Harald Hanche-Olsen

THE KOLMOGOROV-RIESZ COMPACTNESS THEOREM

We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Hellys theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.

Water transport in cation exchange membranes

Abstract The time variation in emf caused by pressure differences has been used to find transference coefficients of water as well as water permeabilities in ion exchange membranes. Previous experimental methods have been corrected and facilitated. The cation exchange membrane CR61 AZL 386 was investigated. Equilibrium solutions contained 10−4 kmol-m−3

The generators of positive semigroups

We characterise the infinitesimal generators of norm continuous one-parameter semigroups of positive maps on certain ordered spaces, with special reference to C∗-algebras.

EXISTENCE OF SOLUTIONS FOR THE AW-RASCLE TRAFFIC FLOW MODEL WITH VACUUM

In this paper, the macroscopic model for traffic flow proposed by Aw and Rascle in 2000 is considered. The model is a 2 × 2 system of hyperbolic conservation laws, or, when the model includes a relaxation term, a 2 × 2 system of hyperbolic balance laws. The main difficulty is the presence of vacuum, which makes control of the total variation of the conservative variables impossible. We allow vacuum to appear and prove the existence of a weak entropy solution to the Cauchy problem.

On the uniform convexity of L^p

We present a short, direct proof of the uniform convexity of L^p spaces for 1<p<\infty.

The initial-boundary-value problem for an Ostrovsky–Hunter type equation

We study the problem of optimal control of a coupled system of forward-backward stochastic Volterra equations. We use Hida-Malliavin calculus to prove a sufficient and a necessary maximum principle for the optimal control of such systems. Existence and uniqueness of backward stochastic Volterra integral equations are proved. As an application of our methods, we solve a recursive utility optimisation problem in a financial model with memory.

An improvement of the Kolmogorov–Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.

On Goursat's Proof of Cauchy's Integral Theorem

1. J. Griggs, C. E. Killian, and C. D. Savage, Venn diagrams and symmetric chain decompositions in the Boolean lattice, Electron. J. Combin. 11 (2004) #R2. 2. B. Gr?nbaum, Venn diagrams and independent families of sets, Math. Mag. 48 (1975) 12-23. 3. P. Hamburger, Doodles and doilies, non-simple symmetric Venn diagrams, Disc. Math. 257 (2002) 423 439. 4. D. W. Henderson, Venn diagrams for more than four classes, this Monthly 70 (1963) 424^26. 5. F. Ruskey, C. Savage, and S. Wagon, The search for simple symmetric Venn diagrams, Notices Amer. Math. Soc. 53 (2006) 1304-1312. 6. F. Ruskey and M. Weston, A survey of Venn diagrams, Electron. J. Combin. 4 (1997; revised 2005) DS5.