This paper considers the image recovery problem by taking group sparsity into account as prior knowledge. is formulated a sparse optimization over intersection of polyhedron and possibly degenerate ellipsoid. It convexly constrained with cardinality objective function. We use capped folded concave function to approximate show that solution set continuous approximation solutions are same. Moreov...

The Hamiltonian shape invariant of a domain $X \subset \mathbb {R}^4$ , as subset $\mathbb {R}^2$ describes the product Lagrangian tori which may be embedded in $X$ . We provide necessary and sufficient conditions to determine whether or not path can lift, that is, realized smooth family tori, when is basic $4$ -dimensional toric such ball $B^4(R)$ an ellipsoid $E(a,b)$ with ${b}/{a} \in {N}_{\...

Upright hollow human faces produce among the strongest depth-inversion illusions (DIIs), but why? We considered the role of depth undulations by comparing four types of hollow objects: an ellipsoid, a human mask, and two symmetric 'Martian'masks, which wavered in depth like the human mask but which lacked face-like features. Illusion strength was quantified either as the critical viewing distan...

Lasserre [32] proved that for every compact set K⊂Rn and even number d there exists a unique homogeneous polynomial g0 of degree with K⊂G1(g0)={x∈Rn:g0(x)≤1} minimizing |G1(g)| among all such polynomials g fulfilling the condition K⊂G1(g). This result extends notion Löwner ellipsoid, not only from convex bodies to arbitrary sets (which was immediate if d=2 by taking hulls), but also ellipsoids ...

In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

the effective factors of forward speed, cylinder rotation, and clearance between a combine’s cylinder and concave on wheat kernel breakage and seed germination were studied in karaj area using a 955 model john dear combine. this study was conducted on three levels of adjustment for each of the variables, 1.2, 1.8 and 2.5 km/hr for forward speed, 800, 900, 1000 rpm for cylinder rotation as well ...

In this article we give an overview of the Ellipsoid Method. We start with a historic introduction and provide a basic algorithm in Section 2. Techniques to avoid two important assumptions required by this algorithm are considered in Section 2.2. After the discussion of some implementation aspects, we are able to show the polynomial running time of the Ellipsoid Method. The second section is cl...