The theorem of Jung establishes a relation between circumradius and diameter of a convex body. The half of the diameter can be interpreted as the maximum of circumradii of all 1-dimensional sections or 1-dimensional orthogonal projections of a convex body. This point of view leads to two series of j-dimensional circumradii, defined via sections or projections. In this paper we study some relati...

Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n + 2 > 4 admits a Lefschetz fibration over the disk D with Stein regular fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of right-handed Dehn twists along embedded Lagrangian n-spheres on the generic fiber. This generalizes the Stein surface case of n = 1, previo...

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product L⊗̂J , and that the obstruction for the comparison map K(L⊗̂J ) → K(...

We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if L ⊂ X is an exact Lagrangian submanifold of an exact symplectic manifold with convex end Λ ⊂ Y , where Y is a contact manifold and Λ is a Legendrian submanifold, and if L has empty concave end, then the linearized Legendrian ...

This theorem is similar to the well known result that any point in the convex hull of a set E in an w-dimensional euclidean space lies in the convex hull of some subset of E containing at most n-\-l points [l, 2 ] . 1 In these theorems the set E is an arbitrary set in the space. The convex hull of E, denoted by H(E), is the set product of all convex sets in the space which contain E. A euclidea...

In this paper we address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank pen...

Geodesic convex sets, Steiner convex sets, and J-convex (alias induced path convex) sets of lexicographic products of graphs are characterized. The geodesic case in particular rectifies [4, Theorem 3.1].

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

We examine decision problems for various classes of convex languages, previously studied by Ang and Brzozowski under the name “continuous languages”. We can decide whether a language L is prefix-, suffix-, factor-, or subword-convex in polynomial time if L is represented by a DFA, but the problem is PSPACE-hard if L is represented by an NFA. If a regular language is not convex, we prove tight u...