Organic Nanoparticles in the Aqueous Phase-Theory,Experiment, and Use

Many active organic compounds and organic effect materials are poorly soluble in water, or even insoluble. Aqueous forms of application thus require special formulation techniques to utilize or optimize the physiological (pharmaceuticals, cosmetics, plant protection, nutrition) or technical (varnishes, printing inks, toners) action. The most interesting properties of nanodispersions of active organic compounds and effect materials include the impressive increase in solubility, the improvement in biological resorption, and the modification of optical, electrooptical, and other physical properties which are achievable only with particle sizes in the middle or lower nanometer range (50-500 nm). Hence in addition to economic and ecological constraints there are also technical demands which appear to urgently require the development of new processes for the production of organic nanoparticles as alternatives to the established mechanical milling processes. In this context attention is drawn to the recent increase in research activities which have as their objective the continuous, automatic preparation of nanodispersed systems by precipitation from molecular solution. In this review the current state of knowledge of the fundamentals of particle formation from homogeneous solution and the effect of solvent and polymer additives on the morphology and supramolecular structure of the nanoparticle will be discussed. The practical implementation of this new formulation technology will be explored in detail for the carotenoids, a class of compounds of both physiological and technical interest.     

Approximation of Integral Operators by Variable-Order Interpolation

Summary. We employ a data-sparse, recursive matrix representation, so-called -matrices, for the efficient treatment of discretized integral operators. We obtain this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the matrix-vector multiplication. We present an error analysis for integral operators of order zero. In particular, we show that the optimal convergence (h) is retained for the classical double layer potential discretized with piecewise constant functions.Corrigendum This revised version was published online in February 2005 due to typesetting mistakes in the author correction process.     

Mixed boundary value problems for nonlinear elliptic equations in multidimensional non-smooth domains

The nonlinear elliptic equation is investigated. It is supposed that u fulfils a mixed boundary value condition and that Ω ? IRⁿ (n ≥ 3) has a piecewise smooth boundary. W^s,2 — regularity (s < 3/2) of u and L^p — properties of the first and the second derivatives of u are proven.     

Examples of Coorbit Spaces for Dual Pairs

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980’s by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of SL₂(?). We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation.     

Updating incomplete factorization preconditioners for model order reduction

When solving a sequence of related linear systems by iterative methods, it is common to reuse the preconditioner for several systems, and then to recompute the preconditioner when the matrix has changed significantly. Rather than recomputing the preconditioner from scratch, it is potentially more efficient to update the previous preconditioner. Unfortunately, it is not always known how to update a preconditioner, for example, when the preconditioner is an incomplete factorization. A recently proposed iterative algorithm for computing incomplete factorizations, however, is able to exploit an initial guess, unlike existing algorithms for incomplete factorizations. By treating a previous factorization as an initial guess to this algorithm, an incomplete factorization may thus be updated. We use a sequence of problems from model order reduction. Experimental results using an optimized GPU implementation show that updating a previous factorization can be inexpensive and effective, making solving sequences of linear systems a potential niche problem for the iterative incomplete factorization algorithm.     

Lower bounds for randomized direct search with isotropic sampling

Randomized direct-search methods for the optimization of a function f:Rⁿ→R that is given by a black box for f-evaluations are investigated. These iterative methods generate new candidate solutions by adding isotropically distributed vectors to the current candidate solution. Lower bounds on the number of f-evaluations necessary for reducing the approximation error in the search space are proved.     

A europium(II) complex with bis-pyridino-18-crown-6

A new Eu(II) complex, bis(perchlorato)(bis-pyridino-18-crown)europium(II), has been obtained in the crystalline form by electrolytic reduction. The metal ion is 10-coordinated and its surrounding consists of four macrocycle O atoms, two N ones and four O atoms from perchlorate anions. The compound shows a very broad absorption band, starting gently from 600 nm towards the UV region, and two weak luminescence bands with maxima at 430 and 500 nm. The performed density functional theory (DFT) calculations have shown that the absorption results from mixed f–d, f–s and charge transfer transitions. The possible mechanism of luminescence is also discussed.