Search results for "Applied Mathematics"
showing 10 items of 4379 documents
New Invariant Domain Preserving Finite Volume Schemes for Compressible Flows
2021
We present new invariant domain preserving finite volume schemes for the compressible Euler and Navier–Stokes–Fourier systems. The schemes are entropy stable and preserve positivity of density and internal energy. More importantly, their convergence towards a strong solution of the limit system has been proved rigorously in [9, 11]. We will demonstrate their accuracy and robustness on a series of numerical experiments.
Truncation, Information, and the Coefficient of Variation
1989
The Fisher information in a random sample from the truncated version of a distribution that belongs to an exponential family is compared with the Fisher information in a random sample from the un- truncated distribution. Conditions under which there is more information in the selection sample are given. Examples involving the normal and gamma distributions with various selection sets, and the zero-truncated binomial, Poisson, and negative binomial distributions are discussed. A property pertaining to the coefficient of variation of certain discrete distributions on the non-negative integers is introduced and shown to be satisfied by all binomial, Poisson, and negative binomial distributions.
$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations
2020
We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…
Non-Stationary Probabilistic Response of Linear Systems Under Non-Gaussian Input
1991
The probabilistic characterization of the response of linear systems subjected to non-normal input requires the evaluation of higher order moments than two. In order to obtain the equations governing these moments, in this paper the extension of the Ito’s differential rule for linear systems excited by non-normal delta correlated processes is presented. As an application the case of the delta correlated compound Poisson input process is treated.
A Stieltjes Approach to Static Hedges
2014
Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…
Jacobi Fields, Conjugate Points
2001
Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.
Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach
2011
In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.
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.