A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...

We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton–...

in  cite{gl}, b. gerla and i. leuc{s}tean introduced the notion of similarity on mv-algebra. a similarity mv-algebra is an mv-algebra endowed with a binary operation $s$ that verifies certain additional properties. also, chirtec{s} in cite{c}, study the notion of similarity on l ukasiewicz-moisil algebras. in particular, strong similarity l ukasiewicz-moisil algebras were defined. in this paper...

In this paper, we introduce a framework allowing to model and analyse efficiently Gene Regulatory Networks in their temporal and stochastic aspects. The analysis of stable states and inference of René Thomas’ discrete parameters derives from this logical formalism. We offer a compositional approach which comes with a natural translation to the Stochastic π-Calculus. The method we propose consis...

Throughout this presentation I have chosen to use a symbolic matrix notation. This choice was not made lightly. I am a strong advocate of index notation, when appropriate. For example, index notation greatly simplifies the presentation and manipulation of differential geometry. As a rule-of-thumb, if your work is going to primarily involve differentiation with respect to the spatial coordinates...

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary ...

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety classes convexities, is presented. In the various convexities this includes classical convex functions, quasi-convex p-convex (p,s)-convex modified (p,h)-convex tgs-convex η-quasi-convex ϕ-convex (α,m)-convex ϕ-quasi-convex and coordinated functions. Quantum H-H via preinvex functions ...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...