Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials
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In this paper, we give a positive answer to the open question: Can there exist 4 limit cycles in quadratic near-integrable polynomial systems? It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3,1) distribution. The method of Melnikov function is used.Quadratic function is one of the important topic in mathematics. The purpose of this study is to describe the mistakes made by students when drawing a quadratic function graph. In this research, the focus of the problem is what type of mistakes made by students in drawing a graph of quadratic functions. The form of error here referred to an error in doing the exercise of drawing quadratic function graph in learning with the PBL model using a true or false strategy assisted by GeoGebra application. The conclusion of this research states that the error in drawing quadratic function graph is dominated by procedural errors. PBL model with true or false strategy with the help of GeoGebra application can be an alternative learning to overcome students' mistakes in drawing quadratic function graphs
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Following an example in [12],we show how to change one coordinate function of analmost perfect nonlinear(APN) function in order to obtain new examples. It turns out thatthis is a very powerful method to construct newAPN functions. In particular, we show that our approach canbe used to construct a ''non-quadratic'' APN function.This new exampleis in remarkable contrast to all recently constructed functions whichhave all been quadratic.An equivalent function has been found independentlyby Brinkmann and Leander [8]. However, theyclaimed that their function is CCZ equivalent to a quadratic one. In thispaper we give several reasonswhy this new function is not equivalent to a quadratic one.
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It is known that the q-Heun equation has polynomial-type solutions in some special cases, and the condition for the accessory parameter E is described by the roots of the spectral polynomial. We investigate the spectral polynomial by considering the ultradiscrete limit.
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In order to improve the accuracy of the FBG temperature sensor,a new packaging method is proposed and the detected temperatures are fitted by quadratic polynomial function. The new packaging method can eliminate the cross-sensitivity of stress. Linear fitting and quadratic polynomial fitting are applied respectively,and the sensor demonstrates good stability and repeatability by quadratic polynomial fitting. The degree of the quadratic polynomial fitting is greater than 0. 9999 and the temperature error is less than 0. 13℃ in the temperature range of 0℃ ~ 80℃. The proposed sensor can be applied in engineering practice with good accuracy and reliability.
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It is known that the q-Heun equation has polynomial-type solutions in some special cases, and the condition for the accessory parameter E is described by the roots of the spectral polynomial. We investigate the spectral polynomial by considering the ultradiscrete limit.
Spectral Analysis
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This paper studied the number of limit cycles in a family of polynomial systems by using the Melnikov method. It computed the Melnikov function and estimated the upper bound degree of it. The result was applied for a Lienard disturbed system of three degree and the maximum number of limit cycles of this system was obtained.
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This chapter discusses quadratic equations and quadratic functions, which are the simplest type of non-linear relationship. It illustrates that a quadratic function, when graphed, produces a characteristically U-shaped curve. The chapter then shows how to solve quadratic equations, including simultaneous quadratic equations. At the end of the chapter two applications of quadratic functions in economics are briefly presented.
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In this paper, we give a positive answer to the open question: Can there exist 4 limit cycles in quadratic near-integrable polynomial systems? It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3,1) distribution. The method of Melnikov function is used.
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