Sparsity Enhanced Beamforming in The Presence of Coherent Signals

In order to find the directions of coherent signals, a sparsity enhanced beam-forming method is proposed. Unlike the conventional minimum variance distortless response (MVDR) method, the minimum variance in the proposed method corresponds to the orthogonal relationship between the noise subspace and the sparse representation of the received signal vector, whereas the distortless response corresponds to the nonorthogonal relationship between the signal subspace and the sparse representation of the received signal vector. The proposed sparsity enhanced MVDR (SEMVDR) method is carried out by the iterative reweighted Lp-norm constraint minimization. for direction finding of coherent signals. Simulation results are shown that SEMVDR has better performance than the existing algorithms, such as MVDR and MUSIC, when coherent signals are present.

New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

In this paper, we study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − κ u Δ ( u 2 ) + μ h 2 ( | x | ) | x | 2 ( 1 + κ u 2 ) u + μ ( ∫ | x | + ∞ h ( s ) s ( 2 + κ u 2 ( s ) ) u 2 ( s ) d s ) u = f ( u ) in R 2 , κ > 0 V ∈ C 1 ( R 2 , R ) and f ∈ C ( R , R ) By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.

A Vectorized Regularization Method for Multivalued Parameters Identification

The identification of multivalued parameters is formulated as a constraint minimization problem called primal problem. We embed it in a family of perturbed problems and we associate a dual problem with it using the conjugate functions. Basing on the primal-dual relationship, under some qualification conditions on the parameters to be identified we elaborate the well posedeness, convergence and stability of the solution assuming. Numerical simulations are described in the end for the identification of discontinuous dispersion tensor in transport equations.

Standing waves of modified Schrödinger equations coupled with the Chern–Simons gauge theory

We are interested in standing waves of a modified Schrödinger equation coupled with the Chern–Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the nonexistence for nontrivial solutions.

FUMILI-based minimization with constraints using method of elimination of differentials

Kinematic filtting is one of the popular particle physics problems where constraint minimization is used. The constraints setting additional relations between parameters p can be given in form of equations φ(p1,..., pn) = 0. Often these equations are non-linear and complicated, and thus it is impossible or impractical to eliminate redundant parameters directly. The article covers employing of the minimization approach called a method of elimination of differentials, that is being developed at JINR as an extension to the FUMILI minimizer, and is intended for kinematic filtting in particle physics experiments.

Existence of nodal solutions for quasilinear elliptic problems in ℝN

We prove the existence of one positive, one negative and one sign-changing solution of a p-Laplacian equation on ℝN with a p-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on the whole of ℝN have scarcely been investigated in the literature. Our assumptions here are similar to those previously used by some authors in bounded domains, and our proof uses fairly elementary critical point theory, based on constraint minimization on the nodal Nehari set. The lack of compactness due to the unbounded domain is overcome by working in a suitable weighted Sobolev space.