We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi’s method by applying it to the same equation studied by Musielak et al. with their own method [Musielak ZE, Roy D and Swift LD. Method to derive Lagrangian and Hamiltonian for a nonlinear dynami...

In this article we consider the boundary stabilization of a wave equation with variable coefficients. This equation has an acceleration term and a delayed velocity term on the boundary. Under suitable geometric conditions, we obtain the exponential decay for the solutions. Our proof relies on the geometric multiplier method and the Lyapunov approach.

In this paper, an effective approach is proposed for designing discrete coefficient 2-D FIR digital filters for sampling structure conversion. After obtaining the initial continuous solution, the conventional Lagrange multiplier approach associated with an appropriate tree search algorithm is used iteratively to optimize the remaining unquantized coefficients of the designed filter in the least...

Auscultation signals are nonstationary in nature. Wavelet packet transform (WPT) has currently become a very useful tool in analyzing nonstationary signals. Sample entropy (SampEn) has recently been proposed to act as a measurement for quantifying regularity and complexity of time series data. WPT and SampEn were combined in this paper to analyze auscultation signals in traditional Chinese medi...

We establish weighted L2−estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L2−norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.

In this article, we consider a nonlinear transmission problem for the wave equation with time dependent coefficients and linear internal damping. We prove the existence of a global solution and its exponential decay. The result is achieved by using the multiplier technique and suitable unique continuation theorem for the wave equation.

We prove a formula for the multiplier ideals of stratified locally conical divisors, generalizing a formula of Mustata for a hyperplane arrangement with a reduced equation. We also give a partial converse to a result of Ein, Lazarsfeld, Smith, and Varolin on the relation between the jumping coefficients and the roots of the Bernstein-Sato polynomial.

The F–thresholds are characteristic p analogs of the jumping coefficients for multiplier ideals in characteristic zero. In this article we give an alternative description of the F–thresholds of an ideal in a regular and F–finite ring R. This enables us to settle two open questions posed in [MTW], namely we show that the F–thresholds are rational and discrete.

We consider various Hilbert spaces of Dirichlet series whose norms are given by weighted l2 norms of the Dirichlet coefficients. We characterize the multiplier algebras for some of these spaces. 0 Introduction Let w = {wn}n=n0 be a sequence of positive numbers. In this paper we are concerned with Hilbert spaces of functions representable by Dirichlet series: H w = {

The conventional input-output model has been widely criticised, both justly and unjustly, for its limiting assumptions. One of these assumptions is homogeneity of degree one. This paper explores some approaches to minimise this limitation of traditional input-output analysis by removing the assumption of linear coefficients for the intermediate and household sectors. As is well documented in th...