The methods of determination of critical micellar concentrations of the amphiphilic systems in aqueous medium

Science is the attempt to make the chaotic diversity of our sense-experience to a logically unified system of thought. A sound theoretical basis and a rational physicochemical understanding based on experimental findings lead to a proper understanding of a topic. Colloid chemistry strengthened its footing by the extensive studies on gold sols by Michael Faraday in 1850s, however, the term “colloid” was coined by Thomas Graham in 1861. Historically, the Stone Age paintings in the Lascaux cave in France and the written records of Egyptian pharaohs were produced with stabilized colloid pigments. The part of colloid science dealing with amphiphilic molecules is so diverse on its own that it is dealt in a separate branch called the “association colloid”. A key development in the study of association colloids was the observation by James McBain that the osmotic pressure of salts of alkali metal fatty acid displayed a pronounced break in the concentration beyond a specific characteristic concentration, after which the osmotic coefficient remained almost constant (Evans and Wennerstrom, 1994). McBain attributed this fact to the self-association of these molecules among themselves (McBain, 1913, McBain, 1944) in solution. Here, we are providing a molecular as well as thermodynamic approach toward the micellization process.     

Spectral analysis for a three-dimensional superradiance problem

In this paper three-dimensional superradiance problem is considered and a differential operator that commutes with the integral operator related to the problem is obtained. All the eigenfunctions of the differential operator are found and a complete set of eigensolutions for the three-dimensional superradiance problem is obtained.     

Prediction of financial distress: An empirical study of listed Chinese companies using data mining

The deterioration in profitability of listed companies not only threatens the interests of the enterprise and internal staff, but also makes investors face significant financial loss. It is important to establish an effective early warning system for prediction of financial crisis for better corporate governance. This paper studies the phenomenon of financial distress for 107 Chinese companies that received the label ‘special treatment’ from 2001 to 2008 by the Shanghai Stock Exchange and the Shenzhen Stock Exchange. We use data mining techniques to build financial distress warning models based on 31 financial indicators and three different time windows by comparing these 107 firms to a control group of firms. We observe that the performance of neural networks is more accurate than other classifiers, such as decision trees and support vector machines, as well as an ensemble of multiple classifiers combined using majority voting. An important contribution of the paper is to discover that financial indicators, such as net profit margin of total assets, return on total assets, earnings per share, and cash flow per share, play an important role in prediction of deterioration in profitability. This paper provides a suitable method for prediction of financial distress for listed companies in China.     

Holomorphic Cartan geometries and Calabi–Yau manifolds

Let M$M$ be a connected complex projective manifold such that _c1(T^(1,0)M)=0$c_1\left(T^{(1,0)}M\right)=0$. If M$M$ admits a holomorphic Cartan geometry, then we show that M$M$ is holomorphically covered by an abelian variety.     

On the finite principal bundles

Let G be a connected linear algebraic group defined over \({\mathbb C}\). Fix a finite dimensional faithful G-module V ₀. A holomorphic principal G-bundle E _G over a compact connected Kähler manifold X is called finite if for each subquotient W of the G-module V ₀, the holomorphic vector bundle E _G (W) over X associated to E _G for W is finite. Given a holomorphic principal G-bundle E _G over X, we prove that the following four statements are equivalent: (1) The principal G-bundle E _G admits a flat holomorphic connection whose monodromy group is finite. (2) There is a finite étale Galois covering \({f: Y \longrightarrow X}\) such that the pullback f*E _G is a holomorphically trivializable principal G-bundle over Y. (3) For any finite dimensional complex G-module W, the holomorphic vector bundle E _G (W) = E ×  ^G W over X, associated to the principal G-bundle E _G for the G-module W, is finite. (4) The principal G-bundle E _G is finite.     

Poincaré families and automorphisms of principal bundles on a curve

Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized by Zariski-open parts of their coarse moduli schemes. Applications are given for the moduli spaces of orthogonal and symplectic bundles. To cite this article: I. Biswas, N. Hoffmann, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Pyrene absorption can be a convenient method for probing critical micellar concentration (cmc) and indexing micellar polarity

The critical micellar concentration (cmc) of both ionic and non-ionic surfactants can be conveniently determined from the measurements of UV absorption of pyrene in surfactant solution. The results on a number of surfactants have agreed with that realized from pyrene fluorescence measurements as well as that obtained following conductometric, tensiometric and calorimetric methods. The absorbance vs [surfactant] profiles for all the major UV spectral peaks of pyrene have been found to be sigmoidal in nature which were analyzed according to Sigmoidal-Boltzmann equation (SBE) to evaluate the cmcs of the studied surfactants. The difference between the initial and the final asymptotes (a(i) and a(f), respectively) of the sigmoidal profile, Delta a = (a(f)-a(i)) and the slope of the sigmoid, S(sig) have been observed to depend on the type of the surfactant. The Delta a has shown a linear correlation with the ratio of the fluorescence intensities of the first and the third vibronic peaks, I1/I3 of pyrene which is considered as a measure of the environmental polarity (herein micellar interior) of the probe (pyrene). Thus, Delta a values have the prospect for use as another index for the estimation of polarity of micellar interior.     

A Higgs bundle on a Hermitian symmetric space,II

Let M : = Γ\G/K be the quotient of an irreducible Hermitian symmetric space G/K by a torsionfree cocompact lattice G ì G{\Gamma \subset G}. Let V be a complex irreducible representation of G. We give a Hodge decomposition of the cohomology of the Γ-module V in terms of the cohomologies of automorphic vector bundles on M associated to the Lie algebra cohomologies H*(\mathfrak p⁺ ,V){H*({\mathfrak p}^{+} ,V)}.