In this paper, Ω is a bounded domain in R (N ≥ 2), with a Lipschitz continuous boundary. The unit normal to ∂Ω outward to Ω is denoted by n. We denote by x·y the usual Euclidean product of two vectors (x, y) ∈ R × R ; the associated Euclidean norm is written |.|. The Lebesgue measure of a measurable subset E in R is denoted by |E|; σ is the Lebesgue measure on ∂Ω (i.e. the (N−1)-dimensional Hau...

foaming conditions of the red beet (beta vulgaris l) puree were optimized using response surface methodology (rsm) with respect to arabic gum concentrations (0.01 – 0.4% w/w), red beet puree (40 _ 60% w/w),egg white concentration( 5 _ 15% w/w) and whipping time (3 – 9 min) for minimum foam density and foam drainage volume as response variables. foams were prepared from various pulp concentratio...

We show that if $w$ is a multilinear commutator word and $G$ finite group in which every metanilpotent subgroup generated by $w$-values of rank at most $r$, then the verbal $w(G)$ bounded terms $r$ only. In case where soluble we obtain better result -- nilpotent $r+1$.

A Markov switching position dependent random map is a random map of a finite number of measurable transformations where the probability of switching from one transformation to another is controlled by a position dependent irreducible stochastic matrix W . Existence of absolutely continuous invariant measures (acim) for a Markov switching position dependent random map was proved in [1] using spe...

In this paper we prove that if a weight w satisfies the C q condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal function, for 1 < p < q <∞.

The main purpose of this project is investigation of the organophosphorus hydrolase (OPH) enzyme activity in water in oil (w/o) and oil in water (o/w) creams and investigation of the OPH enzyme stability in formulated creams. OPH enzyme was extracted and purified from strain flavobacterium. The w/o and o/w creams were prepared using different formulations. In order to achieve an emulsion with m...

and Applied Analysis 3 In two main theorems in 20 , the authors proved the following results, which we now incorporate in the next theorem. Theorem A. Assume p ≥ 1 and φ is a holomorphic self-map of Π . Then the following statements true hold. a The operator Cφ : H Π → A∞ Π is bounded if and only if sup z∈Π Im z ( Imφ z )1/p < ∞. 1.8 b The operator Cφ : H Π → B∞ Π is bounded if and only if sup ...

Contents Preface v 1 Continuous-time stochastic processes 1 1.1 Measurability and stopping times. . Bibliography 133 iv CONTENTS Preface This monograph concerns itself with the theory of continuous-time martingales with continuous paths and the theory of stochastic integration with respect to continuous semimartingales. To set the scene for the theory to be developed, we consider an example. As...