Polynomial–exponential equations and Zilber's conjecture

Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtain the result by proving (unconditionally) that certain polynomial–exponential equations have only finitely many rational solutions. This answers affirmatively a question of David Marker, who asked, and proved in the case of algebraic coefficients, whether at least the one variable case of Zilber's strong exponential-algebraic closedness conjecture can be reduced to Schanuel's conjecture

Impact and Influence Factors of Additive Manufacturing on Product Lifecycle Costs

At first sight the direct costs of Additive Manufacturing (AM) seem too high in comparison to traditional manufacturing. Considering the whole lifecycle costs of parts changes the point of view. Due to the modification of the new production process and new supply chains during a parts lifecycle, producing companies can strongly benefit from AM. Therefore, a costing model for assessing lifecycle costs with regard to specific applications and branches has been developed. The costing model represents the advantages of AM monetary. For the evaluation of this model and the influence factors, different case studies have been performed including different approaches in part redesign. Deeper research is and will be carried out with respect to the AM building rates and the comparability of various AM machines, as these facts are hardly comparable for end users. This paper will present the methodology as well as the results of the case studies conducted over the whole product lifecycle.Mechanical Engineerin

Validation of seat-off and seat-on in repeated sit-to-stand movements using a single body fixed sensor

The identification of chair rise phases is a prerequisite for quantifying sit-to-stand movements. The aim of this study is to validate seat-off and seat-on detection using a single-body-fixed sensor against detection based on chair switches. A single sensor system with three accelerometers and three gyroscopes was fixed around the waist. Synchronized on-off switches were placed under the chair. Thirteen older adults were recruited from a residential care home and fifteen young adults were recruited among college students. Subjects were asked to complete two sets of five trials each. Six features of the trunk movement during seat-off and seat-on were calculated automatically, and a model was developed to predict the moment of seat-off and seat-on transitions. The predictions were validated with leave-one-out cross-validation. Feature extraction failed in two trials (0.7%). For the optimal combination of seat-off predictors, cross-validation yielded a mean error of 0ms and a mean absolute error of 51ms. For the best seat-on predictor, cross-validation yielded a mean error of -3ms and a mean absolute error of 127ms. The results of this study demonstrate that seat-off and seat-on in repeated sit-to-stand movements can be detected semi-automatically in young and older adults using a one-body-fixed sensor system with an accuracy of 51 and 127ms, respectively. The use of the ambulatory instrumentation is feasible for non-technically trained personnel. This is an important step in the development of an automated method for the quantification of sit-to-stand movements in clinical practice. © 2012 Institute of Physics and Engineering in Medicine

How to assess a company's open innovation situation?

Open Innovation (OI) supports companies in systematically collaborating with external partners, offering various advantages. However, companies still face several challenges when applyingOI, e.g., identifying relevantOI partners, collaborationmethods, and project risks. Often, insufficient planning is the reason for subsequent deficits in OI projects. The analysis of relevant context factors ('situation') is important, which affect and constrain OI. To date, a general approach for analyzing (open) innovation situations or guidelines for developing one do not exist. Usually researchers develop their own situation analysis, including extensive literature reviews and experiencing similar challenges. This publication sets the basis for successfully planning OI projects. It focuses on developing an analysis approach for OI situations and supports other researchers in developing their own analysis approaches. The resultant objectives of the publication are to: (1) provide a list of potential situation analysis criteria; (2) provide a guideline for developing a situation analysis; (3) provide initial indications of relevant OI-specific situation criteria. The criteria were derived from the literature and qualitatively evaluated by three industry partners to assess their usability. Although this work is exploratory, and the results are not automatically generalizable, it is an important contribution for ensuring the success of OI, and for analyzing enablers and barriers to knowledge transfer from academia to industry

Objective measures of rollator user stability and device loading during different walking scenarios

Walking aids are widely used by older adults, however, alarmingly, their use has been linked to increased falls-risk, yet clinicians have no objective way of assessing user stability. This work aims to demonstrate the application of a novel methodology to investigate how the type of walking task, the amount of body weight supported by the device (i.e., device loading), and task performance strategy affect stability of rollator users. In this context, ten users performed six walking tasks with an instrumented rollator. The combined stability margin “SM” was calculated, which considers user and rollator as a combined system. A Friedman Test was used to investigate the effects of task on SM and a least-squares regression model was applied to investigate the relationship between device loading and SM. In addition, the effects of task performance strategy on SM were explored. As a result, it was found that: the minimum SM for straight line walking was higher than for more complex tasks (p<0.05); an increase in device loading was associated with an increase in SM (p<0.05); stepping up a kerb with at least 1 rollator wheel in ground contact at all times resulted in higher SM than lifting all four wheels simultaneously. Hence, we conclude that training should not be limited to straight line walking but should include various everyday tasks. Within person, SM informs on which tasks need practicing, and which strategy facilitates stability, thereby enabling person-specific guidance/training. The relevance of this work lies in an increase in walking aid users, and the costs arising from fall-related injuries. Supplementary data is available in Figshare

A wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141