Improving an inequality for the divisor function

We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.Comment: 8 pages, to appear in Bull. AustM

The Coherence Problem: Mapping the Theory and Delivery of Infrastructure Resilience Across Concept, Form, Function, and Experienced Value

In this contribution we explore the interface between the functional characteristics of infrastructures as artefacts and social need supplier. Specifically we are concerned with the ways in which infrastructure performance measures are articulated and assessed and whether there are incongruities between the technical and broader, social goals which infrastructure systems are intended to aspire to. Our analysis involves comparing and contrasting system design and performance metrics across the technical — social boundary, generating new insights for those tasked with the design and operation of networked infrastructures. The assessment delivered in the following sections is inherently interdisciplinary and cross-sectoral in nature, bringing thinking from the social and environmental sciences together with contributions from mathematics and engineering to offer a commentary which is relevant to all types of physical infrastructure

NiH2 capacity fade during early cycling

Tests were conducted on nickel hydrogen batteries to determine the charge efficiency of the nickel electrode as a function of rate and temperature, cell discharge capacity, and capacity fade. Test procedures and results are presented in outline and graphic form

Mechanics of materials model

The Mechanics of Materials Model (MOMM) is a three-dimensional inelastic structural analysis code for use as an early design stage tool for hot section components. MOMM is a stiffness method finite element code that uses a network of beams to characterize component behavior. The MOMM contains three material models to account for inelastic material behavior. These include the simplified material model, which assumes a bilinear stress-strain response; the state-of-the-art model, which utilizes the classical elastic-plastic-creep strain decomposition; and Walker's viscoplastic model, which accounts for the interaction between creep and plasticity that occurs under cyclic loading conditions

Design and development of a motion compensator for the RSRA main rotor control

The RSRA, an experimental helicopter, is equipped with an active isolation system that allows the transmission to move relative to the fuselage. The purpose of the motion compensator is to prevent these motions from introducing unwanted signals to the main rotor control. A motion compensator concept was developed that has six-degree-of-freedom capability. The mechanism was implemented on RSRA and its performance verified by ground and flight tests

3x+13x+1 inverse orbit generating functions almost always have natural boundaries

The $3x+k$ function $T_{k}(n)$ sends $n$ to $(3n+k)/2$ resp. $n/2,$ according as $n$ is odd, resp. even, where $k \equiv \pm 1~(\bmod \, 6)$. The map $T_k(\cdot)$ sends integers to integers, and for $m \ge 1$ let $n \rightarrow m$ mean that $m$ is in the forward orbit of $n$ under iteration of $T_k(\cdot).$ We consider the generating functions $f_{k,m}(z) = \sum_{n>0, n \rightarrow m} z^{n},$ which are holomorphic in the unit disk. We give sufficient conditions on $(k,m)$ for the functions $f_{k, m}(z)$ have the unit circle $\{|z|=1\}$ as a natural boundary to analytic continuation. For the $3x+1$ function these conditions hold for all $m \ge 1$ to show that $f_{1,m}(z)$ has the unit circle as a natural boundary except possibly for $m= 1, 2, 4$ and $8$. The $3x+1$ Conjecture is equivalent to the assertion that $f_{1, m}(z)$ is a rational function of $z$ for the remaining values $m=1,2, 4, 8$.Comment: 15 page