Optimal number representations in negative base

We present some general properties of solutions of an equation which appeared in a problem posed by Z. Boros and Z. Daróczy. Using them we solve this equation in some classes of functions assuming regularity of solutions. We also present some facts concerning regular solutions of two related equations.     

Simplified modelling of joints and beam-like structures for BIW optimization in a concept phase of the vehicle design process

The paper proposes an engineering approach for the replacement of beam-like structures and joints in a vehicle model. The final goal is to provide the designer with an effective methodology for creating a concept model of such automotive components, so that an NVH optimization of the body in white (BIW) can be performed at the earliest phases of the vehicle design process. The proposed replacement methodology is based on the reduced beam and joint modelling approach, which involves a geometric analysis of beam-member cross-sections and a static analysis of joints. The first analysis aims at identifying the beam center nodes and computing the equivalent beam properties. The second analysis produces a simplified model of a joint that connects three or more beam-members through a static reduction of the detailed joint FE model.In order to validate the proposed approach, an industrial case-study is presented, where beams and joints of the upper region of a vehicle's BIW are replaced by simplified models. Two static load-cases are defined to compare the original and the simplified model by evaluating the stiffness of the full vehicle under torsion and bending in accordance with the standards used by automotive original equipment manufacturer (OEM) companies. A dynamic comparison between the two models, based on global frequencies and modal shapes of the full vehicle, is presented as well.     

The Isolation of Single MMX Chains from Solution: Unravelling the Assembly–Disassembly Process

Herein, we provide a systematic theoretical and experimental study of the structural and optical properties of MMX (M=metal, X=halide) chains. The influence of solvent, temperature, and concentration has been analyzed to find suitable parameters for initial building‐block associations in solution. By using density functional calculations, we have computed the dissociation energy of different MMX oligomers (up to the tetramer) in the gas phase. On the basis of these findings, we discuss the most likely disassembly scenario and propose a new interpretation of these compounds. We also calculated the charge redistribution that occurs upon MM+XMMX binding in vacuum. Time‐dependent density functional theory (TDDFT) is used to calculate the UV/visible spectra of different MMX chains up to the tetramer in the gas phase. The implications of these theoretical findings in the analysis of our experiments are discussed in the text. The overall body of data presented suggests a new way of looking at such linear structures. By taking into account these new data, we have been able to isolate single/few MMX chains on mica.     

Rhenium measurements on North Atlantic seaweed samples by ID-ICP-MS: An observation on the Re concentration factors

Summary The estimation of the Re concentration factor (CF) has been carried out to provide additional field information on the biochemical similarities between Re and Tc. Re concentration in brown seaweed samples from the North Atlantic Coast were measured using ID-ICP-MS. The chemical yields were quantitative, and the concentrations were distributed within a narrow range of 65-80 ng/g d.w. CF of Re was approximately 1.2 ^. 10⁴ on average, i.e., one order of magnitude less than that found for ⁹⁹Tc.     

Paper-based chromatic toxicity bioassay by analysis of bacterial ferricyanide reduction

Water quality assessment requires a continuous and strict analysis of samples to guarantee compliance with established standards. Nowadays, the increasing number of pollutants and their synergistic effects lead to the development general toxicity bioassays capable to analyse water pollution as a whole. Current general toxicity methods, e.g. Microtox^®, rely on long operation protocols, the use of complex and expensive instrumentation and sample pre-treatment, which should be transported to the laboratory for analysis. These requirements delay sample analysis and hence, the response to avoid an environmental catastrophe. In an attempt to solve it, a fast (15 min) and low-cost toxicity bioassay based on the chromatic changes associated to bacterial ferricyanide reduction is here presented. E. coli cells (used as model bacteria) were stably trapped on low-cost paper matrices (cellulose-based paper discs, PDs) and remained viable for long times (1 month at −20 °C). Apart from bacterial carrier, paper matrices also acted as a fluidic element, allowing fluid management without the need of external pumps. Bioassay evaluation was performed using copper as model toxic agent. Chromatic changes associated to bacterial ferricyanide reduction were determined by three different transduction methods, i.e. (i) optical reflectometry (as reference method), (ii) image analysis and (iii) visual inspection. In all cases, bioassay results (in terms of half maximal effective concentrations, EC₅₀) were in agreement with already reported data, confirming the good performance of the bioassay. The validation of the bioassay was performed by analysis of real samples from natural sources, which were analysed and compared with a reference method (i.e. Microtox). Obtained results showed agreement for about 70% of toxic samples and 80% of non-toxic samples, which may validate the use of this simple and quick protocol in the determination of general toxicity. The minimum instrumentation requirements and the simplicity of the bioassay open the possibility of in-situ water toxicity assessment with a fast and low-cost protocol.