We consider the optimization approach to the acousto-electric imaging problem. Assuming that the electric conductivity distribution is a small perturbation of a constant, we investigate the least-squares estimate analytically using (multiple) Fourier series, and confirm the widely observed fact that acousto-electric imaging has high resolution and is statistically stable. We also analyze the case of partial data and the case of limited-view data, in which some singularities of the conductivity can still be imaged.

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An asymptotic formula for the density of states of the polyharmonic periodic operator (−δ)^{$l$}+$V$in$R$^{$n$},$n$≥2,$l$>1/2 is obtained. Special consideration is given to the case of the Schrödinger equation$n$=3,$l$=1,$V$being a periodic potential, where the second term of the asymptotic is found.

We study $\mathbb{Z}_{2}$ -graded identities of simple Lie superalgebras over a field of characteristic zero. We prove the existence of the graded PI-exponent for such algebras.