The management of the water supply system becomes crucial day by because limited natural sources and rapidly increasing population all over world. However, distribution systems have various technical problems energy loss in can be counted one these problems. In this study, a designated area Yaka district Konya was examined using Hardy-Cross method and, hydraulic simulation softwares EPANET, Wat...

The denseness of rational functions with prescribed poles in the Hardy space and disk algebra is considered. Notations. C complex plane D unit disk fz : jzj < 1g Tunit circle fz : jzj = 1g H p Hardy space of analytic functions on D kfk 1 := supfjf(z)j : z 2 D g, the H 1 norm A(D) disk algebra of functions analytic on D and continuous on D P n set of polynomials of degree at most n

In this paper, we prove that the distance function of an open connected set in R with a C boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex. We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various impro...

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using notion of a Bessel pair. These offer significantly more information existence/nonexistence extremal functions inequalities. are in spirit Brezis-Vázquez Euclidean spaces. As direct consequences, we establish several type that provide substantial improvements as well simple understandings to many known Hardy-Poinca...