Space separating special geffert normal form for succinct representation of star-controlled insertion-deletion systems

The paper extends the notion of the Special Normal Form (SNF) for Boolean functions to ternary logic functions. An algorithm to minimize the generalized Galois field (GF) expressions for ternary functions by using SNF is presented.

It is shown that a Hamiltonian system in the neighbourhood of an equilibrium may be given a special normal form in case four of the eigenvalues of the linearized system are of the form $\lambda_1, -\lambda_1, \lambda_2, -\lambda_2,$ with $\lambda_1$ and $\lambda_2$ independent over the reals, i.e., $\lambda_1/\lambda_2 \notin \mathbf R$. That is, for a real Hamiltonian system and concerning the variables $x_1, y_1, x_2, y_2$ the equilibrium is of either type <em>center–saddle</em> or <em>complex–saddle</em>. The normal form exhibits the existence of a four–parameter family of solutions which has been previously investigated by Moser. This paper completes Moser's result in that the convergence of the transformation of the Hamiltonian to a normal form is proven.

It is shown that a Hamiltonian system in the neighbourhood of an equilibrium may be given a special normal form in case the eigenvalues of the linearized system satisfy non–resonance conditions of Melnikov’s type. The normal form possesses a two dimensional (local) invariant manifold on which the solutions are known. If the eigenvalue is pure imaginary then these solutions are the natural continuation of a normal mode of the linear system. The latter result was first proved by Lyapounov. The present paper completes Lyapounov’s result in that the convergence of the transformation of the Hamiltonian to a normal form is proven and the condition that the eigenvalues be pure imaginary is removed.

We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate chang

This paper presents a new approach for observer design for a class of nonlinear singular systems which can be transformed into a special normal form. The interest of the proposed form is to facilitate the observer synthesis for the studied nonlinear singular systems. Necessary and sufficient geometrical conditions are deduced in order to guarantee the existence of a diffeomorphism which transforms the studied nonlinear singular systems into the proposed normal form.

A new method of organizing an information storage and retrieval system is proposed and theoretically evaluated. The method uses a special normal form into which the queries entering the system are transformed. This normal form enables one to determine easily the decomposition of the set of records relevant to a query into the minimal number of segments of records stored in consecutive storage locations, and to compute the addresses of the beginning and end of each of these segments.

Semi-global stabilization of minimum phase nonlinear systems in special normal forms

A Partial-State Observer for a Class of MIMO Nonlinear Systems

On the computational completeness of graph-controlled insertion–deletion systems with binary sizes

Composing regular expressions for test questions is often a difficult thing for the teachers; so many teachers avoid using regular expression questions. Similar problems hinder students learning regular expressions as a part of computer science. There are many programs developed to help composing and learning of the regular expressions, but they are using different forms of regular expression visualization. The goal of this research was to compare efficiency of different forms of regular expression representation for their learning and composing, methods for linking them together and with regular expression text. A set of helping tools for regular expressions authors (as a plugin for Moodle CMS) was developed, using three form of regular expression representation: syntax tree (visualizes expression structure), explanation graph (visualizes paths of expression execution) and text description – and testing tool, showing regular expression match with test strings. Developed instruments was used by students learning regular expressions, the students fill a survey after that. Students were divided into four groups by their year of study and country. Survey shows that different group of students prefer different instruments. Most generally popular ones were explanation graph and regular testing, but even text description – a general outsider – was leading in the group of students from Africa learning in English language. The survey also shows that ability to select part of regular expression representation and see that part selected in other representations and regular expression text was very useful in linking representations together and understanding complex expressions. About a quarter of students used other regular expression construction tools before taking part in this experiment, most of them said that developed tools were better than those they used before. Several teachers, which had used regular expressions in their questions, have written reviews stating that developed instruments make learning regular expressions easier and help debug regular expressions in their questions. So, the survey of students and teachers reviews shows that system of several regular expression representations linked together by subexpression selection is more effective that any particular representation in itself; different classes of users prefer different forms of representation. Including helping tools for regular expression authors in the quiz creation software allows increasing the use of regular expressions for quiz questions and helps test and debug them.

Bent functions are functions that have the largest distance to all linear functions. Due to this property bent functions hedge statistical attacks against cryptosystems. This contribution reflects some steps on the way of the specification of Boolean bent functions by O. S. Rothaus, over the description of such bent functions using Boolean differential equations by Bernd Steinbach, the enumeration of bent functions by Natalia Tokareva, the evaluation of classes of bent functions using the Special Normal Form (SNF) by Bernd Steinbach and Christian Posthoff, the embedding of bent functions into other properties needed in cryptosystems by Jon T. Buttler and Tsutomu Sasao, the extension of such properties by Chunhui Wu and Bernd Steinbach, to the generalization to multi-valued bent function by Claudio Moraga et al.

We provide an alternative solution to the problem of semi‐global stabilization of a class of minimum phase nonlinear systems which is considered in Reference 17. Our method yields a stabilizinglinearstate feedback law in contrast to anonlinearstate feedback law proposed in Reference 17. We eliminate the peaking phenomenon by inducing a specific time‐scale structure in the linear part of the closed‐loop system. This time‐scale structure consists of a very slow and a very fast time scale. The crucial component in our method is the relation between the slow and the fast time scales. Our proposed linear state feedback control law has asingletunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in somea priorigiven (arbitrarily large) bounded set.

Identifying and characterizing geometric structure in the flow of a nonlinear dynamical system can facilitate understanding, model simplification, and solution approximation. The approach addressed in this paper uses information from finite-time Lyapunov exponents and vectors associated with the tangent linear dynamics. We refer to this approach as finite-time Lyapunov analysis (FTLA). FTLA identifies the potential for flow structure based on the stability and timescales implied by the spectrum of finite-time Lyapunov exponents. The corresponding Lyapunov vectors provide a basis for representing a splitting of the tangent space at phase points consistent with the splitting of the spectrum. A key property that makes FTLA viable is the exponential convergence of the splitting as the finite time increases. Tangency conditions for the vector field are used to determine points on manifolds of interest. The benefits of the FTLA approach are the dynamical model need not be in a special normal form, the manifolds of interest need not be attracting nor of known dimension, and the manifolds need not be associated with a fixed point or periodic orbit. After a brief review of FTLA, it is applied to spacecraft stationkeeping around a libration point in the circular restricted three-body problem. This application requires locating the stable and unstable subspaces at points on periodic and aperiodic orbits. For the periodic case, the FTLA subspaces are shown to agree with the Floquet subspaces; for the quasi-periodic case, the accuracy of the FTLA subspaces is demonstrated by simulation.

The problem of robust stabilization for nonlinear systems with mismatched uncertainties is further studied by extending the results of Liao (1992) to the case where nonlinear systems either fail to have well-defined relative degree or have unstable zero dynamics. The approach is based on the approximate input/output linearization introduced by Hauser (1992) and an appropriate transformation introduced by Allgower (1997) which transforms the given nonlinear system into a special normal form. The proposed feedback controller guarantees that all the states will remain bounded.

The authors provide an alternative solution to the problem of semiglobal stabilization of a class of minimum phase nonlinear systems that was considered by A.R. Teel (1991). The method used yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed by Teel. The peaking phenomenon is eliminated by inducing a specific time-scale structure in the linear part of the closed-loop system. This structure consists of a very slow and a very fast time scale. The crucial component in the method is the relation between the slow and the fast time-scales. The proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set. >