Let M be a closed simply connected manifold and 0 < δ ≤ 1. Klingenberg and Sakai conjectured that there exists a constant i0 = i0(M, δ) > 0 such that the injectivity radius of any Riemannian metric g on M with δ ≤ Kg ≤ 1 can be estimated from below by i0. We study this question by collapsing and Alexandrov space techniques. In particular we establish a bounded version of the KlingenbergSakai co...

At first, this may seem obvious, but in fact the problem is already non-trivial even in the case of four-sided pyramids, which can possibly have some obtuse dihedral angles (see Figure 1). Formally, we have the following result: Collapsing Walls Theorem. Let P ⊂ R be a pyramid over a convex polygon Q. For a face F of P , denote by eF the edge between F and the base: eF = F ∩Q, and let AF denote...

BACKGROUND This was a retrospective analysis of children in one center who had primary (idiopathic) FSGS. DESIGN, SETTING, PARTICIPANTS, AND MEASUREMENTS There were 41 patients: 34.1% female, 65.9% male, 80.5% black, and 19.5% white. At presentation, the mean age was 10.9 +/- 0.9 yr. The mean time of follow-up was 3.9 +/- 0.5 yr. RESULTS During the observation period, the systolic BP (SBP) ...

Given a word w over a finite alphabet Σ and a finite deterministic automaton A = 〈Q ,Σ, δ〉, the inequality |δ(Q , w)| ≤ |Q | − n means that under the natural action of the wordw the image of the state setQ is reduced by at leastn states. Awordw isn-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we...

Fibring is recognized as one of the main mechanisms in combining logics, with great significance in the theory and applications of mathematical logic. However, an open challenge to fibring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that fibring imposes unwanted interconnections between the given ...

We investigate modular properties of term rewriting systems, the basic operational formalism for equational speciications. First we study suucient conditions for the preservation of the termination property under disjoint (and more general) combinations of term rewriting systems. By means of a reened analysis of existing approaches we show how to prove several new asymmetric preservation result...

—Fault collapsing is the process of reducing the number of faults by using redundance and equiva-lence/dominance relationships among faults. Exact global fault collapsing can be easily applied locally at the logic gates, however, it is often ignored for library modules due to its high demand of resources such as execution time and/or memory. In this paper, we present an efficient and exact glob...

We analyze the time evolution of a spherically-symmetric collapsing matter from the point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation Gμν = 8πG〈Tμν〉 by using the four-dimensional Weyl anomaly with a large c coefficient. Here, 〈Tμν〉 contains the contribution from both the collapsing matter and Hawking radiation. The s...

The implementation of functional logic languages by means of graph 7 rewriting requires a special handling of collapsing rules. Recent advances about 8 the notion of a needed step in some constructor systems offer a new approach 9 to this problem. We present two results: a transformation of a certain class of 10 constructor-based rewrite systems that eliminates collapsing rules, and a rewrite11...

This manuscript studies manifolds-with-boundary collapsing in the Gromov-Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The main result establishes a disc bundle structure for any manifold-with-boundary having two-...