Let S be the standard class of univalent functions in the unit disk, and let So be the class of nonvanishing univalent functions g with g(0) = 1. It is shown that the regions of variability {g(r): g £ So} and {(1 — r2)f'(r) : f £ S} are very closely related but are not quite identical. Let 5 be the class of functions / analytic and univalent in the unit disk D, with /(0) = 0 and /'(O) = 1. Let ...

regular and schlicht (univalent) in | z | < 1, i.e. assuming distinct values w for distinct values of z. The functions f(z) e S map | z | < 1 1 : 1 conformally onto a simply connected domain D in the w plane. During the last international Congress at Harvard Professors Schaeffer and Spencer [12] reported on the progress, largely due to their own work, on the so-called coefficient problem for S,...

The Andreev-Koebe-Thurston circle packing theorem is generalized and improved in two ways. First, we get simultaneous circle packings of the map and its dual map so that, in the corresponding straight-line representations of the map and the dual, any two edges dual to each other are perpendicular. Necessary and sufficient condition for a map to have such a primal-dual circle packing representat...

water quality prediction is a valuable tool for pollutant control in aquatic environments. a river system is selected and one-dimensional flow is assumed for the simulation of pollutant transport in this paper. advective and diffusive terms of transport equation are considered separately. different functions of advective transport are proposed and applied for a specified velocity on the discret...

chess is considered as a cognitive game because of severe engagement of the mental resources during playing. the purpose of this study is evaluation of frontal lobe function of chess players with matched non-players. wisconsin card sorting test (wcst) data showed no difference between the player and non-player groups in preservation error and completed categories but surprisingly showed signifi...

In this paper we start a new approach to the uniformization problem of Riemann surfaces and algebraic curves by means of computational procedures. The following question is studied: Given a compact Riemann surface S described as the quotient of the Poincaré upper half-plane divided by the action of a Fuchsian group, find explicitly the polynomial describing S as an algebraic curve (in some norm...

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...