Ring stain effect at room temperature in silver nanoparticles yields high electrical conductivity

We demonstrate that metallic rings formed spontaneously at room temperature via evaporation of aqueous drops containing silver nanoparticles (20-30 nm in diameter) exhibit high electrical conductivity (up to 15% of that for bulk silver). The mechanism underlying this self-assembly phenomena is the "ring stain effect", where self-pinning is combined with capillary flow to form a ring consisting of close-packed metallic nanoparticles along the perimeter of a drying droplet. Our macroscopic and microscopic (applying conductive atomic force microscopy) transport measurements show that the conductivity of the ring, which has a metallic brightness, is orders of magnitude larger than that of corresponding aggregates developed without the ring formation, where high conductivity is known to appear only after annealing at high temperature.     

On charge conjugation

The group of automorphisms of the conformal algebra su(2, 2) has four components giving the usual four components of symmetries of space time. Only two of these components extend to symmetries of the conformal superalgebra — the identity component and the component which induces the parity transformation,P, on space time. There is no automorphism of the conformal superalgebra which inducesT or PT on space time. Automorphisms of su(2, 2) which belong to these last two components induce transformations on the conformal superalgebra which reverse the sign of the odd brackets. In this sense conformal supersymmetry prefers CP to CPT. The operator of charge conjugation acting on spinors, as is found in the standard texts, induces conformal inversion and hence a parity transformation on space time, when considered as acting on the odd generators of the conformal superalgebra. Although it commutes with Lorentz transformations, it does not commute with all of su(2, 2). We propose a different operator for charge conjugation. Geometrically it is induced by the Hodge star operator acting on twistor space. Under the known realization of conformal states from the inclusion SU(2, 2) Sp(8) and the metaplectic representations, its action on states is induced by the unique (up to phase) antilinear intertwining operator between the two metaplectic representations. It is consistent with the split orthosymplectic algebras and hence, by the inclusion of the superconformal in the orthosymplectic, with the orthosymplectic algebra.     

Synthesis of vicinal bromo-fluoro organic compounds using elemental fluorine

The direct action of fluorine on bromine at ?78° produces BrF which, without any isolation or purification, adds readily across various double bonds providing there is some hydrogen donor in the reaction mixture. Only trans addition of the elements of BrF was observed. When the reaction was applied to enons an easy elimination of HF can take place thus producing α-bromo enons.In our previous work we described the reaction of some olefins with IF, a reagent which was prepared $\text{in}$$\text{situ}$ by the action of F₂ on I₂[1]. The literature deals with several other fluorohalogens, among them the three known bromo-fluoro compounds, BrF, BrF₃ and BrF₅, although only the last two are well characterized[2]. However, because of the instability and the high reactivity of these compounds, they have hardly been employed in organic chemistry[3].We wish to describe here for the first time, an efficient and convenient method of synthesizing vicinal bromo-fluoro compounds using the primary source of the fluorine atoms, namely elemental fluorine itself[4].When a mixture of F₂/N₂ is bubbled through a cold (?78°C), dilute solution of Br₂ (20 mmolar) in CFCl₃ (Freon) the bromine disappears and mainly BrF is produced. However, despite previous efforts, it seems that this compound cannot be isolated since it disproportionates easily to the very reactive BrF₃ and halogen on the aromatic ring can not be ascertained. The third product proved to be the corresponding bromo-ethoxy compound XV (15% yield). Prolonged chromatography or traces of HF from the reaction mixture results in the elimination of HF thus producing, quantitatively, 6-bromocumarin XVI[8]. 2-Bromo-3-fluoro cyclopentanone XVII (oil) if formed in 90% yield and isolated in almost pure form. As in the case of cumarin, XVII readily loses HF producing the 2-bromoclopentenone (XVIII)[9] in quantitative yield.     

Flow cytometry: a new method to investigate the properties of water-in-oil-in-water emulsions

We present a new and facile method to evaluate w/o/w emulsions containing fluorescent markers by flow cytometry. Flow cytometry allows simultaneous measurement of w/o/w emulsion droplets "marked" with a fluorescent marker or "blank" without the need for complicated sample preparation. The yield of preparation of the w/o/w emulsion and the release rate of the fluorescent marker FITC-BSA were investigated by this new method. The release fraction (after 24 h) of FITC-BSA from the w/o/w emulsion decreased with increasing concentration of FITC-BSA inside the internal phase, just like the release fraction of NaCl as marker from the w/o/w emulsion. Flow cytometry results show that the yield and release behavior in w/o/w emulsions are in agreement with results reported by more complicated methods.     

FORMATION OF OIL IN GLYCEROIVWATER EMULSIONS: EFFECT OF SURFACTANT ETHYLENE OXIDE CONTENT

Oil-in-glycerol/water emulsions at various ratios of water to glycerol in the external phase were prepared with polyoxyethylated octylphenols and light mineral oil. As the water concentration in the external phase decreased, oil droplet size decreased down to a minimum size beyond which oil separation occurred. Also, the cloud points of various surfactants were depressed toward room temperature as the water content of the glycerol/water mixtures decreased. It was possible therefore to correlate the concentration of water needed for formation of the smallest droplets to the concentration of water needed for depression of the cloud point of each surfactant to room temperature.     

Sulfation Patterns of Saccharides and Heavy Metal Ion Binding

Sulfated saccharides are an essential part of extracellular matrices, and they are involved in a large number of interactions. Sulfated saccharide matrices in organisms accumulate heavy metal ions in addition to other essential metal ions. Accumulation of heavy metal ions alters the function of the organisms and cells, resulting in severe and irreversible damage. The effect of the sulfation pattern of saccharides on heavy metal binding preferences is enigmatic because the accessibility to structurally defined sulfated saccharides is limited and because standard analytical techniques cannot be used to quantify these interactions. We developed a new strategy that combines enzymatic and chemical synthesis with surface chemistry and label-free electrochemical sensing to study the interactions between well-defined sulfated saccharides and heavy metal ions. By using these tools we showed that the sulfation pattern of hyaluronic acid governs their heavy metal ions binding preferences.     

On the volume product of polygons

We present a method that allows us to prove that the volume product of polygons in ℝ² with at most n vertices is bounded from above by the volume product of regular polygons with n vertices. The same method shows that the volume product of polygons is bounded from below by the volume product of triangles (or parallelograms in the centrally symmetric case). These last results give a new proof of theorems of K. Mahler. The cases of equality are completely described.     

On braided fusion categories I

We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also give a comprehensive and self-contained exposition of the known results on braided fusion categories without assuming them pre-modular or non-degenerate. The guiding heuristic principle of our work is an analogy between braided fusion categories and Casimir Lie algebras.     

Mathematics education: Procedures, rituals and man's search for meaning

An attempt is made to analyze mathematical behavior from more general psychological perspectives. The mathematical language is a special case of the human language, which is a form of expression. Many people use common language in a meaningless way. The same is true about the mathematical language. Rituals are other forms of expression. Many people identify rituals in many mathematical contexts (procedures, argumentation). Thus, quite often, they behave in a meaningless way as required by many rituals. On the other hand, the community of mathematics education struggles for meaningful learning. This can be regarded as a special case of man's search for meaning. The general claims will be illustrated by some examples from various mathematical contexts.