Given an unknown signal x0 ∈ R and linear noisy measurements y = Ax0 + σv ∈ R, the generalized `2-LASSO solves x̂ := argminx 12‖y −Ax‖ 2 2 + σλf(x). Here, f is a convex regularization function (e.g. `1-norm, nuclearnorm) aiming to promote the structure of x0 (e.g. sparse, lowrank), and, λ ≥ 0 is the regularizer parameter. A related optimization problem, though not as popular or well-known, is of...

in this paper,  we introduce the notion of  generalized multivalued  $f$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  our results extend and improve the results announced by many others with less hypothesis. also, we give some illustrative examples.

Codebooks with small inner-product correlation are applied in many practical applications including direct spread code division multiple access communications, space-time codes and compressed sensing. It is extremely difficult to construct codebooks achieving the Welch or Levenshtein bound. In this paper, we firstly generalize Jacobi sums over finite fields and secondly obtain asymptotically op...

We find a new, asymptotically better, bound g 6 1 4 d2 + O(d) on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except g = 0 (the original conjecture).

We find a new, asymptotically better, bound g 6 1 4 d + O(d) on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except g = 0 (the original conjecture).