Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Social Media, Gender and the Mediatisation of War: Exploring the German Armed Forces’ Visual Representation of the Afghanistan Operation on Facebook

Studies on the mediatisation of war point to attempts of governments to regulate the visual perspective of their involvements in armed conflict – the most notable example being the practice of ‘embedded reporting’ in Iraq and Afghanistan. This paper focuses on a different strategy of visual meaning-making, namely, the publication of images on social media by armed forces themselves. Specifically, we argue that the mediatisation of war literature could profit from an increased engagement with feminist research, both within Critical Security/Critical Military Studies and within Science and Technology Studies that highlight the close connection between masculinity, technology and control. The article examines the German military mission in Afghanistan as represented on the German armed forces’ official Facebook page. Germany constitutes an interesting, and largely neglected, case for the growing literature on the mediatisation of war: its strong antimilitarist political culture makes the representation of war particularly delicate. The paper examines specific representational patterns of Germany’s involvement in Afghanistan and discusses the implications which arise from what is placed inside the frame of visibility and what remains out of its view

Diagnostic guidelines for the histological particle algorithm in the periprosthetic neo-synovial tissue

Background The identification of implant wear particles and non-implant related particles and the characterization of the inflammatory responses in the periprosthetic neo-synovial membrane, bone, and the synovial-like interface membrane (SLIM) play an important role for the evaluation of clinical outcome, correlation with radiological and implant retrieval studies, and understanding of the biological pathways contributing to implant failures in joint arthroplasty. The purpose of this study is to present a comprehensive histological particle algorithm (HPA) as a practical guide to particle identification at routine light microscopy examination. Methods The cases used for particle analysis were selected retrospectively from the archives of two institutions and were representative of the implant wear and non-implant related particle spectrum. All particle categories were described according to their size, shape, colour and properties observed at light microscopy, under polarized light, and after histochemical stains when necessary. A unified range of particle size, defined as a measure of length only, is proposed for the wear particles with five classes for polyethylene (PE) particles and four classes for conventional and corrosion metallic particles and ceramic particles. Results All implant wear and non-implant related particles were described and illustrated in detail by category. A particle scoring system for the periprosthetic tissue/SLIM is proposed as follows: 1) Wear particle identification at light microscopy with a two-step analysis at low (× 25, × 40, and × 100) and high magnification (× 200 and × 400); 2) Identification of the predominant wear particle type with size determination; 3) The presence of non-implant related endogenous and/or foreign particles. A guide for a comprehensive pathology report is also provided with sections for macroscopic and microscopic description, and diagnosis. Conclusions The HPA should be considered a standard for the histological analysis of periprosthetic neo-synovial membrane, bone, and SLIM. It provides a basic, standardized tool for the identification of implant wear and non-implant related particles at routine light microscopy examination and aims at reducing intra-observer and inter-observer variability to provide a common platform for multicentric implant retrieval/radiological/histological studies and valuable data for the risk assessment of implant performance for regional and national implant registries and government agencies

The diamond integral on time scales

We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder’s, Cauchy–Schwarz’s, and Minkowski’s inequalities