In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

In this paper we use the support of a Boolean function to establish some algebraic properties. These properties allow us to obtain the degree of a Boolean function without having to calculate its algebraic normal form. Furthermore, we derive some algorithms and compute the average time to obtain the degree of some Boolean functions from its support.

Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...

We present δ-calculus, a computational interpretation of Linear Logic, in the form of a typed process algebra whose structures correspond to Proof Nets, and where typing derivations correspond to linear sequent proofs. Term reduction shares the properties of cut elimination in the logic, and immediately we can obtain a number of inherited qualities, among which are termination, deadlock-freedom...

Observers are usually formulated as explicit systems of di erential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Di erential-Algebraic Equation). We review the general idea of DAE observer design of [10]. We give two special normal forms for which DAE observer design yields an observer with linear...

In this paper we describe an aggregation-based algebraic multigrid method for the solution of discrete k-form Laplacians. Our work generalizes Reitzinger and Schöberl’s algorithm to higher-dimensional discrete forms. We provide conditions on the tentative prolongators under which the commutativity of the coarse and fine de Rham complexes is maintained. Further, a practical algorithm that satisf...

We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the state-space of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by sub-spaces that are invariant under the transit...

By a " construction " we mean here a function which takes each structure of one type to some structure of another type; " algebraic " means " such as occurs in algebra ". One example of an algebraic construction is the function F which takes each integral domain R to its field of fractions F(R). Word-constructions, defined below, yield a normal form for algebraic constructions; they also consti...

We present a robust algorithm to construct an “inner” simplicial hull Σ as a single step of subdivision of an input polyhedron P in three dimensional space. Similar to traditional subdivision schemes P becomes the ‘control net’ for free-form modeling while an inner surface triangulation T of Σ is a second level mesh. Free-Form C1 cubic A-patches and C2 quintic A-patches can then be constructed ...