Inverse Operator Method Research Articles

DYNAMIC MEASUREMENTS AS A PROBLEM OF INVERTING CONTROLLED SYSTEMS

The process of dynamic measurements of variable physical quantities is considered. It is assumed that the mathematical model of the measuring channel is known and is a linear stationary dynamic system with one input and one output. The measured physical process enters the input of the system, and the result of measurements takes place at the output, generally, in the form of a digital code. Thus, the measurement problem is to the restore the input signal of a dynamic system with a known output. This interpretation of the dynamic measurement problem corresponds to one of the classical problems of control theory – the inversion problem. In control theory, the solution to the inversion problem is, generally, based on finding the inverse operator of the original dynamical system. When implementing the method of inverse operators, many problems arise, among which the problems of stability, physical feasibility, roughness and correctness of inverse operators should be noted. The paper proposes a simplified approach to solving the inversion problem. Input and output signals are interpolated by cubic splines, the coefficients of which are found by solving a linear system of algebraic equations.

Methods for early recognition of OFDM data

A technique of early recognition (recovery) of data transmitted using OFDM technology by an incompletely received signal is considered. Theoretically, this approach is able to increase the speed of information transfer, as well as the resistance of the de-encoder to the loss of part of the transmitted signal. The article proposes a mathematical formulation of the OFDM signal early recognition problem, and also discusses several methods for solving it: a regularization method, an iterative method based on the fast Fourier transform, a gradient method based on learning, and an inverse operator method. The possibility of simultaneously using several methods to improve the accuracy of information recovery is considered. The results of numerical experiments presented in this work confirm the practical potential of the proposed approach.

Performance of high velocity stream heat exchangers subjected to external heat transfer

Performance is analyzed for kinetic energy variation in high velocity stream heat exchangers that are subjected to external heat transfer. Analytical solutions are obtained using the method of inverse operators. They are verified against the reported expressions in the appropriate limits for constant kinetic energy system as well as for perfectly insulated conditions. Kinetic energy decay in hot stream enhances performance that exceeds the conventional heat exchanger effectiveness. For kinetic-to-thermal energy ratio and dimensionless characteristic length constant each equaling unity on the hot side, the terminal effectiveness under balanced operation is 136% for counter-flow arrangement and 82% for parallel-flow in the absence of external heat load. On the contrary, decay on the cold side lowers performance. For unbalanced flow, kinetic energy change in the higher heat capacity rate fluid has a lesser impact on the effectiveness. Thermal interaction with the ambient generally has a deleterious effect on the hot stream effectiveness of the cryogenic system. However, the performance improves under certain conditions such that the rise in fluid temperature caused by kinetic energy deterioration promotes heat loss to the surroundings.

Strategy for the teaching of linear differential equations with constant coeffcients through the inverse operator method

One of the most desirable aspects of teaching mathematics is the development of a wide variety of strategies that improve the quality of learning in students. This work shows how the implementation of a method based on inverse operators to solve linear differential equations produces better results than other, more traditional, methods. We tested our hypothesis over a group conformed by 80 students from the Biochemistry and Mechatronics Engineering Departments of the Technological Institute of Colima, part of the National Technological Institute of México. The experimental design was comprised by two groups of students: the traditional methods were implemented to the first group of students (named as the control group) while the inverse operator method was taught to the other (named as the test group). The statistical test over the results shows a significant difference between the approval rating of both groups, suggesting that there is enough evidence to conclude that the teaching of inverse operators is an efficient alternative for the solution of linear differential equations with constant coefficients.

Controllability of Fractional Nonlinear Systems in Banach Spaces

This paper investigates the solution of fractional dynamical systems with the inverse operator method and Mittag-Leffler function. Controllability of linear fractional dynamical systems is studied by obtaining the Grammian operator. Sufficient conditions for both nonlinear and integrodifferential systems are established by the contraction principle. Some examples are provided to illustrate the theory.

Note on controllability of linear fractional dynamical systems

In this article, we obtain the solutions of some fractional differential systems with different orders using the inverse operator method and Mittag–Leffler function. Moreover, the controllability of time-invariant linear fractional system is investigated. Some examples are provided to illustrate the theory.

