The theory of prime ends and spatial mappings

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal mappings. In particular, it is found a series of effective conditions on the function Q(x) for a homeomorphic extension of the given mappings to the boundary by prime ends in domains with regular boundaries. The developed theory is applied, in particular, to mappings of the classes of Sobolev and Orlicz-Sobolev and also to finitely bi-Lipschitz mappings that a far-reaching extension of the well--known classes of isometric and quasiisometric mappings.Comment: 40 pages, we improve modulus estimates and on this basis prove a series of new criteria for homeomorphic extension of spatial mappings to the boundary by prime ends in terms of inner dilatation

A New 3 dB Power Divider for MM Wavelengths

This paper presents a new type of 3-dB power divider that achieves wide band, low-loss and symmetric power division. In the paper we discuss the design considerations and present results of measurements at 10 and 100 GHz. The power divider symmetry is examined as a function of the termination loads mismatch. The simplicity of the presented divider makes it very suitable for application at mm and submm bands. The predicted and the measured performance are in very good agreement