We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions the geometric Brownian motion with delay. The are written terms parameters explicit case decay. For decay, they easily resolvable numerically. analytical method is based on construction a Lyapunov functional (asymptotic decay) forward-backward estimate (exponential decay).

The guesswork of a quantum ensemble quantifies the minimum number guesses needed in average to correctly guess state ensemble, when only one can be queried at time. Here, we derive analytical solutions problem subject finite set conditions, including solution for any qubit with uniform probability distribution. As explicit examples, compute regular polygonal and polyhedral ensemble.

[1] In this study, we directly derive first-order analytical solutions to the pressure head moments (mean and variance) for one-dimensional steady state unsaturated flow in randomly heterogeneous layered soil columns under various random boundary conditions. We assume that the constitutive relation between the unsaturated hydraulic conductivity and the pressure head follows an exponential model...

In this paper, an analytical solution to the problem of optimal dielectric coating design mirrors for gravitational wave detectors is found. The technique used solve based on Herpin's equivalent layers, which provide a simple, constructive, and solution. performance Herpin-type exceeds that periodic almost equal numerical, non-constructive optimized obtained by brute force. Note existence expli...

The relative motion of an outline the rendezvous problem has been studied by assuming that chief satellite is in circular symmetric orbits. legitimacy perturbation techniques and nonlinear are investigated. deputy equations with respect to fixed references at center general case. We found periodic solutions linear for using Lindstedt–Poincaré technique. Comparisons among analytical motions obta...

The stochastic transport of suspended particles through a periodic pattern of obstacles in microfluidic devices is investigated by means of the Fokker-Planck equation and numerical simulations. Asymmetric arrays of obstacles have been shown to induce the continuous separation of DNA molecules, with particles of different size migrating in different directions within the microdevice (vector sepa...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

We apply Lie algebraic methods of the type developed by Baker, Campbell, Hausdorff, and Zassenhaus to the initial value and eigenvalue problems for certain special classes of partial differential operators which have many important applications in the physical sciences. We obtain detailed information about these operators including explicit formulas for the solutions of the problems of interest...

A setting of the change-point estimation problem with a “smooth” change is investigated. A special class of such models, where the change is defined as a gradual shift in the parameter, is considered. We show that these models can be analyzed via explicitly given procedures. It is demonstrated that M -estimators can consistently estimate the change in the parameter structure as well as the addi...