We prove the inequality h(x)~ G(x, y)h(y) < cG(x, y) +c, where G is the Green function of a plane domain D , h is positive and harmonic on D , and c is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains c may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plan...

The robust control of networked predictive control systems with random network delay in the feedback channel is studied in this paper. The stabilisation of systems with constant time-delay is discussed by converting the corresponding Lyapunov inequality to a non-linear inequality. To obtain the maximum domain of uncertainties, the non-linear inequality is evolved as a non-linear optimisation co...

The purpose of this article is to obtain the sharp estimates first four initial logarithmic coefficients for class BTs bounded turning functions associated with a petal-shaped domain. Further, we investigate estimate Fekete-Szegö inequality, Zalcman inequality on and Hankel determinant H2,1Ff/2 H2,2Ff/2 entry coefficients.

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

We deal with the mathematical analysis of the coupling problem in a bounded domain of R, n ≥ 1, between a purely quasilinear first-order hyperbolic equation set on a subdomain and a parabolic one, set on its complementary. We start by providing the definition of a weak solution through an entropy inequality on the whole domain. The uniqueness property relies on a pointwise inequality along the ...

In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality. ...

We give a new proof of the isoperimetric inequality in plane, based on Steiner's formula for area convex neighborhood. This establishes directly, without requiring that we separately establish existence an optimal domain. In doing so, this bypasses main difficulty all proofs Steiner outlined plane inequality.