For n ≥ 2 a construction is given for a large family of compact convex sets K and L in Rn such that the orthogonal projection Lu onto the subspace u⊥ contains a translate of the corresponding projection Ku for every direction u, while the volumes of K and L satisfy Vn(K) > Vn(L). It is subsequently shown that, if the orthogonal projection Lu onto the subspace u⊥ contains a translate of Ku for e...

Given a smooth projective variety X over a field k of characteristic zero, we consider the composition of the de Rham cohomology cycle class map over k from the Chow group CH q (X × k K), where K is the field of fractions of henselization A h of the local ring of a smooth closed point of a variety over the field k with an appropriate projection:

We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative L spaces associated to the right von Neumann algebra of G. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful ...

We obtain the following characterization of Hilbert spaces. Let E be a Banach space whose unit sphere S has a hyperplane of symmetry. Then E is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group Iso E of E has a dense orbit in S; b) the identity component G 0 of the group Iso E endowed with the strong operator topology acts topologically irreducible on E...

In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by L-divergence and rare sources from a convex, closed set asymptotically conditionally concentrate on an L-projection. L-projection on a linear family of sources belongs to Λ-family o...

Let L ⊂ J(M) be a Legendrian submanifold of the 1-jet space of a Riemannian n-manifold M . A correspondence is established between rigid flow trees in M determined by L and boundary punctured rigid pseudo-holomorphic disks in T ∗M , with boundary on the projection of L and asymptotic to the double points of this projection at punctures, provided n ≤ 2, or provided n > 2 and the front of L has o...

Figure 1: Accomplishments of procams-based cybernetics research: (a) Palm interface [8], (b) extended hand interface [5], (c) wearable projection [4], (d) shape deformation interface, (e) deformation visualization, (f) see-through projection and (g) front cover projection for book search support, (h) shadow interface for browsing graphical information on a tabletop [1], (i) shadow pointing, (j)...

For a convex body K ⊂ Rn and i ∈ {1, . . . , n− 1}, the function assigning to any i-dimensional subspace L of Rn, the i-dimensional volume of the orthogonal projection of K to L, is called the i-th projection function of K. Let K, K0 ⊂ Rn be smooth convex bodies of class C2 +, and let K0 be centrally symmetric. Excluding two exceptional cases, we prove that K and K0 are homothetic if they have ...