Emulsion films stabilized by natural and polymeric surfactants

This review is organized in two parts: the first one deals with w/o/w emulsion films stabilized by polymeric surfactants and steric surface forces; the second part is dedicated to o/w/o emulsion films typical for petroleum systems. It summarizes recently published results on both topics.     

Series transformation formulas of Euler type,Hadamard product of series,and harmonic number identities

The Hadamard multiplication theorem for series is used to establish several Euler-type series transformation formulas. As applications we obtain a number of binomial identities involving harmonic numbers and an identity for the Laguerre polynomials. We also evaluate in a closed form certain power series with harmonic numbers.     

Evaluation of series with binomial sums

We present three formulas for summation in closed form (or certain transformation) of series constructed with binomial expressions. Examples and application are provided, involving the Hurwitz zeta function, the dilogarithm, and the digamma function.     

On values of the Riemann zeta function at positive integers

Lithuanian Mathematical Journal - We give new proofs of some known results on the values of the Riemann zeta function at positive integers and obtain some new theorems related to these values....     

Sinclair type inequalities for the local spectral radius and related topics

We generalize the well-known Sinclair lemma for Hermitian elements, proving pointwise versions for generalized scalar operators and unbounded skew-Hermitian operators.     

Foams and foam films stabilized by CnTAB: influence of the chain length and of impurities

Quantitative comparison of foam films and the corresponding foams is very demanding. One problem is the fact that investigations of foam films are usually performed at constant capillary pressures P, whereas in foams P is a function of the height of the foam column. A way out of this dilemma is to examine films and foams at the same P. The method of choice for the foam films is the thin film pressure balance (TFPB), whereas the corresponding investigation of foams is based on the foam pressure drop technique (FPDT). An extensive TFPB study on foam films stabilized by the cationic alkyltrimethylammonium bromides C(n)TAB with n=10, 12, 14, and 16 was performed by Bergeron. For this series a steep increase of the foam film stability was observed when the chain length was increased from n=12 to n=14. Moreover, the influence of impurities was found to be limited to the films stabilized by C(12)TAB. In order to study the correlation between the properties of films and foams, the present study deals with the respective foam properties investigated with the FPDT. It was found that both the steep increase in the film stability and the influence of impurities are also reflected in the properties of the foam.     

Norm Estimates for Commutators of Operators

Given two self-adjoint Hilbert space operators A, B, and a continuousfunction f, we prove several inequalities of the form ||f(A)X–Xf(B)||C(f)||AX–XB|| involving the L_p-norm of the derivative f' and the Besov B^r_,1-normof f.     

Evaluation of Binomial Series with Harmonic Numbers

We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.