Mesophases in a Gel from Hydroxypropyl Cellulose/Polyacrylamide

The objective of the present work is to analyze the different mesophases observed in a gel synthesized from hydroxypropyl cellulose (HPC) and polyacrylamide (PAAm) and its phase behavior in water. Hydroxypropyl cellulose is a material derived from cellulose it is non toxic and degradable. HPC is widely used in pharmaceutics, food additives, stabilizer, thickener, etc., HPC is approved by the FDA for use in the food industry. HPC has the characteristic that it forms liquid crystals, depending on the solvent and on the concentration of the polymer. In this work a lower critical solution temperature (LCST) and an upper critical solution temperature (UCST) were observed, the resulting gel showed anisotropic, nematic and cholesteric phases in water, the phase formed depended on the concentration of the polymer.     

On deformations of spherical isometric foldings

The behavior of special classes of isometric foldings of the Riemannian sphere S ² under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding f _s defined by f _s (x, y, z) = (x, y, |z|).     

Supply chain interactions due to store-brand introductions: The impact of retail competition

Store-brand products are of increasing importance in retailing, often causing channel conflict as they compete with national brands. Focusing on the interactions that arise in single-manufacturer single-retailer settings, previous research suggests that one main driver of store-brand profitability to the retailer is that it leads to a reduction of the national-brand wholesale price. Under retail competition, the Robinson Patman Act then introduces an interesting trade-off: A retailer that introduces a store brand incurs the associated costs and risks, while sharing this benefit with its competition. We show that the resulting interactions can cause retailers to play “chicken”, either of them preferring a store-brand introduction by the competitor. Such interactions do not arise in channels with a single retailer, as has been the object of most previous research, and we show that some of the key insights derived from single-retailer models fail to hold when retailers compete. We conduct a numeric study, and our findings suggest that retailers are more likely to randomize their store-brand introduction strategies when customers have strong store preferences, and when the retailers’ store-brand products are similar to the national-brand product in terms of customer valuations and production cost.     

Sample entropy of ECG time series of fearful flyers: preliminary results

Research within the framework of the nonlinear dynamical systems (NDS) in the field of anxiety disorders has shown that greater irregularity/complexity appears in the output from healthy systems. In this study we measured the Heart rate variability (HRV) and the sample sntropy (SampEn) of the ECG mV time series of fearful flyers (N = 15) and a matched control group (N = 15) when confronted with three combinations of feared stimuli (pictures, sounds, and pictures with sounds) as well as relaxing stimuli (pictures and sounds). Fearful flyers had lower SampEn than controls in all conditions, including baseline. Non-phobics showed significant entropy decreases from baseline in two out of three exposure conditions. No differences on HRV were found between groups, and HRV was not sensitive to condition changes. The main finding of the study is that the SampEn calculated on very short ECG mV recordings (10 to 60 seconds, easy to obtain in clinical settings) may be a useful diagnostic measure since it can distinguish fearful from non-fearful flyers.     

Digital technologies and the challenge of constructing an inclusive school mathematics

This article addresses research related to the use of digital technologies in the teaching and learning of mathematics in Brazil. Its scope is limited to the context of school mathematics and, more specifically, to an ongoing research programme which involves the development of collaborative research partnerships with teachers of mathematics. The paper begins with a brief presentation of the introduction of computers into the Brazilian educational scenario in the 1980s, highlighting how computer technology was heralded as a key to permitting new pedagogical approaches appropriate to the constructivist philosophy of that time. It goes on to consider recent developments in the theoretical frameworks used to interpret mathematics learning in the presence of digital technologies and the importance of focusing on the learning system as a whole, considering epistemological, cognitive and pedagogic dimensions concomitantly. In this vein, it is argued that for any real integration to take place, the mathematical practices afforded by digital tools must be considered legitimate by all the actors in this process and, perhaps most notably, by teachers. The rest of the paper focuses on our approaches to involve teachers in making decisions about technology use in their own classrooms. The strategy used was based on the realisation of research activities underpinned by the idea of the collaborative design of learning situations and the goal of including the wide diversity of learners that characterises Brazilian mathematics classrooms.     

A bound on the treewidth of planar even-hole-free graphs

The class of planar graphs has unbounded treewidth, since the k×k grid, ∀k∈N, is planar and has treewidth k. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.     

Distribution of stable isotopes in surface water along the Danube River in Serbia†

Stable hydrogen and oxygen isotopes were analysed in water samples from the River Danube and its tributaries during a longitudinal survey performed in August 2005 on Serbian territory. Danube river water data ranged from?80‰ to?66‰ for δ²H, and from?11.2‰ to?9.3‰ for δ¹⁸O with δ values increasing downstream. The isotopic signatures of the adjacent tributaries (the Tisza, the Sava and the Velika Morava) sampled at the locations close to their confluence with the Danube (Titel, Ostru?nica and Ljubi?evski most, respectively) just about the time of the campaign were enriched (?67‰ and?63‰ for δ²H, and?9.3‰ and?8.9‰ for δ¹⁸O) with respect to the Danube water because of their catchment effects. Hydrogen and oxygen stable isotope values were used in combination with measured physico-chemical and biological parameters to trace hydrological and transport processes in these river systems. The mixing relationships between the Danube main stream and its tributaries were estimated using the mass balance for isotopic composition and electrical conductivity as conservative parameters. Evidence of an incomplete mixing process at the ?enta location, 8 km below the confluence of the Tisza river, with its participation of 88% was shown by its oxygen-18 content. The correlations between river water isotope composition and physico-chemical and biological parameters are discussed.     

On the sum of digits of some sequences of integers

Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a _n } _n=1 ^∞ that for almost all n the sum of digits of a _n in base b is at least c _b log n, where c _b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.     

Gromov hyperbolicity of planar graphs

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ?² with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ?² such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ?² with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ?² with tiles which are parallelograms would be non-hyperbolic.