Search results for " math"

Stochastic Response on Non-Linear Systems under Parametric Non-Gaussian Agencies

1992

The probabilistic response characterization of non-linear systems subjected to non-normal delta correlated parametric excitation is obtained. In order to do this an extension of both Ito’s differential rule and the Fokker-Planck equation is presented, enabling one to account for the effect of the non-normal input. The validity of the approach reported here is confirmed by results obtained by means of a Monte Carlo simulation.

A novel approach to nonlinear variable-order fractional viscoelasticity.

2020

This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear superposition principle, i.e. the theoretical basis on which linear viscoelastic fractional operators are formulated, does not apply in standard form because the fractional order is not constant with time. Moving from this consideration, the paper proposes a novel approach where the system response is derived by a consistent application of the Boltzmann principle to an equivalent system, built at every time instant based on the fractional order at that instant and the response at all the previous ones. The ap…

Modal analysis for random response of MDOF systems

1990

The usefulness of the mode-superposition method of multidegrees of freedom systems excited by stochastic vector processes is here presented. The differential equations of moments of every order are written in compact form by means of the Kronecker algebra; then the method for integration of these equations is presented for both classically and non-classically damped systems, showing that the fundamental operator available for evaluating the response in the deterministic analysis is also useful for evaluating the response in the stochastic analysis.

Variable fractional Fourier processor: a simple implementation: erratum

1997

Bounds for Bessel functions

1989

We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.

New Types of Jacobian-Free Approximate Riemann Solvers for Hyperbolic Systems

2017

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems with complex Jacobians, as the relativistic magnetohydrodynamics (RMHD) equations. The proposed solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method. Som…

A Leibniz variety with almost polynomial growth

2005

Abstract Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V ˜ 1 defined by the identity y 1 ( y 2 y 3 ) ( y 4 y 5 ) ≡ 0 . We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V ˜ 1 has almost polynomial growth, i.e., the sequence of codimensions of V ˜ 1 cannot be bounded by any polynomial function but any proper subvariety of V ˜ 1 as polynomial growth.

Liftings and extensions of operators in Brownian setting

2020

We investigate the operators T on a Hilbert space H which have 2-isometric liftings S with the property S ∗ S H ⊂ H . We show that such liftings are closely related to some extensions of T, which h...

Solvability of the divergence equation implies John via Poincaré inequality

2014

Abstract Let Ω ⊂ R 2 be a bounded simply connected domain. We show that, for a fixed (every) p ∈ ( 1 , ∞ ) , the divergence equation div v = f is solvable in W 0 1 , p ( Ω ) 2 for every f ∈ L 0 p ( Ω ) , if and only if Ω is a John domain, if and only if the weighted Poincare inequality ∫ Ω | u ( x ) − u Ω | q d x ≤ C ∫ Ω | ∇ u ( x ) | q  dist  ( x , ∂ Ω ) q d x holds for some (every) q ∈ [ 1 , ∞ ) . This gives a positive answer to a question raised by Russ (2013) in the case of bounded simply connected domains. In higher dimensions similar results are proved under some additional assumptions on the domain in question.

Partial *-Algebras of Operators in a PIP-Space

2009

The family of operators on a pip-space V is endowed with two, possibly different, partial multiplications, where partial means that the multiplication is not defined for any pair A,B of elements of Op(V) but only for certain couples. The two multiplications, to be called strong and weak, give rise to two different structures that coincide in certain situations. In this chapter we will discuss first the structure of Op(V) as partial *-algebra in the sense of [AIT02] and then the possibility of representing an abstract partial *-algebra into Op(V).