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In this paper we develop a mathematical model of the distribution of microwave electric field in heterogenous biological tissue of mammary gland. We use this model to investigate the efficiency of the medical diagnostic method based on microwave thermometry. Also we run a numerical modeling of electromagnetic field in biotissue of mammary gland for various sets of the spatial structure of biotissue. The small-scale structure is caused by a complex combination of several components: blood flows, fat tissue, muscle tissue, milk lobules, skin. Next we vary in the model the spatial structure of the tissue to evaluate the effect of the heterogeneous structure of the tissue on the distribution of the electromagnetic field in the volume of mammary gland.

In this paper we study the spectrum of the Schrödinger operator on the weighted quasimodel manifolds. We obtain the discreteness criterion for this problem with some restrictions on the potential and geometry of the manifold.