array combined with aspects of computational geometry and agent communication and interaction principals, the model is capable of providing haptic update rates of over 1000Hz with real-time visual feedback. Iterating through over 1000 voxels per millisecond to determine collision and haptic response while making use of Vieta’s Theorem for extraneous force culling.

Tackling trigonometry - up the slippery slope?

This paper challenges mathematics teachers to go back and re-examine ideas as far as possible from the genuine beginner's point of view rather than in terms of being experts on the subject. It suggests tasks that teachers can do to achieve this. Topics covered are the shock of the new, the best single short lesson on trigonometry, the difficulty of remembering not knowing, first student trigonometric steps (scouts and flagpoles), first human steps in trigonometry (examining the stars), rotation becomes number, showing relations and learning ideas, plus a lengthy discussion on trigonometry.

Using Excel to generate empirical sampling distributions

Teachers in many introductory statistics courses demonstrate the Central Limit Theorem by using a computer to draw a large number of random samples of size n from a population distribution and plot the resulting empirical sampling distribution of the sample mean. There are
many computer applications that can be used for this (see, for example, the Rice Virtual Lab in Statistics: http://www.ruf.rice.edu/~lane/rvls.html). The effectiveness of such demonstrations has been questioned (see delMas et al (1999))) but in the work presented in this paper we do not rely on sampling distributions to convey or teach statistical concepts; only that the sampling distribution is independent of the distribution of the population, provided the sample size is sufficiently large.

We describe a lesson that starts out with a demonstration of the CTL, but sample from a (finite) population where actual census data is provided; doing this may help students more easily relate to the concepts – they can see the original data as a column of numbers and if the samples are shown they can also see random samples being taken. We continue with this theme of sampling from census data to teach the basic ideas of inference. We end up with standard resampling/bootstrap procedures.

We also demonstrate how Excel can provide a tool for developing a learning objects to support the program; a workbook called Sampling.xls is available from www.deakin.edu.au/~rodneyc/PS > Sampling.xls.

Classification of face images using local iterated function systems

There has been an increasing interest in face recognition in recent years. Many recognition methods have been developed so far, some very encouraging. A key remaining issue is the existence of variations in the input face image. Today, methods exist that can handle specific image variations. But we are yet to see methods that can be used more effectively in unconstrained situations. This paper presents a method that can handle partial translation, rotation, or scale variations in the input face image. The principal is to automatically identify objects within images using their partial self-similarities. The paper presents two recognition methods which can be used to recognise objects within images. A face recognition system is then presented that is insensitive to limited translation, rotation, or scale variations in the input face image. The performance of the system is evaluated through four experiments. The results show that the system achieves higher recognition rates than those of a number of existing approaches.