On a new class of analytic functions associated with conic domain

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.     

On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation

Fronts are traveling waves in spatially extended systems that connect two different spatially homogeneous rest states. If the rest state behind the front undergoes a supercritical Turing instability, then the front will also destabilize. On the linear level, however, the front will be only convectively unstable since perturbations will be pushed away from the front as it propagates. In other words, perturbations may grow but they can do so only behind the front. It is of interest to show that this behavior carries over to the full nonlinear system. It has been successfully done in a case study by Ghazaryan and Sandstede [A. Ghazaryan, B. Sandstede, Nonlinear convective instability of Turing-unstable fronts near onset: a case study, SIAM J. Appl. Dyn. Syst. 6 (2007) 319–347]. In the present paper, analogous results are obtained for the same system as in Ghazaryan and Sandstede (2007), but for a different parameter regime.     

Maximally equidistributed pseudorandom number generators via linear output transformations

This article discusses construction of maximally equidistributed (ME) linear feedback shift register generators by using linear output transformations. We introduce a new strategy to find linear output transformations attaining the ME property, and apply it to the WELL generators and the Mersenne Twister. As a result, we found a modified version of the WELL generators with the ME property, having fewer operations than the original ME WELL generators. We also found a ME Mersenne Twister which is faster than the WELL generators with a period of 2¹⁹⁹³⁷−1$2^{19937}-1$ on some platforms. The C codes of the obtained generators are available at http://www3.ocn.ne.jp/∼harase/megenerators.html.     

On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

In this paper, to obtain an efficient parallel algorithm to solve sparse block-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism. Moreover, some theoretical results concerning these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block tridiagonal H-matrices is also described. In addition, the validity of these preconditioners is illustrated with some numerical experiments arising from the second order elliptic partial differential equations and oil reservoir simulations.     

On the surface area of the -star graph

We present an explicit formula for the surface area of the (n,k)-star graph, i.e., the number of nodes at a certain distance from the identity node in the graph, by identifying the unique cycle structures associated with the nodes in the graph, deriving a distance expression in terms of such structures between the identity node of the graph and any other node, and enumerating those cycle structures satisfying the distance restriction.The above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group, when the aforementioned distance expression is available.     

On the decoding of binary cyclic codes with the Newton identities

We revisit in this paper the concept of decoding binary cyclic codes with Gröbner bases. These ideas were first introduced by Cooper, then Chen, Reed, Helleseth and Truong, and eventually by Orsini and Sala. We discuss here another way of putting the decoding problem into equations: the Newton identities. Although these identities have been extensively used for decoding, the work was done manually, to provide formulas for the coefficients of the locator polynomial. This was achieved by Reed, Chen, Truong and others in a long series of papers, for decoding quadratic residue codes, on a case-by-case basis. It is tempting to automate these computations, using elimination theory and Gröbner bases.Thus, we study in this paper the properties of the system defined by the Newton identities, for decoding binary cyclic codes. This is done in two steps, first we prove some facts about the variety associated with this system, then we prove that the ideal itself contains relevant equations for decoding, which lead to formulas.Then we consider the so-called online Gröbner basis decoding, where the work of computing a Gröbner basis is done for each received word. It is much more efficient for practical purposes than preprocessing and substituting into the formulas. Finally, we conclude with some computational results, for codes of interesting length (about one hundred).     

Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems

This paper presents a novel quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems via H^∞ approach. In the proposed algorithm, a self-constructing neural fuzzy network (SCNFN) is developed with both structure and parameter learning phases, so that the number of fuzzy rules and network parameters can be adaptively determined. Based on the SCNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an optimal NFN-based controller is designed to overcome the effects of unstructured uncertainty and approximation error by integrating the NFN identifier, linear optimal control and H^∞ approach as a whole. The adaptive tuning laws of network parameters are derived in the sense of quadratic stability technique and Lyapunov synthesis approach to ensure the network convergence and H^∞ synchronization performance. The merits of the proposed control scheme are not only that the conservative estimation of NFN approximation error bound is avoided but also that a suitable-sized neural structure is found to sufficiently approximate the system uncertainties. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.     

A surface blending approach for displacement features on freeform surfaces

Embedding a number of displacement features into a base surface is common in industrial product design and modeling, where displaced surface regions are blended with the unmodified surface region. The cubic Hermite interpolant is usually adopted for surface blending, in which tangent plane smoothness across the boundary curve is achieved. However, the polynomial degree of the tangent field curve obtained symbolically is considerably higher, and the reduction of the degree of a freeform curve is a non-trivial task. In this work, an approximation surface blending approach is proposed to achieve tangential continuity across the boundary curve. The boundary curve is first offset in the tangent field with the user-specified tolerance, after which it is refined to be compatible with the offset curve for surface blending. Since the boundary curve is offset in a three-dimensional (3D) space, the local self-intersection in the offset curve is addressed in a 2D space by approximately mapping the offset vectors in the respective tangent planes to the parameter space of the base surface. The proposed algorithm is validated using examples, and the normal vector deviation along the boundary curve is investigated.