We consider various ways to represent irrational numbers by subrecursive functions: via Cauchy sequences, Dedekind cuts, trace functions, several variants of sum approximations and continued fractions. Let S be a class of subrecursive functions. The set of irrational numbers that can be obtained with functions from S depends on the representation. We compare the sets obtained by the different r...

We use the calculus of adiabatic pseudo-differential operators to study the adiabatic limit behavior of the eta and zeta functions of a differential operator δ constructed from an elliptic family of operators with base S. We show that the regularized values η(δt, 0) and tζ(δt, 0) have smooth limits as t → 0, and we identify the limits with the holonomy of the determinant bundle, respectively wi...

We announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure theory of misère quotients, including a connection between the combinatorial structure of normal and misère play.

The error that a wrong treatment plan be delivered was very serious. We vigorously explore effective method to analyze the factors which lead to this error, thus effectively improves radiotherapy quality. Fault tree analysis has been used for radiotherapy planning errors analysis in this study. After a fault tree was constructed from top to bottom then import the reliability data of basic event...

Abstract This erratum corrects Eqs. (6) and (15), Table 1, Fig. 2 of the original article. An additional footnote is added at end first paragraph in Section III. Finally, discussing use energy-dependent width for $$\rho ^0$$ ? 0 propagator modified.

The aim of this study was to determine whether prolonged loss of NO activity, in endothelial NO synthase knockout (eNOS / ) mice, influences endothelin (ET) ETA receptor–mediated smooth muscle contraction and, if so, to define the underlying mechanism(s). In isolated endothelium-denuded abdominal aortas, contractions to the selective ETA receptor agonist ET-1(1-31) were significantly increased ...

Endothelin-1 binding to endothelin A receptors (ETA) elicits profibrogenic, proinflammatory, and proliferative effects that can promote a wide variety of diseases. Although ETA antagonists are approved for the treatment of pulmonary hypertension, their clinical utility in several other diseases has been limited by fluid retention. ETA blocker-induced fluid retention could be due to inhibition o...

Time synchronisation is one of the most important and fundamental middleware services for wireless sensor networks. However, there is an apparent disconnect between existing time synchronisation implementations and the actual needs of current typical sensor network applications. To address this problem, we formulate a set of canonical time synchronisation services distilled from actual applicat...

The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous work has illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. It has also been shown that eta-reduction is useful for adapting substitution calculi for practical problems like higher order u...

We investigate the modular group as a finitely presented group. It has a large collection of interesting quotients. In 1987 Conder substantially identified the onerelator quotients of the modular group which are defined using representatives of the 300 inequivalent extra relators with length up to 24. We study all such quotients where the extra relator has length up to 36. Up to equivalence, th...