Errors in the approximations of functions by the use of functionals

A scheme of approximation, which should prove useful in applied problems, has been developed. Its usefulness is based upon the fact that it permits some choice in the selection of the set of functionals for a given set of functions. Thus it may eliminate the often serious problem of evaluation of the constants in an approximation. At the same time the choice of functions is limited only by the condition that they be linearly independent. It is shown that in the infinite case, whatever functional set was selected reduces, at least formally, to that set regularly associated with the chosen functions;Remainder operators have been determined for these approximations. Thus a means is presented for evaluating the remainders in a large class of expansions. As examples we mention expansions in terms of orthogonal polynomials such as those of Legendre or Laguerre;A means of extension to trigonometric series is pointed out;One problem indicated by the present work is that of actually forming the remainder operators for a large number of specific series. Such information would aid in the selection of suitable sets of functionals in applied problems

Patterns of successful CRM:More about solutions than software

Customer Relationship Management (CRM), much hyped during the dot com years, has always been more than software. The CRM industry was tainted by high profile missteps, partly due to its focus on software, rather than solutions (Patton, 2001). However, managers must understand that CRM is a solution, not software that integrates both technology and operational improvements. With the ability to coordinate across all customer contact points, decision makers must recognize that CRM is an organizational process that integrates information from previously disparate channels (sales, marketing, customer service via phone, text chat, or web) to better serve customers (Day and Van der Bulte, 2002). This paper examines the fundamentals of CRM, its goals and common pitfalls, and its prerequisite for this long-term, successful implementation with the goal of extracting patterns of successful CRM deployments

Method and Apparatus for Linewidth Reduction in Distributed Feedback or Distributed Bragg Reflector Semiconductor Lasers using Vertical Emission

The linewidth of a distributed feedback semiconductor laser or a distributed Bragg reflector laser having one or more second order gratings is reduced by using an external cavity to couple the vertical emission back into the laser. This method and device prevent disturbance of the main laser beam. provide unobstructed access to laser emission for the formation of the external cavity. and do not require a very narrow heat sink. Any distributed Bragg reflector semiconductor laser or distributed feedback semiconductor laser that can produce a vertical emission through the epitaxial material and through a window in the top metallization can be used. The external cavity can be formed with an optical fiber or with a lens and a mirror of grating

Creating possibility spaces for the development of circular bioeconomy initiatives

To help move society towards more sustainable states, policies have been developed in various countries to create a circular bioeconomy (CBE) in biobased sectors such as forestry and agriculture. In operationalizing CBE, initiatives must be created in which feedback loops between life-cycle stages are established to enable a "stock" of resources to be recirculated in the economy. By creating such feedback loops, CBE aims to decouple economic growth from natural resource depletion and degradation. However, few CBE initiatives have been developed. This implementation gap has partly arisen because policies to promote CBE are somewhat theoretical and do not seem to be informed by the practical realities of implementing CBE initiatives on the ground. While CBE policies do not and should not set out detailed implementation plans to address these issues, they do need to better account for how favourable circumstances and contexts can be created for the development of CBE initiatives. In response, this paper critically examines how possibility spaces can be created for the development of CBE initiatives. Assemblage thinking is used in longitudinal case study research focused on a major CBE initiative situated in the south of Sweden: Foodhills. Assemblage thinking is both an approach and method widely used in geography to study how spaces for action such as the construction of CBE initiatives are created. As such, the paper identifies and unpacks multiple issues arising in the development of CBE initiatives on the ground including geographical relations, actor networks and power

Design and operating concept for an innovative naturally ventilated library

Recent years have seen increased use of natural ventilation, daylighting, and cooling techniques in UK buildings. This paper describes the design and operating concept of a large, naturally ventilated and illuminated city centre library for Coventry University in the UK. The novel design concept includes four lightwells acting as ventilation inlets, each of which is fed with fresh air from a plenum below the ground floor. A central lightwell and perimeter stacks draw air across each floor plate and provide air extract routes. This strategy enables fresh air to reach the core of the building whilst keeping the external façade sealed for reasons of security and preventing urban noise and pollution. Computer simulation demonstrates that the building is likely to be well ventilated and thermally comfortable. The building and the analyses should increase the confidence of engineers and architects designing sustainable buildings

An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming

In recent years many advances have been made in solution techniques for specially structured 0–1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra (1981) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988). This method allows us to avoid the ellipsoidal approximations required in Lenstra’s algorithm. We report on the solution of a number of small (but difficult) examples, up to 100 integer variables. Our computer code uses the linear programming optimizer CPlex as a subroutine to solve the linear programming problems that arise

Understanding the exercise of agency within structural inequality: the case of personal debt

This article contributes to debates about agency (meaning the behaviour of individuals) and structure, by drawing on empirical research into personal debt. Consideration of debt allows for debate about agency and structure beyond the narrow confines of welfare, and for the examination of agency in relation to citizens at different points in the broader socio-economic structure, not solely poor people. Based on the research findings, themselves grounded in interviewees' experience, the question of why two people in the same material circumstances will have different experiences becomes reframed as why two people whose exercise of agency is the same, face very different outcomes? It is argued that while the research supports a ‘both-and’ rather than ‘either-or’ approach to understanding agency and structure, a ‘both-and’ approach still does not fully capture the experience of interviewees. The key point is that the exercise of agency is overlaid onto structural inequality, and it is understanding the exercise of ‘agency within structure’ that is critical

Predicting the Young’s Modulus of Silicate Glasses using High Throughput Molecular Dynamics Simulations and Machine Learning

The application of machine learning to predict materials' properties usually requires a large number of consistent data for training. However, experimental datasets of high quality are not always available or self-consistent. Here, as an alternative route, we combine machine learning with high-throughput molecular dynamics simulations to predict the Young's modulus of silicate glasses. We demonstrate that this combined approach offers good and reliable predictions over the entire compositional domain. By comparing the performances of select machine learning algorithms, we discuss the nature of the balance between accuracy, simplicity, and interpretability in machine learning