Give a way of calculating the area and the estimation of the diameter of the filled-in Julia set for polynomials and Mandelbrot set, get some answers to the problem proposed by A.Douady.
Let R be a commutative ring and f:R→R a power map defined by f(r)=r￣nLet x and y be two periodic points of f witli periods k and l respectively. Setand.In this paper we prove:(1)There exists a periodic map h_x:W_x→W_x of period k such that fh_x=h_xf|W_x and h_x(x)=f(x);(2)If l is a factor of kand y = ux for some u ∈ R, then there exsits a map ξ_u∶W_x→W_y satisfying (a)and(c)If l=k and x=vy also holds for some v ∈ R,then the maps ξ_u andξ_v∶W_y→W_x are mutually inverse.
In 1978.A.R.Camina studied some conditions which almost Characterize Frobenius groups. In this paper,we give a new characteristic of finite groups which satisfy Camina’s conditions and establish some results on these groups.The most basic situation for this new characteristic appears exactly when a finite group has one irreducible character vanishing on all but two conjugacy classes.
Consider the regression model(I),where the(x_i,t_i)are fixed and nonrandom design points,x_i= (x_(i1),…,x_(ip))',β=(β_1,…,β_p)'is an unknown function over[0,1],βis a unknown parameter to be estimated, 0
