we consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmpxypxypxy++++2(,)(,)(,)nnmnmyqxyqxyqxy++&=++. for where and are homogeneous polynomials of degree i. inside this class of polynomial differential equation we consider a subclass of darboux integrable systems. moreover, under additional conditions we proved such darboux integrable systems can have at most 1 limit cycle.

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

The era of Society 5.0 brought significant developments to the world education. Teachers and community must be skilled have adequate abilities in welcoming society 5.0. Infrastructure, human resource development (HR), synchronization between education use technology, these four things a major role entering sociaty that will create qualified graduates. This paper aims provide an overview learnin...

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

let g be a simple graph and (g,) denotes the number of proper vertex colourings of gwith at most  colours, which is for a fixed graph g , a polynomial in  , which is called thechromatic polynomial of g . using the chromatic polynomial of some specific graphs, weobtain the chromatic polynomials of some nanostars.

this paper presents a gain scheduled autopilot for pitch channel of a flying vehicle. the selected method is based on polynomial fuzzy systems. the method does not involve linearization about operating point. first the polynomial fuzzy model of pitch channel of the flight body is derived. next, using polynomial fuzzy system methodology the controller is design such that the outputs of the nonli...

in this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. finally, to illustrate some numericalexamples are solved.