Dispersion Stability and Particle Characterization by Sedimentation Kinetics in a Centrifugal Field

ABSTRACT

The analysis of sedimentation or flotation (creaming) by detecting the transmission profile over the entire sample height in an analytical centrifuge (using a Stability Analyzer) is described and illustrated for a diverse range of practical dispersions and emulsions. It is also illustrated how to use extrapolated results to estimate dispersion shelf life stability for samples in a gravitational field. Formulation optimization, such as choosing appropriate surfactant levels, is also shown to be a practical application of such methods.     

An Application of Groupoids of Fractions to Inverse Semigroups

We describe an application of category theory to the theory of inverse semigroups: we prove the P-theorem for E-unitary inverse semigroups using groupoids of fractions of their associated division categories.     

A paired queueing system arising in multimedia synchronization

One of the most important and distinguishing features of multimedia applications is the integration of multiple media streams that have to be presented in a synchronized fashion. In this paper, a queueing system with a special service mechanism arising in multimedia synchronization is considered. The system is characterized by arrival of two types of customers (media streams), and servicing of customers (processing of packets) in pairs with one customer from each type for a pair. The exact transient system size probabilities are obtained as the stationary solutions do not exist for this system and these are illustrated numerically. The density function of the first return to the origin for the queueing system is also obtained.     

The Levels-Recursive Algorithm for Vector Valued Interpolants by Triple Branched Continued Fractions

1 Introduction Let Πl,m,n be a set of points in three dimensional space R3, Πl,m,n = {(xi, yj, zk), i = 0, 1, · · · l; j = 0, 1, · · · m; k = 0, 1, · · · n}. Let a d?dimensional vector vi,j,k be given at every point (xi, yj, zk) ∈ Πl,m,n and     

Quadruple systems of the projective special linear group PSL(2,q), q ≡ 1 (mod 4)

We determine the distribution of quadruple systems among the orbits of 4‐element subsets under the action of PSL(2,q) on the projective line when q ≡ 1 (mod 4). © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 339–351, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10043     

Inhibition of thermal induced protein denaturation of extract/fractions of Withania somnifera and isolated withanolides

This study describes the in vitro inhibition of protein denaturation of extract/fractions of Withania somnifera and isolated withanolides including 20β hydroxy-1-oxo(22R)-witha-2,5,24 trienolide (1), (20R,22R-14α,20α)-dihydroxy-1-oxowitha-2,5,16,24 tetraenolide (2). The results showed that the extract/fractions of the plant evoked profound inhibitory effect on thermal-induced protein denaturation. The chloroform fraction caused the most dominant attenuation of 68% at 500 μg/mL. The bioactivity-guided isolation from chloroform fraction led to the isolation of compounds 1 and 2 that showed profound protein inhibition with 78.05% and 80.43% effect at 500 μg/mL and thus strongly complimented the activity of extract/fractions. In conclusion, extract/fractions of W. somnifera possessed strong inhibition of protein denaturation that can be attributed to these isolated withanolides.     

Efficient remainder rule

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra.     

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

Classroom teachers need a well‐developed deep understanding of fractions and pedagogic practices so they can provide meaningful experiences for students to explore and construct ideas about fractions. This study sought to examine prospective elementary teachers' understandings of fraction by focusing specifically on their use of fractions meanings and interpretations. Results indicated that prospective elementary teachers bring with them to their final methods course a limited understanding of fractions and that experiences in methods courses resulted only in minor improvement of those limited understandings. The limited part‐whole understanding of fractions that prospective elementary teachers entered the course with was resilient. The implications of this study suggest a need for prospective elementary teachers to continue to develop their conceptual understanding of fractions and for changes to the content and instructional strategies of mathematics content courses designed for prospective elementary teachers.     

Parametric excitation of waves on a free boundary of a horizontal fluid layer

We consider the dynamical stability of horizontal fluid layer, performing harmonic oscillations in vertical direction. The continued fractions approach allowed us to avoid the conventional restriction to the case of small viscosity and almost-resonant frequencies. Our numerical results cover a wide range of the parameters (viscosity, amplitude and frequency of the oscillation, and depth of the layer). To cite this article: V.I. Yudovich et al., C. R. Mecanique 332 (2004).     

On sums of degrees of the partial quotients in continued fraction expansions of Laurent series

For any formal Laurent series with coefficients cn lying in some given finite field, let x=[a₀(x);a₁(x),a₂(x),…] be its continued fraction expansion. It is known that, with respect to the Haar measure, almost surely, the sum of degrees of partial quotients grows linearly. In this note, we quantify the exceptional sets of points with faster growth orders than linear ones by their Hausdorff dimension, which covers an earlier result by J. Wu.