Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

We construct a Lipschitz function on \er^{2} which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and was also cited by other authors

Weak solutions for some compressible multicomponent fluid models

The principle purpose of this work is to investigate a "viscous" version of a "simple" but still realistic bi-fluid model described in [Bresch, Desjardin, Ghidaglia, Grenier, Hillairet] whose "non-viscous" version is derived from physical considerations in \cite[Ishii, Hibiki]{ISHI} as a particular sample of a multifluid model with algebraic closure. The goal is to show existence of weak solutions for large initial data on an arbitrarily large time interval. We achieve this goal by transforming the model to an academic system which resembles to the compressible Navier-Stokes equations, with however two continuity equations and a momentum equation endowed with pressure of complicated structure dependent on two variable densities. The new "academic system" is then solved by an adaptation of the Lions--Feireisl approach for solving compressible Navier--Stokes equation, completed with several observations related to the DiPerna--Lions transport theory inspired by [Maltese, Michalek, Mucha, Novotny, Pokorny, Zatorska] and [Vasseur, Wen, Yu]. We also explain how these techniques can be generalized to a model of mixtures with more then two species. This is the first result on the existence of weak solutions for any realistic multifluid system

Retrodirective Antenna Array Using High Frequency Offset

The paper deals with the design of a simple retrodirective antenna array exhibiting by high frequency offset between received and transmitted wave. Analysis of the beam pointing error using antenna array model developed in MATLAB is described. The frequencies of transmitted wave and received wave are chosen on the basis of this analysis. Then a suitable structure for further design is determined and particular blocks of complete retrodirective antenna array are briefly described and their measured parameters are presented. Relatively high frequency offset between received and transmitted wave makes it possible to use frequency filters for received and transmitted signal separation which led to significant reduction of the circuit complexity