We present a subdivision based algorithm to compute the solution of an under-constrained piecewise polynomial system of n − 2 equations with n unknowns, exploiting properties of B-spline basis functions. The solution of such systems is, typically, a two-manifold in R. To guarantee the topology of the approximated solution in each sub-domain, we provide subdivision termination criteria, based on...

where Ω is a smooth bounded domain in R, n 2, and gi(x, u, v) : Ω̄×R×R → R, i = 1, 2, are differentiable functions subject to further restrictions to be named below. We assume that gi(x, u, v), i = 1, 2, satisfy suitable conditions on a bounded rectangle so that a positive strict lower solution pair and a positive strict upper solution pair can be constructed. These assumptions suffice to prove ...

The paper studies language equations of the type X ⋄ L = R and L ⋄ Y = R, where L and R are given languages and ⋄ is an invertible binary word(language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R i...

‎In this paper‎, ‎indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations‎. ‎Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin‎. ‎To solve the pr...

Products: | R&S  SMW200A | R&S  FSW The R&S  SMW200A together with the R&S  FSW is a state of the art testing solution that significantly reduces the required hardware for testing power amplifiers with envelope tracking and/or digital pre-distortion. This application note introduces the test solution in detail and presents corresponding measurement examples.

A bijective map r : X −→ X, where X = {x1, · · · , xn} is a finite set, is called a set-theoretic solution of the Yang-Baxter equation (YBE) if the braid relation r12r23r12 = r23r12r23 holds in X. A non-degenerate involutive solution (X, r) satisfying r(xx) = xx, for all x ∈ X, is called squarefree solution. There exist close relations between the square-free set-theoretic solutions of YBE, the...

We define the principal matrix solution Z(t, s) of the linear Volterra vector integro-differential equation x (t) = A(t)x(t) + t s B(t, u)x(u) du in the same way that it is defined for x = A(t)x and prove that it is the unique matrix solution of ∂ ∂t Z(t, s) = A(t)Z(t, s) + t s B(t, u)Z(u, s) du, Z(s, s) = I. Furthermore, we prove that the solution of x (t) = A(t)x(t) + t τ B(t, u)x(u) du + f (...

We discuss several fundamental questions concerning the problem of minimizing a nonlinear function subject to a set of inequality constraints. We begin by asking: What makes the problem intrinsically diicult to solve, and which characterizations of the solution make its solution more tractable? This leads to a discussion of two important methods of solution: active set and interior points. We m...

In this paper we examine nonlinear integrodifferential inclusions in R . For the nonconvex problem, we show that the solution set is a retract of the Sobolev space W (T,R ) and the retraction can be chosen to depend continuously on a parameter λ. Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retr...

We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...