Ricci flow on surfaces with cusps

We consider the normalized Ricci flow ? _t g = (ρ ? R)g with initial condition a complete metric g ₀ on an open surface M where M is conformal to a punctured compact Riemann surface and g ₀ has ends which are asymptotic to hyperbolic cusps. We prove that when χ(M) < 0 and ρ < 0, the flow g(t) converges exponentially to the unique complete metric of constant Gauss curvature ρ/2 in the conformal class.     

Arbitrage conditions for electricity markets with production and storage

Computational Management Science - This work analyzes the notion of arbitrage for market models with electricity production from fuel. Several generators, fuel storage, and the related fuel and...     

The classification of locally conformally flat Yamabe solitons

This paper addresses the classification of locally conformally flat gradient Yamabe solitons. In the first part it is shown that locally conformally flat gradient Yamabe solitons with positive sectional curvature are rotationally symmetric. In the second part the classification of all radially symmetric gradient Yamabe solitons is given and their correspondence to smooth self-similar solutions of the fast diffusion equation on Rⁿ${\mathbb{R}}^n$ is shown. In the last section it is shown that any eternal solution to the Yamabe flow with positive Ricci curvature and with the scalar curvature attaining an interior space–time maximum must be a steady Yamabe soliton.     

Investigating the spectrum of biological activity of ring-substituted salicylanilides and carbamoylphenylcarbamates

In this study, a series of twelve ring-substituted salicylanilides and carbamoylphenylcarbamates were prepared and characterized. The compounds were analyzed using RP-HPLC to determine lipophilicity. They were tested for their activity related to the inhibition of photosynthetic electron transport (PET) in spinach (Spinacia oleracea L.) chloroplasts. Moreover, their site of action in the photosynthetic apparatus was determined. Primary in vitro screening of the synthesized compounds was also performed against mycobacterial, bacterial and fungal strains. Several compounds showed biological activity comparable with or higher than the standards 3-(3,4-dichlorophenyl)-1,1-dimethylurea, isoniazid, penicillin G, ciprofloxacin or fluconazole. The most active compounds showed minimal anti-proliferative activity against human cells in culture, indicating they would have low cytotoxicity. For all compounds, the relationships between lipophilicity and the chemical structure are discussed.     

SmartMetals: a new method for metal identification based on fuzzy logic

This paper presents a method of searching, identifying and cross‐referencing metal alloys based on their chemical composition and/or mechanical properties, typically obtained by analysis and tests. The method uses a general pattern similar to the approach of a human expert, and relies on a classification of metals based on metallurgical expertise and fuzzy logic for identifying metals and comparing their chemical and mechanical properties. The algorithm has been tested and deployed in real applications for fast metal identification and finding of unknown equivalents, by the leading companies in the field. The same principles can also be used in other domains for similar problems, such as organic and inorganic materials identification and generic drugs comparison. Copyright © 2009 John Wiley & Sons, Ltd.     

Möbius-like groups of homeomorphisms of the circle

An orientation preserving homeomorphism of is Möbius-like if it is conjugate in to a Möbius transformation. Our main result is: given a (noncyclic) group whose every element is Möbius-like, if has at least one global fixed point, then the whole group is conjugate in to a Möbius group if and only if the limit set of is all of . Moreover, we prove that if the limit set of is not all of , then after identifying some closed subintervals of to points, the induced action of is conjugate to an action of a Möbius group. Said differently, is obtained from a group which is conjugate to a Möbius group, by a sort of generalized Denjoy's insertion of intervals. In this case is isomorphic, as a group, to a Möbius group.

This result has another interpretation. Namely, we prove that a group of orientation preserving homeomorphisms of whose every element can be conjugated to an affine map (i.e., a map of the form ) is just the conjugate of a group of affine maps, up to a certain insertion of intervals. In any case, the group structure of is the one of an affine group.

     

A new type of a spectrometric microtitration set up

A spectrometric microtitrator was developed from a spectrometer with a microreaction chamber and a tri-colour light-emitting diode (LED) as the light source. A novel, vertical, optical geometry of the spectrometric microtitration chamber was introduced and tested. This novel geometry also required a new method for mixing the titrated solution. A laboratory-made 50 μl syringe pump was used for the addition of the titration reagent. The 10-channel module for light effects, which makes possible a low-cost hardware approach to changing the titration protocols, was used for coordinating the operation of the microtitration set up. The system, with 10 channels and a regulated speed of operation, is flexible enough to allow an operator to generate different titration protocols. The performance test showed that the speed of titration-reagent addition can be regulated in the range from 0.87 to 21.8 μl min⁻¹. The smallest achievable volume addition is equal to 35 nl. The mixing rate can be continuously regulated by an electrical pulse that initiates the mixing cycle. The quickest rate is every 1.6 s, and the slowest rate is every 4.8 s. The spectrometric microtitration set up was successfully tested for several different real-life spectrometric titrations, including an iodometric titration, a determination of CO₂ in deionised water, and EDTA titrations of copper(II) ions with no indicator. The volume of the examined solution can be as small as 220 μl. The titration-reagent consumption is usually between 10 and 35 μl. Coefficients of variation of the end point volume determination (n = 5) at different experimental conditions and different average volumes of consumed reagents (7.06, 12.17 and 22.88 μl) were 2.4, 1.3 and 1.2%, respectively. The novel geometry of the spectrometric microtitration chamber proved to be useful for real-life applications.     

Spontaneous breaking of minimal surface condition: labyrinths in free standing smectic films

We present a study of thin free standing films made of intercalated smectic-C liquid crystal in which, upon lowering the temperature, the minimal surface area condition is broken. A periodic modulation of the film thickness is obtained and a labyrinth structure of crests and valleys is formed. Thickness variation is coupled to the spatial variation of the molecular orientation. The transition to the labyrinth structure is explained to be driven by the mass density difference between the surface and the bulk layers.     

Chemical Constituents of Polyalthia rumphii

Chemistry of Natural Compounds -