Walking Through Cantor's Paradise and Escher's Garden: Epistemological Reflections on the Mathematical Infinite (I)

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature: understanding of infinity as a never-ending process, understanding infinity as a set of an infinite number of elements, and understanding some well-known paradoxes. Infinity can be understood in a number of ways, some of which are incompatible, and can involve value judgments or assumptions that are neither explicit nor desired. In its definition, we distinguish several aspects, teleological, artistic (Escher 2000 Escher, M. C. Estampas y dibujos. Colonia: Ed. Taschen, 2000. (In Spanish). [Google Scholar]), some essential, some potential, and others actual. Cantor's work on set theory is linked to infinity and has implications for belief in God.     

Fuzzy Structure of Complex Belief Systems: Fuzzy Relations and Fuzzy Belief Sets

In previous work, Nescolarde-Selva and Usó-Doménech (2014a Nescolarde-Selva, J. and J. L. Usó-Doménech. “Semiotic Vision of Ideologies.” Found Sci 19 (2014a): 263–282.[Crossref], [Web of Science ®] , [Google Scholar], b) discussed the theory that complex belief systems have a topological structure. In this article it is suggested that this structure is also fuzzy. We introduce the concepts of fuzzy sets in the context of beliefs (substantive and derived), and between derived beliefs themselves. Also introduced are the concepts of fuzzy covering and fuzzy invariance and the relationships between them.     

A new generation of unshaped refractories

The world trends in the development and consumption of refractory materials are considered. A brief overview of the advance in the foreign production of zero-cement refractory castables (ceramic castables) is given. The importance of controlled gelation techniques for accelerated structure formation in refractories is emphasized. __________ Translated from Novye Ogneupory, No. 1, pp. 35–41, January, 2006.     

Unique Crystal Structure of a Novel Surfactant Protein from the Foam Nest of the Frog Leptodactylus vastus

Breeding by releasing eggs into stable biofoams (“foam nests”) is a peculiar reproduction mode within anurans, fish, and tunicates; not much is known regarding the biochemistry or molecular mechanisms involved. Lv‐ranaspumin (Lv‐RSN‐1) is the predominant protein from the foam nest of the frog Leptodactylus vastus. This protein shows natural surfactant activity, which is assumed to be crucial for stabilizing foam nests. We elucidated the amino acid sequence of Lv‐RSN‐1 by de novo sequencing with mass‐spectrometry and determined the high‐resolution X‐ray structure of the protein. It has a unique fold mainly composed of a bundle of 11 α‐helices and two small antiparallel β‐strands. Lv‐RSN‐1 has a surface rich in hydrophilic residues and a lipophilic cavity in the region of the antiparallel β‐sheet. It possesses intrinsic surface‐active properties, reducing the surface tension of water from 73 to 61 mN m^?1 (15 μg mL^?1). Lv‐RSN‐1 belongs to a new class of surfactants proteins for which little has been reported regarding structure or function.     

Mythical systems: mathematic and logical theory

The process of elaboration of the symbolic universe leads to exciting insights regarding the search for human emotional security. The symbols end up as explanatory axes of universal reality and on them are constructed myths that form a superstructure for belief systems. Human society is a multi-level system with a material structure (society), an ideological superstructure (belief systems, values, etc.) and a super superstructure with two parts: mythical (origin and justification) and utopic (final goal). All mythical belief systems have a numinous-religious nature.     

Thermal,mechanical and water adsorption properties of corn starch–carboxymethylcellulose/methylcellulose biodegradable films

The objective of this study was to investigate the effect of the addition of methylcellulose and carboxymethylcellulose on the thermal, mechanical and water adsorption properties of starch-based films plasticized with glycerol or polyethylene glycol (PEG). Mechanical tests showed that as the methylcellulose and carboxymethylcellulose proportion increased, starch films became more resistant to break, resulting in higher TS values. Besides there has been a positive effect on the elasticity of starch films realized by a considerable increase in E% values. Depending on the plasticizer type, either single or dual glass transitions were seen in DSC thermograms. One glass transition temperature was observed for films plasticized with glycerol, on the contrary, dual glass transitions were detected for PEG plasticized films. This behavior was attributed to the phase separation of the PEG. In addition, the presence of an endothermic peak in the thermograms of PEG plasticized films was taken as another indicator of the phase separation. As a result, it was suggested that PEG was not as compatible as glycerol with the composite polysaccharide matrix and plasticizer type was the main factor that shaped the thermal profiles of the film samples. Water adsorption isotherm data showed that samples displayed nonlinear sorption profile which is typical for hydrophilic films. In all films tested, equilibrium moisture contents, increased almost linearly up to a a_w of 0.65–0.85, beyond where a sharp increase was noted. Adsorption data was adequately fitted by BET and GAB models. Eventually, it can be concluded that film forming properties of starch can be improved by incorporation of methylcellulose and carboxymethylcellulose to the polymer matrix.