An affine iterated function system (IFS, [4]) over the reals is given by a set of contractive affine transformations on a complete metric space R for some positive natural number k. Thus an interesting problem is to decide, whether a given matrix M describes a contraction mapping, i.e. whether there exists some s < 1 such that |Mz| ≤ s|z| for each z ∈ R, where | · | denotes the Euclidean norm. ...

In this work, we use quantum color cellular automata to study pattern formation and image processing in quantum-diffusion Schrödinger systems with triplet-valued (color-valued) diffusion coefficients. Triplet numbers have the real part and two imaginary parts (with two imaginary units 1  and 2  , where 3 1   ). They form 3-D triplet algebra. Discretization of the Schrödinger equation gives ...

In this paper we solve two problems in linear systems theory: the computation of the inner–outer and spectral factorizations of a continuous–time system considered in the most general setting. We show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the trans...

In the present paper, we give necessary and sufficient conditions for a birational Galois section of a projective smooth curve over either the field of rational numbers or an imaginary quadratic field to be geometric. As a consequence, we prove that, over such a small number field, to prove the birational section conjecture for projective smooth curves, it suffices to verify that, roughly speak...

The goal of this work is self-perception modeling of autonomous agents in virtual story telling. It’s inspired from work of psychologists and neuro-physiologists. From psychology , we use fuzzy cognitive maps (FCM) to model and implement believable agents’ behaviours. These cognitive maps allow us to give not only sensation but also perception, in the sense that our agents perceive environment ...

We consider the symmetric Darlington synthesis of a p × p rational symmetric Schur function S with the constraint that the extension is of size 2p × 2p and we investigate what happens when we impose that S and its extension have real coefficients. In this case, under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the an upper bound for th...

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imagi...

Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal co...