After the improvement by Courtois and Meier of the algebraic attacks on stream ciphers and the introduction of the related notion of algebraic immunity, several constructions of infinite classes of Boolean functions with optimum algebraic immunity have been proposed. All of them gave functions whose algebraic degrees are high enough for resisting the Berlekamp-Massey attack and the recent Rønjo...

In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

Minimum cost variance control (MCV) optimizes the variance of the cost function while the cost mean is kept at a prespecified level. The solutions of the infinite time horizon full-state-feedback MCV problem are found using the Hamilton-Jacobi theory. In the solutions of infinite time horizon MCV control problem, a pair of coupled algebraic Riccati equations arises. This paper considers the exi...

Regular languages can be studied not just for finite words, but also for finite trees, infinite words and infinite trees. Almost all of the theory of regular languages, such as closure under boolean operations, works also for these extensions, but the constructions are significantly more challenging and mathematically interesting. For instance, automata for infinite words can be determinised un...

This work integrates the Kenzo system within Sagemath as an interface and optional package. Our makes it possible to communicate both computer algebra programs enhances SageMath with new capabilities in algebraic topology, such computation of homotopy groups some kind spectral sequences, dealing particular simplicial objects infinite nature. The allows computing that were not known before.

The dispersion equation governing the guided propagation of TE and TM fast wave modes of a circular cylindrical waveguide loaded by metal vanes positioned symmetrically around the wave-guide axis is derived from the exact solution of a homogeneous boundary value problem for Maxwell’s equations. The dispersion equation takes the form of the solvability condition for an infinite system of linear ...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A,M,Φ), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and Φ generalizes the concept of the z-transform to bijective linear mappings from a vector sp...