A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called ”off shell” Bethe Ansatz [1]. The highest weight property of the solutions is proved.

This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation r t xΔ t γ Δ p t x g t 0 on an arbitrary time scale T with sup T ∞, where g t ≥ t and ∫∞ to Δs/ r1/γ s < ∞. Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify th...

A nonhomogeneous system of linear recurrence equations can be recognized by an automaton A over a one-letter alphabet A = {z}. Conversely, the automaton A generates precisely this nonhomogeneous system of linear recurrence equations. We present the solutions of these systems and apply the z-transform to these solutions to obtain their series representation. Finally, we show some results that si...

Global asymptotic stability of rational difference equations is an area of research that has been well studied. In contrast to the many current methods for proving global asymptotic stability, we propose an algorithmic approach. The algorithm we summarize here employs the idea of contractions. Given a particular rational difference equation, defined by a function Q : R → R, we attempt to find a...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...

Inference mechanisms and interpretations of fuzzy rule bases are studied together from the point of view of systems of fuzzy relation equations. A proper use of an inference mechanism connected to a fuzzy relation interpreting a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations which are motiva...

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal ope...

in this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and...