Dynamic surface tension of micellar solutions studied by the maximum bubble pressure method

A theoretical model for the dynamic surface tension of an air bubble expanding in micellar surfactant solution is proposed. The model accounts for the effect of expansion of the bubble surface during the adsorption of surfactant molecules (monomers) and the effect of disintegration of polydisperse micelles on the surfactant diffusion. Assuming small deviations from equilibrium and constant rate of expansion analytical expression for the surface tension and the subsurface concentration of monomers as a function of time is derived. The characteristic time of micellization is computed from the experimental data for two surfactants (sodium dodecyl sulfate and nonylphenol polyglycol ether) obtained by the maximum bubble pressure method.     

Effect of bovine serum albumin on the surface properties of ionic liquid-type Gemini surfactant

The effect of bovine serum albumin on the surface properties of IL-type gemini surfactant ([C₁₀-4-C₁₀im]Br₂), have been investigated by surface tension method. The critical micelle concentration (CMC) as a function of BSA concentrations at various temperatures was investigated. The CMC of [C₁₀-4-C₁₀im]Br₂ increases with increasing the concentration of BSA as well as the temperature of the system. The interfacial parameters viz; maximum surface excess concentration (Γ_max), the minimum area per molecule (A_min), and surface pressure at CMC (Π_cmc) were calculated. In addition, thermodynamic parameters of adsorption and micellization were evaluated by using surface tension data. The results indicated that the binding of [C₁₀-4-C₁₀im]Br₂ to BSA is spontaneous and exothermic in nature. The process is entropy driven and hydrophobic interactions are the major driving forces.     

Maximum principles for a class of nonlinear second order elliptic differential equations

In this paper we investigate maximum principles for functionals defined on solutions to special partial diff'erential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

Was Pauling Mistaken about Metals?

Pauling described metallic bonds using resonance. The maximum probability domains in the Kronig–Penney model can show a picture of it. When the walls are opaque (and the band gap is large) the maximum probability domain for an electron pair essentially corresponds to the region between the walls: the electron pairs are localized within two consecutive walls. However, when the walls become transparent (and the band gaps closes), the maximum probability domain can be moved through the system without a significant loss in probability.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.     

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.      

On an Inequality of Pual Turan Concerning Polynomials-Ⅱ

Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.