Weakly Nonlinear Mass Transfer in an Internally Soluted and Modulated Porous Layer

The effect of solutal modulation on a rotating porous media is studied. Using solvability condition, the finite amplitude equation is derived at third order of the system. A weakly nonlinear analysis is applied to investigate mass transfer in a porous medium. In this article, the stationary convection is discussed in the presence of solutal Rayleigh number. The amplitude equation (GLE) is solved numerically. Using this GLE the Sherwood number is evaluated in terms of the various system parameters. The effect of individual parameters on mass transport is discussed in detail. It is found that the mass transfer is more for modulated system than un-modulated case. Further, internal solute number Si enhance or diminishes the mass transfer. Finally it is also found that, solutal modulation can be effectively applied in either enhancing or diminishing the mass transfer.

A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition

A parameter identification inverse problem in the form of nonlinear least squares is considered. In the lack of stability, the frozen iteratively regularized Gauss–Newton (FIRGN) algorithm is proposed and its convergence is justified under what we call a generalized normal solvability condition. The penalty term is constructed based on a semi-norm generated by a linear operator yielding a greater flexibility in the use of qualitative and quantitative a priori information available for each particular model. Unlike previously known theoretical results on the FIRGN method, our convergence analysis does not rely on any nonlinearity conditions and it is applicable to a large class of nonlinear operators. In our study, we leverage the nature of ill-posedness in order to establish convergence in the noise-free case. For noise contaminated data, we show that, at least theoretically, the process does not require a stopping rule and is no longer semi-convergent. Numerical simulations for a parameter estimation problem in epidemiology illustrate the efficiency of the algorithm.

BOUNDARY VALUE PROBLEM WITH SHIFT FOR A FRACTIONAL ORDER DELAY DIFFERENTIAL EQUATION

В работе доказана теорема существования и единственности решения краевой задачи со смещением для дифференциального уравнения дробного порядка с запаздывающим аргументом. Решение задачи выписано в терминах функции Грина. Получено условие однозначной разрешимости и показано, что оно может нарушаться только конечное число раз. In this paper we prove existence and uniqueness theorem to a boundary value problem with shift for a fractional order ordinary delay differential equation. The solution of the problem is written out in terms of the Green function. We find an explicit representation for solvability condition and show that it may only be violated a finite number of times

Necessary condition for solvability of the control problem of an asynchronous spectrum of linear almost periodic systems with trivial averaging of the coefficient matrix

We consider a linear control system with an almost periodic matrix of coefficients. The control has a form of feedback and is linear in phase variables. It is assumed that the feedback coefficient is almost periodic and its frequency modulus, i.e. the smallest additive group of real numbers, including all Fourier exponents of this coefficient, is contained in the frequency module of the coefficient matrix.The following problem is formulated: choose such a control from an admissible set so that the closed system has almost periodic solutions, the frequency spectrum (a set of Fourier exponents) of which contains a predetermined subset, and the intersection of the solution frequency modules and the coefficient matrix is trivial. The problem is called the control problem of the spectrum of irregular oscillations (asynchronous spectrum) with a target set of frequencies.The aim of the work aws to obtain a necessary solvability condition for the control problem of the asynchronous spectrum of linear almost periodic systems with trivial averaging of coefficient matrix The estimate of the power of the asynchronous spectrum was found in the case of trivial averaging of the coefficient matrix.

Backstepping-based output regulation of ordinary differential equations cascaded by wave equation with in-domain anti-damping

Output regulation is considered in this paper for ordinary differential equations cascaded by a wave equation, in which both the body equations and the uncontrolled end are subject to disturbances. The disturbances are generated by an exosystem. A backstepping state-feedback regulator is first designed to force the output to track the reference signal. The design is based on solving cascaded regulator equations, and the solvability condition of the equations is characterized in terms of a transfer function and the eigenvalues of the exosystem. An observer-based output-feedback regulator is then designed to solve the output regulation problem. Finally, the regulator tracking performance is illustrated through numerical simulations.

RESEARCH OF STABILIZATION CONDITIONS AND ROBUST STABILITY OF DISCRETE ALMOST CONSERVATIVE SYSTEMS

Conditions for the stabilizability of discrete almost conservative systems in which the coefficient matrix of a conservative part has no multiple eigenvalues are investigated. It is known that a controllable system will be stabilized if its coefficient matrix is asymptotically stable. The system stabilization algorithm is constructed on the basis of the solvability condition for the Lyapunov equation and the positive definiteness of P0 and Q1. This theorem shows how to find the parameters of a controlled system under which it will be asymptotically stable for sufficiently small values of the parameter e (P > 0, Q > 0). In addition, for a small parameter e that determines the almost conservatism of the system, an interval is found in which the conditions for its stabilizability are satisfied (Theorem 2).