In this paper we consider design of observers for non-linear models containing both dynamic and algebraic equations, so called differential-algebraic equations (DAE) or descriptor models. The observer is formulated as a DAE and the main results of the paper include conditions that ensure local stability of the observer and also that the observer has index 1. Design methodology is presented and ...

The paper studies language equations of the type X ⋄ L = R and L ⋄ Y = R, where L and R are given languages and ⋄ is an invertible binary word(language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R i...

If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of the computed solution that is obtained in this way solves a nearby real linear system. Thus, it is “numerically safe” to obtain real solutions to real linear systems via the complex Schur decomposition. Th...

This paper presents an interactive mathematical tutor application to assist middle school students with solving single-variable linear and quadratic equations and two-variable systems of linear equations. The system uses a gestural, pen-based interface to mimic and enhance the traditional step-by-step method of solving algebraic problems on paper. After the student handwrites each step, the sys...

Max-algebra, where the classical arithmetic operations of addition and multiplication are replaced by a ⊕ b := max(a, b) and a ⊗ b := a + b offers an attractive way for modelling discrete event systems and optimization problems in production and transportation. Moreover, it shows a strong similarity to classical linear algebra: for instance, it allows a consideration of linear equation systems ...

in this paper, we use the continuous legendre wavelets on the interval [0,1] constructed by razzaghi m. and yousefi s. [6] to solve the linear second kind integral equations. we use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. then we reduced the integral equation to the solution of linear algebraic ...

accurate and nondestructive methods to determine individual leaf areas of plants are useful tools in physiological and agronomic research. a determination of the individual leaf area (la) of such species in brassicaceae family as red cabbage (brassica oleracea var. cappitata l. f. rabra), cabbage (brassica oleracea var. cappitata l. f. alba) and broccoli (brassica oleracea var. italica l.) ...

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equation...