On Central Cantor Sets with Self-Arithmetic Difference of Positive Lebesgue Measure

We prove the existence of C^r - (but not C^r+1-) regular centralCantor sets with zero Lebesgue measure such that their selfarithmetic difference is a Cantor set with positive Lebesguemeasure. This is motivated by a conjecture in the field of bifurcationsof dynamical systems posed by Jacob Palis.     

Positioning of new brands in an experiment

This paper deals with an experimental investigation of positioning new brands. For this purpose, a management game was carried out with students. The brands introduced in the cause of the game were analysed in respect to their positions in a two-dimensional feature space. We try to find out which of the two strategies, niche policy and imitation, is more frequently used in complex decision situations and if there is a difference in profits. Furthermore, we want to find out, whether differences of prices and advertising exist in our experiment depending on the positioning strategy used.     

Gompertz zero-inflated cure rate regression models applied to credit risk data

In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil.     

Metal oxidation states in biological water splitting

A central question in biological water splitting concerns the oxidation states of the manganese ions that comprise the oxygen-evolving complex of photosystem II. Understanding the nature and order of oxidation events that occur during the catalytic cycle of five S_i states (i = 0–4) is of fundamental importance both for the natural system and for artificial water oxidation catalysts. Despite the widespread adoption of the so-called “high-valent scheme”—where, for example, the Mn oxidation states in the S₂ state are assigned as III, IV, IV, IV—the competing “low-valent scheme” that differs by a total of two metal unpaired electrons (i.e. III, III, III, IV in the S₂ state) is favored by several recent studies for the biological catalyst. The question of the correct oxidation state assignment is addressed here by a detailed computational comparison of the two schemes using a common structural platform and theoretical approach. Models based on crystallographic constraints were constructed for all conceivable oxidation state assignments in the four (semi)stable S states of the oxygen evolving complex, sampling various protonation levels and patterns to ensure comprehensive coverage. The models are evaluated with respect to their geometric, energetic, electronic, and spectroscopic properties against available experimental EXAFS, XFEL-XRD, EPR, ENDOR and Mn K pre-edge XANES data. New 2.5 K ⁵⁵Mn ENDOR data of the S₂ state are also reported. Our results conclusively show that the entire S state phenomenology can only be accommodated within the high-valent scheme by adopting a single motif and protonation pattern that progresses smoothly from S₀ (III, III, III, IV) to S₃ (IV, IV, IV, IV), satisfying all experimental constraints and reproducing all observables. By contrast, it was impossible to construct a consistent cycle based on the low-valent scheme for all S states. Instead, the low-valent models developed here may provide new insight into the over-reduced S states and the states involved in the assembly of the catalytically active water oxidizing cluster.     

Improving the water resistance of epoxy–anhydride matrices by the incorporation of bentonite

Epoxy–anhydride‐based polymers are commonly used as a matrix in pipeline systems exposed to water during their in‐service life. Water absorption at moderate temperatures and/or at long exposure times could lead to irreversible hydrolysis reaction decreasing considerably the polymer overall performance. A strategy to enhance the barrier properties of epoxy resins is to add nanofillers to traditional matrices. In this work, we added bentonite and chemically modified bentonite to this purpose. Water absorption of the resulting materials at three different temperatures (22°C, 80°C, and 93°C) was studied, and simultaneously, the evolution during the immersion tests of glass transition temperature and flexural modulus was recorded. Long‐term gravimetric results showed that composites with chemically modified bentonite produce a delay on the hydrolysis of epoxy–anhydride matrix, which is a relevant result, because of the tough application and uses of the system, from the technological point of view. Copyright © 2016 John Wiley & Sons, Ltd.     

Using liquid crystals as a readout system in urinary albumin assays

Detecting human serum albumin (HSA) in urine samples is a standard procedure for the diagnosis of kidney problems and the prognosis of patients with chronic kidney diseases (CKDs). In this study, we developed a HSA assay by incorporating a thin layer of liquid crystals (LCs) as a readout system such that the presence of HSA in urine samples can be detected as optical signals. In combination with dilution protocols, this assay can be used to estimate the concentration range of HSA simply by counting the number of bright spots. Our results show that the assay can detect HSA at concentrations as low as 15 μg mL(-1). It is anticipated that this assay can provide a faster and simpler alternative for the diagnosis and prognosis of patients with kidney diseases.