In order to solve the A-body Schrödinger equation both accurately and efficiently for open-shell nuclei, a novel many-body method coined as Bogoliubov perturbation theory (BMBPT) was recently formalized applied at low orders. Based on breaking of U(1) symmetry associated with particle-number conservation, this must operate under constraint that average number particles is self-consistently adju...

This paper is concerned with the regularity of shape optimizers a class isoperimetric problems under convexity constraint. We prove that minimizers sum perimeter and perturbative term, among convex shapes, are $$C^{1,1}$$ -regular. To end, we define notion quasi-minimizer fitted to context show any such The proof relies on cutting procedure which was introduced similar results in calculus varia...

We propose a new optimal consumption model in which the degree of addictiveness habit formation is directly controlled through constraint on admissible consumption. In particular, we assume that individual unwilling to consume at rate below certain proportion 0<α≤1 of her habit, exponentially-weighted average past rates. α=1 prohibits process decrease and corresponds completely addictive model....

The problem of covert communication over Multiple-Input Multiple-Output (MIMO) Additive White Gaussian Noise (AWGN) channels is investigated, in which a transmitter attempts to reliably communicate with legitimate receiver while avoiding detection by passive adversary. capacity the MIMO AWGN characterized under variational distance covertness constraint when channel matrices are static and know...