Let BY denote the unit ball of a normed linear space Y . A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y , there exists a linear projection P : Y → X such that P (BY ) ⊂ A. The main results of the paper: (1) Each minimal-volume sufficient enlargem...

Finite-dimensional linear programs satisfy strong duality (SD) and have the “dual 8 pricing” (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of 9 the right-hand-side vector, there exists a dual solution that correctly “prices” the perturbation by 10 computing the exact change in the optimal objective function value. These properties may fail in 11 semi-inf...

We provide a general framework to construct finite-dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give precise estimates of the distance between the approximation space and the admissible set. This framework applies to the approximation of convex functions by piecewise-...

A subset S of a Riemannian manifoldN is called extrinsically homogeneous if S is an orbit of a subgroup of the isometry group of N . In [Th], Thorbergsson proved the remarkable result that every complete, connected, full, irreducible isoparametric submanifold of a finite dimensional Euclidean space of rank at least 3 is extrinsically homogeneous. This result, combined with results of [PT1] and ...

Finite-dimensional linear programs satisfy strong duality (SD) and have the “dual 8 pricing” (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of 9 the right-hand-side vector, there exists a dual solution that correctly “prices” the perturbation by 10 computing the exact change in the optimal objective function value. These properties may fail in 11 semi-inf...

We begin by considering certain analogues, in finite 3-dimensional affine spaces, of the ordinary cube. From the properties of these structures (as geometric lattices having point sets which are threefold Cartesian products) we derive the notion of an (abstract) finite cube. By studying the additional properties (including the properties of certain groups associated with the cube) of members of...

In this paper a previously proven uniqueness theorem for nonnegative cohomology theories on the same space is extended to cohomology theories on the same finite-dimensional space. In this form it is applicable to extraordinary cohomology theories. An example is given to show that the theorem does not hold without finite dimensionality.

in this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. weshow that obtained result is an extension of the result ofrodr'{i}guez-l'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

In almost all papers in the literature, the results on exact controllability hold only for finite dimensional Banach spaces, since compactness of the semigroup and the bounded invertibility of an operator implies finite dimensional. In this note we show that the existence theory on controllability in the literature, can trivially be adjusted to include the infinite dimensional space setting, if...

The issue of how to deal with the modular transformations – large diffeomorphisms – in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular transformations on the reduced configuration space is so bad that it is possible to rule out all finite dimensional unitary representations of the modular group on the ...