Concept Of Characteristic Function Research Articles

Complex Neutrosophic Subsemigroups and Ideals

In this article we study the idea of complex neutrosophic subsemigroups. We define the Cartesian product of complex neutrosophic subsemigroups, give some examples and study some of its related results. We also define complex neutrosophic (left, right, interior) ideal in semigroup. Furthermore, we introduce the concept of characteristic function of complex neutrosophic sets, direct product of complex neutrosophic sets and study some results prove on its.

Model reference adaptive vector control for induction motor without speed sensor

The wide applications of vector control improve the high-accuracy performance of alternating current (AC) adjustable speed system. In order to obverse the full-order flux and calculate the real-time speed, this article introduces the motor T equivalent circuit to build a full-order flux observer model, where the current and flux variables of stator and rotor are adopted. Model reference adaptive control is introduced to build the AC motor flux observer. The current output is used as feedback to build the feedback matrix. The calculation method of motor speed, which is part of the inputs of flux observation, is applied to realize the adaptive control. The concept of characteristic function is introduced to calculate the flux, of which the foundation is the variables of composite form of voltage and current models. The characteristic function is deduced as a relative-state variable function. The feedback matrix is improved and designed to ensure the motor flux observer is a smooth switch between current and voltage model in low and high speeds, respectively. Experimental results show that the feedback and characteristic model are feasible, and the vector control with speed sensorless based on the full-order flux observer has better performance and anti-disturbance.

A half-wave rectifier circuit as a bilinear stochastic differential system

Abstract Bilinear stochastic differential systems have found striking applications in diverse fields, e.g. autonomous systems under noise influence, population models, theoretical biology and switched electrical networks. Because of their surprising applications, this paper develops the closed-form solution for a Stratonovich time-varying bilinear Stochastic Differential Equation (SDE). Subsequently, the analytic result of this paper is applied to a simple, but an appealing half-wave rectifier electronic circuit. Furthermore, we derive the mean and variance expressions of the state satisfying the rectifier SDE. The stochastic differential rule in combination with the concept of characteristic function of the Gaussian stochastic process plays the key role to develop the theory of this paper. The results of this paper will be useful to accomplish the noise analysis of bilinear systems arising from systems and control literature.

Axiomatization in cooperative game theory

We develop a theory of cooperative games based on a new concept of characteristic function. This approach substantially reduces the number of solutions and shows that noncooperative equilibria lead in some cases to a unique cooperative solution.

COHERENT EFFECTS IN SINGLE SCATTERING AND RANDOM ERRORS IN ANTENNA TECHNOLOGY

Lack of knowledge prevents us from exactly calculating the behavior of electromagnetic fields. We study two extremes in this respect: scattering against randomly distributed particles ( no idea of the position or orientation of the scatterers), and random errors in antenna technology ( small deviations from what we think are the proper parameters). Random variables are used to model our lack of knowledge, and far field expressions are studied. Using the concept of characteristic functions from probability theory, results for arbitrary probability distributions are obtained. We explain an anomaly in the forward scattering direction in single scattering theory, present simple formulas for the directivity, side lobe level, and beam efficiency for a general array antenna with random errors, and a simple formula for the scattering coefficient from a general frequency selective structure with random errors. (Less)

On the inverse scattering problem for dielectric cylindrical scatterers

A solution of the inverse scattering problem for dielectric circular cylindrical scatterers has been presented on the basis of the exact electromagnetic theory of scattering. Two new contributions have been made. First, a new concept of characteristic functions has been introduced. It has been shown that the extremum properties of these functions determine the radii uniquely from the coefficients of the cylindrical wave expansion of the scattered field amplitude. Second, it has been shown that the complex amplitude coefficients can be uniquely retrieved from the measurement of the far-field irradiance alone and that no phase information is necessary. This has been achieved by giving a Fourier representation for the scattered far-field irradiance; the Fourier coefficients are obtained in terms of the amplitude coefficients. Determination of the amplitude coefficients from the Fourier coefficients is facilitated by a special relation that has been found to exist between the real and the imaginary parts of each amplitude coefficient. Some results of our numerical investigation have also been included.

Characteristic Functions and Sets

The simple concept of characteristic function is a powerful tool for the study of the algebra of sets; it has not as yet been used in our teaching. The present paper is written to show the interest of this concept. However, this tool must be used only with pupils who have had much experience with sets. During the long period of learning our task is to form and build up concepts; the child must learn in various situations and at the same time “he accumulates,” says Dienes, “a capital to which he will later on refer.” It is only after this stage that we can provide powerful tools and “elegant” methods.