Метод обобщенного обратного оператора в задаче оптимального управления линейными многосвязными статическими объектами

Метод обобщенного обратного оператора в задаче оптимального управления линейными многосвязными статическими объектами

A New Kinetic Equation for Compton Scattering

A kinetic equation for Compton scattering is given that differs from the Kompaneets equation in several significant ways. By using an inverse differential operator, this equation allows treatment of problems for which the radiation field varies rapidly on the scale of the width of the Compton kernel. This inverse operator method describes, among other effects, the thermal Doppler broadening of spectral lines and continuum edges and automatically incorporates the process of Compton heating/cooling. It is well adapted for inclusion into a numerical iterative solution of radiative transfer problems. The equivalent kernel of the new method is shown to be a positive function and with reasonable accuracy near the initial frequency, unlike the Kompaneets kernel, which is singular and not wholly positive. It is shown that iterations of the inverse operator kernel can be easily calculated numerically, and a simple summation formula over these iterations is derived that can be efficiently used to compute Comptonized spectra. It is shown that the new method can be used for initial-value and other problems with no more numerical effort than the Kompaneets equation and that it more correctly describes the solution over times comparable to the mean scattering time.

An approximate solution to the model of a sparged packed bed electrode reactor

An approximate analytical solution to the mathematical model of a sparged packed bed electrochemical reactor (SPBER) in which a gaseous reactant undergoes direct anodic oxidation is presented. The model is based on two strongly nonlinear partial differential equations and is solved by the inverse operator method (IOM). The solution is used to study the direct anodic oxidation of propylene. The approximate IOM solution is useful in that it enables the direct investigation of the effect of model parameters on the operation of the reactor. Current density against electrode potential, polarization data, for the anodic oxidation of propylene in the SPBER is presented. Nonlinear parameter estimate methods are used to fit the model to experimental data to obtain physically meaningful values of kinetic parameters.

A new solution method for state equations of nonlinear system

Along with the computation and analysis for nonlinear system being more and more involved in the fields such as automation control, electronic technique and electrical power system, the nonlinear theory has become quite a attractive field for academic research. In this paper, we derives the solutions for state equation of nonlinear system by using the inverse operator method (IOM) for the first time. The corresponding algorithm and the operator expression of the solutions is obtained. An actual computation example is given, giving a comparison between IOM and Runge-kutta method. It has been proved by our investigation that IOM has some distinct advantages over usual approximation methods in that it is computationally convenient, rapidly convergent, provides accurate solutions not requiring perturbation, linearization, or the massive computations inherent in discrietization methods such as finite differences. So the IOM provides an effective method for the solution of nonlinear system, is of potential application valuable in nonlinear computation.

INVERSE OPERATOR METHOD FOR SOLUTIONS OF NONLINEAR DYNAMICAL EQUATIONS AND SOME TYPICAL APPLICATIONS

In this paper, the inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coulped generalized Duffing equations are investigated by the use of the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields.

Kinetic theory for the volume viscosity in binary mixtures of polyatomic and noble gases

A kinetic expression for the volume viscosity of binary mixtures of polyatomic and noble gases in terms of effective collision cross sections is derived within the framework of first order Chapman-Enskog theory using an inverse operator method. It is shown that the rotational relaxation rate, which is directly related to the volume viscosity, depends linearly on the composition of the mixture if it is assumed that coupling to higher order polynomials in internal and translational energy may be neglected. This result agrees with earlier predictions.

A convenient computational form for the Adomian polynomials

Recent important generalizations by G. Adomian (“Stochastic Systems”, Academic Press 1983) have extended the scope of his decomposition method for nonlinear stochastic operator equations (see also iterative method, inverse operator method, symmetrized method, or stochastic Green's function method) very considerably so that they are now applicable to differential, partial differential, delay, and coupled equations which may be strongly nonlinear and/or strongly stochastic (or linear or deterministic as subcases). Thus, for equations modeling physical problems, solutions are obtained rapidly, easily, and accurately. The methodology involves an analytic parametrization in which certain polynomials A n , dependent on the nonlinearity, are derived. This paper establishes simple symmetry rules which yield Adomian's polynomials quickly to high orders.