Consider a variant of the graph diameter of a polyhedron where each step in a walk between two vertices travels maximally in a circuit direction instead of along incident edges. Here circuit directions are non-trivial solutions to minimally-dependent subsystems of the presentation of the polyhedron. These can be understood as the set of all possible edge directions, including edges that may ari...

We present an affine-invariant approach for solving linear programs. Unlike previous approaches, the potential strong polynomiality of the new approach does not require that graphs of polytopes have polynomial diameter (the Hirsch conjecture or weaker versions). We prove that two natural realizations of the approach work efficiently for deformed products [1], a class of polytopes that generaliz...

The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Löbell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Löbell polyhedron. For polyhedra from this family we give trigonometric relations between essential dihedral angles and lengths and obtain volume formulae in v...

By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities deflning the polytope. By analogy with a result of Dedieu, Malajovich and Shub, we conjecture that the average diameter of a bounded cell of an arrangement is less than the dimension. We prove continuous analogues of two...

Symbiotic is a tool for detection of bugs described by finite state machines in C programs. The tool combines three well-known techniques: instrumentation, program slicing, and symbolic execution. This paper briefly describes the approach of Symbiotic including its strengths, weaknesses, and modifications for SV-COMP 2013. Architecture and installation of the tool are described as well. 1 Verif...

and Applied Analysis 3 We now introduce a property lying between U-space and semi-KK. Definition 1.8. We say that a Banach space X is semi-uniform Kadec-Klee if for every ε > 0 there exists a δ > 0 such that semi-UKK : {xn} ⊂ SX xn ⇀ x 〈 xn − x, fn 〉 ≥ ε, for some {fn } ⊂ SX∗ satisfying fn ∈ ∇xn ∀n ⎫ ⎪ ⎪⎬ ⎪ ⎪⎭ ⇒ ‖x‖ ≤ 1 − δ. 1.10 In this paper, we prove that semi-UKK property is a nice generali...

It is proved that L(`p, `q) has the KK property if and only if it has the UKK property if and only if 1 < q < 2 < p < ∞. It is also proved that L(c0, `1) has the UKK property and that L(c0, `q) can be renormed to have the weak-star UKK property if (and only if) 1 ≤ q < 2. In all other cases L(`p, `q) has no equivalent UKK norm. Finally, it is proved that none of these spaces is either strictly ...

Proof. Let 11 and V be countable bases for X and Y, respectively, and let 3 have as sub-base the collection of sets {fCC(X, Y) \f(U) C V), with UCM and VCÜ. Then 3 certainly has a countable base. Clearly 3 also makes (/, x)—>/(x) jointly continuous, and hence [l, p. 223] is finer than the compact-open topology. Finally, every subset of C(X, Y) is certainly Lindelöf and separable for the countab...