Biodegradable PEO/cellulose‐based solid–solid phase change materials

A series of poly(ethylene oxide) (PEO) blends with cellulose (CEL) or cellulose derivatives—carboxymethyl cellulose (CMC), cellulose acetate (CAC), and cellulose ether (CET)—has been investigated as phase change materials for thermal energy storage. For PEO/CEL blends solid–solid phase transition has been observed in the whole concentration's range; for PEO/CMC and PEO/CET blends solid–solid phase transition has been found for PEO content 25 or 50 and 25 wt%, respectively. Otherwise, solid–liquid phase transition takes place. MTDSC investigations revealed that for PEO/CEL and PEO/CMC blends transition the strongest recrystallization effect (as evidenced by exothermic effect in reversing heat flow) as melting process occurred. FTIR analysis shows a shift of the stretching vibration bands of both the proton‐donor O? H groups from CEL and PEO due to intermolecular hydrogen interactions between the blends' components. Copyright © 2010 John Wiley & Sons, Ltd.     

Stable cellulose nanospheres for cellular uptake

Pure, perfectly spherical cellulose nanoparticles with sizes of ≈80-260 nm can be prepared by dialysis starting from trimethylsilylcellulose (TMSC). The aqueous suspensions obtained are storable for several months. Subsequent covalent labeling of the cellulose nanoparticles with FITC has no influence on particle size, shape, and stability. The particles can be sterilized and suspended in biological media without structural changes. Incorporation of FITC-labeled cellulose nanoparticles into living human fibroblasts is studied using confocal LSM. In contrast to cellulose nanocrystals, fast cellular uptake is found for the nanospheres without transfection reagents or attachment of a receptor molecule. This suggests an influence of the geometry of biocompatible nanomaterials on endocytosis.     

Semi-synthetic polysaccharide sulfates as anticoagulant coatings for PET, 1--cellulose sulfate

In the present study, blood-compatible PET surfaces were prepared by coating with anticoagulant cellulose sulfates that were synthesized homogeneously in ionic liquids. The adsorption behavior of polysaccharides on PET films was investigated using QCM-D. It was demonstrated that pre-coating with different amino-group-containing polysaccharides improves the affinity toward cellulose sulfate. Moreover, the effect of different degrees of sulfation on the adsorption process was evaluated. Based on these results, several layer-by-layer coated PET foils were prepared that showed significantly improved blood compatibility compared to the initial untreated material.     

Potential theory of infinite dimensional Lévy processes

We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data.     

Weyl's theorem and tensor products: A counterexample

Approximately fifty percent of Weyl's theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon.     

Valuations and closure operators on finite lattices

Let L be a lattice. A function f:L→R (usually called evaluation) is submodular if f(x∧y)+f(x∨y)≤f(x)+f(y), supermodular if f(x∧y)+f(x∨y)≥f(x)+f(y), and modular if it is both submodular and supermodular. Modular functions on a finite lattice form a finite dimensional vector space. For finite distributive lattices, we compute this (modular) dimension. This turns out to be another characterization of distributivity (Theorem 3.9). We also present a correspondence between isotone submodular evaluations and closure operators on finite lattices (Theorem 5.5). This interplay between closure operators and evaluations should be understood as building a bridge between qualitative and quantitative data analysis.     

Permuting operations on strings and their relation to prime numbers

Some length-preserving operations on strings only permute the symbol positions in strings; such an operation X gives rise to a family {X_n}_n≥2 of similar permutations. We investigate the structure and the order of the cyclic group generated by X_n. We call an integer n X-prime if X_n consists of a single cycle of length n (n≥2). Then we show some properties of these X-primes, particularly, how X-primes are related to X^′-primes as well as to ordinary prime numbers. Here X and X^′ range over well-known examples (reversal, cyclic shift, shuffle, twist) and some new ones based on the Archimedes spiral and on the Josephus problem.     

A new technique of using homotopy analysis method for solving high‐order nonlinear differential equations

In this paper, a new technique of homotopy analysis method (HAM) is proposed for solving high‐order nonlinear initial value problems. This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method (HAM) by transform the nth‐order nonlinear differential equation to a system of n first‐order equations. Second‐ and third‐ order problems are solved as illustration examples of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

A solution approach for optimizing long- and short-term production scheduling at LKAB’s Kiruna mine

We present a mixed-integer program to schedule long- and short-term production at LKAB’s Kiruna mine, an underground sublevel caving mine located in northern Sweden. The model minimizes deviations from monthly preplanned production quantities while adhering to operational constraints. Because of the mathematical structure of the model and its moderately large size, instances spanning a time horizon of more than a year or two tend to be intractable. We develop an optimization-based decomposition heuristic that, on average, obtains better solutions faster than solving the model directly. We show that for realistic data sets, we can generate solutions with deviations that comprise about 3-6% of total demand in about a third of an hour.