One image reduction algorithm for RGB color images

We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimization of penalty functions on discrete product lattices.

Optimal fault tolerant Jacobian matrix generators for redundant manipulators

The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained. In this study, an optimal fault-tolerant Jacobian matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Understanding and developing structure - its importance for mathematics learning

This issue comes at a time when mathematics education research is becoming more intently focused on the development of "structure" as salient to generalised mathematics learning. Not surprisingly the attention on structure creates particular synergies with the increasingly rich field of research on algebraic thinking and arithmetic processes, particularly in the early years. In many ways, this special issue is concerned with describing the process of "structuring" that enables abstraction and generalisation. A recent MERJ special issue, Abstraction in Mathematics Education (Mitchelmore & White, 2007), illustrated theories of abstraction aligning these to notions of underlying structure. The importance of structure in the transition from school to university was also highlighted by Godfrey and Thomas (2008), and Novotna and Hoch (2008) in the previous special issue of MERJ (Thomas, 2008). In this special issue we present six papers that provide evidence of developing structure as critical for all learners of mathematics throughout schooling.

Direct method for optimal power management in hybrid electric vehicles

Hybrid electric vehicles are powered by an electric system and an internal combustion engine. The components of a hybrid electric vehicle need to be coordinated in an optimal manner to deliver the desired performance. This paper presents an approach based on direct method for optimal power management in hybrid electric vehicles with inequality constraints. The approach consists of reducing the optimal control problem to a set of algebraic equations by approximating the state variable which is the energy of electric storage, and the control variable which is the power of fuel consumption. This approximation uses orthogonal functions with unknown coefficients. In addition, the inequality constraints are converted to equal constraints. The advantage of the developed method is that its computational complexity is less than that of dynamic and non-linear programming approaches. Also, to use dynamic or non-linear programming, the problem should be discretized resulting in the loss of optimization accuracy. The propsed method, on the other hand, does not require the discretization of the problem producing more accurate results. An example is solved to demonstrate the accuracy of the proposed approach. The results of Haar wavelets, and Chebyshev and Legendre polynomials are presented and discussed. © 2011 The Korean Society of Automotive Engineers and Springer-Verlag Berlin Heidelberg.

Real solutions number of the switching angles in the selective harmonic eliminated PWM

With the purpose of solving the real solutions number of the nonlinear transcendental equations in the selective harmonic eliminated PWM (SHEPWM) technology, the nonlinear transcendental equations were transformed to a set of polynomial equations with a set of inequality constraints using the multiple-angle formulas, an analytic method based on semi-algebraic systems machine proving algorithm was proposed to classify the real solution number of the switching angles. The complete classifications of the real solution number and the analytic boundary point of the single phase and three phases SHEPWM inverter with switch points of N=3 and the single phase SHEPWM inverter with switch points of N=4 are obtained. The results indicate that the relationship between the modulation ratio and the real solution number can be demonstrated theoretically by this method, which has great implications for the solution procedure of switching angles and the improvement of harmonic elimination effects of the inverter.

Aggregation for Atanassov's intuitionistic and interval valued fuzzy sets: the median operator

Atanassov's intuitionistic fuzzy sets (AIFS) and interval valued fuzzy sets (IVFS) are two generalizations of a fuzzy set, which are equivalent mathematically although different semantically. We analyze the median aggregation operator for AIFS and IVFS. Different mathematical theories have lead to different definitions of the median operator. We look at the median from various perspectives: as an instance of the intuitionistic ordered weighted averaging operator, as a Fermat point in a plane, as a minimizer of input disagreement, and as an operation on distributive lattices. We underline several connections between these approaches and summarize essential properties of the median in different representations.