Related papers: High-Order Variational Calculation for the Frequen…
For two linear evolution differential equations systems - a normal ordinary differential equations system and a partial differential equations system with Stokes operator in a main part - with rapidly oscillating by time coefficients in a…
In this paper we develop and use the two-timing method for a systematic study of a scalar advection caused by a general oscillating velocity field. Mathematically, we study and classify the multiplicity of distinguished limits and…
Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
The Bou\'e-Dupuis variational formula gives a representation for log Laplace transforms of bounded measurable functions of a finite dimensional Brownian motion on a compact time interval as an infimum of a suitable cost over a collection of…
In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…
We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and…
Time variation of fundamental constants would not be surprising in the framework of theories involving extra dimensions. The variation of any one constant is likely to be correlated with variations of others in a pattern that is diagnostic…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant. We study the stability of the trivial solution of this Hill equation and we show that a criterion due to…
It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
Charge-transfer excited states are highly relevant for applications in molecular electronics. However, the accurate calculation of these states in large systems is challenging since wave function methods are prohibitively expensive,…
Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
The article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models viz. Fractional continuously variable order mass-spring damper systems. Here, we use the…
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal…