Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

An inverse problem of the elasticity n elastic inclusions embedded into an half-plane is analysed. The boundary free traction. and are subjected to antiplane shear, conditions ideal contact hold in interfaces between half-plane. shapes not prescribed have be determined by enforcing uniform stresses inside inc...

Hoping for a richer supply of phenomena, we should wonder about limits of two-dimensional things (surfaces). It was convenient that all the circles in the solenoids were uniformized compatibly, that is, were compatibly expressed as quotients of R. For ease of description, we choose to look at surfaces X which are quotients of the upper half-plane H in C, with quotient mappings H→ X that fit tog...

In 1911 W. Blaschke and J. Grnwald described the group ~ of proper motions of the euclidean plane d' in the following way: Let (P, fg)be the real three-dimensional projective space, let ~ C P be an isomorphic image of g, and let U ~ f# such that ~ tA U is the projective closure of in P. Then there is a bijection x : ~ ~ P ' := P \ U called the kinematic mapping and an injective mapping ~ × ~ ~ ...

A catalog record for this book is available from the British Library. Harmonic mappings in the plane / Peter Duren. Includes bibliographical references and index.

The finest stereoacuity is known to depend on the disparity of a target relative to other visible points. Here we show that a more important factor in determining sensitivity to displacement can be the disparity of a target relative to an invisible interpolation plane through other neighboring points. We tested the sensitivity of observers to displacements of the central column of a regular gri...

The present paper deals with the mixed mode fracture analysis of a weakened orthotropic half-plane with multiple cracks propagation. The orthotropic half-plane contains Volterra type glide and climb edge dislocations. It is assumed that the medium is under in-plane loading conditions. The distributed dislocation technique is used to obtain integral equations for the dynamic problem of multiple ...