Hyperbolic Laplace Operator and the Weinstein Equation in {\mathbb{R}^3}

We study the Weinstein equation $$\Delta u - \frac{k}{{x}_{2}} \frac{\partial}{\partial{x}_{2}} + \frac{l}{x^{2}_{2}}u = 0$$ , on the upper half space ${\mathbb{R}^3_{+} = \{ (x_{0}, x_{1}, x_{2}) \in \mathbb{R}^{3} | x_2 > 0\}}$ in case ${4l \leq (k + 1)^{2}}$ . If l =  0 then the operator ${x^{2k}_{2} (\Delta - \frac{k}{x_{2}} \frac{\partial}{\partial{x}_{2}})}$ is the Laplace- Beltrami operator of the Riemannian metric ${ds^2 = x^{-2k}_{2} (\sum^{2}_{i = 0} dx^{2}_{i})}$ . The general case ${\mathbb{R}^{n}_{+}}$ has been studied earlier by the authors, but the results are improved in case ${\mathbb{R}^3_{+}}$ . If k =  1 then the Riemannian metric is the hyperbolic distance of Poincaré upper half-space. The Weinstein equation is connected to the axially symmetric potentials. We compute solutions of the Weinstein equation depending only on the hyperbolic distance and x ₂. The solutions of the Weinstein equation form a socalled Brelot harmonic space and therefore it is known that they satisfy the mean value properties with respect to the harmonic measure. However, without using the theory of Brelot harmonic spaces, we present the explicit mean value properties which give a formula for a harmonic measure evaluated in the center point of the hyperbolic ball. Earlier these results were proved only for k =  1 and l =  0 or k =  1 and l =  1. We also compute the fundamental solutions. The main tools are the hyperbolic metric and its invariance properties. In the consecutive papers, these results are applied to find explicit kernels for k-hypermonogenic functions that are higher dimensional generalizations of complex holomorphic functions.     

Synthesis of copolymer-stabilized silver nanoparticles for coating materials

Silver ions being less toxic than silver nanoparticles, a more safe material can be obtained to be used as antimicrobial coating. This can be achieved by using thiol chemistry and covalently attach the silver nanoparticles in the coating. Our aim is to produce a coating having antimicrobial properties of silver ions but with the silver nanoparticles firmly attached in the coating. Here, we present a way to produce silver nanoparticles that can be used as a component in a coating or as such to produce an antimicrobial coating. The silver nanoparticles presented here are stabilized by a copolymer (poly(butyl acrylate–methyl methacrylate)) that is soft and has well-known good film-producing properties. The reversible addition-fragmentation chain transfer radical polymerization technique used to prepare the polymers provides conveniently a thiol group for effective binding of the silver nanoparticles to the polymers and thus to the coating.     

Harmonic Forms on Conformal Euclidean Manifolds: The Clifford Multivector Approach

In this paper we express the theory of harmonic differential forms on conformal Euclidean manifolds in terms of the so called Clifford multivector fields. The aim is to give good definitions for d and d* operators in Clifford multivector case. Using these definitions we derive a formula for the Laplace operator. Three fundamental examples are included in the end of the paper and connections to existing theory is discussed.     

The cyclic [N(PiPr2E)2]+ (E = Se, Te) cations: a new class of inorganic ring system

The two-electron oxidation of [(tmeda)NaN(PiPr2E)2] with iodine produces the cyclic [N(PiPr2E)2]+ (E = Se, Te) cations, which exhibit long E-E bonds in the iodide salts.     

Synthesis, spectroscopic, and structural investigation of the cyclic [N(PR2E)2]+ cations (E = Se, Te; R = iPr, Ph): the effect of anion and R-group exchange

Two-electron oxidation of the [N(PiPr2E)2]- anion with iodine produces the cyclic [N(PiPr2E)2]+ (E =Se, Te) cations, which exhibit long E-E bonds in the iodide salts [N(PiPr2Se)2]I (4) and [N(PiPr2Te)2]I (5). The iodide salts 4 and 5 are converted to the ion-separated salts [N(PiPr2Se)2]SbF6 (6) and [N(PiPr2Te)2]SbF6 (7) upon treatment with AgSbF6. Compounds 4-7 were characterized in solution by multinuclear NMR, vibrational, and UV-visible spectroscopy supported by DFT calculations. A structural comparison of salts 4-7 and [N(PiPr2Te)2]Cl (8) confirms that the long E-E bonds in 4, 5, and 8 can be attributed primarily to the donation of electron density from a lone pair of the halide counterion into the E-E sigma* orbital (LUMO) of the cation. The phenyl derivative [N(PPh2Te)2]I (9) was prepared in a similar manner. However, the attempted synthesis of the selenium analogue, [N(PPh2Se)2]I, produced a 1:1 mixture of [N(PPh2Se)2(mu-Se)][I] (10) and [SeP(Ph2)N(Ph2)PI] (11). DFT calculations of the formation energies of 10 and 11 support the observed decomposition. Compound 10 is a centrosymmetric dimer in which two six-membered NP2Se3 rings are bridged by two I- anions. Compound 11 produces the nine-atom chain {[N(PPh2)2Se]2(mu-O)} (12) upon hydrolysis during crystallization. The reaction between [(TMEDA)NaN(PiPr2Se)2] and SeCl2 in a 1:1 molar ratio yields the related acyclic species [SeP(iPr2)N(iPr2)PCl] (13), which was characterized by multinuclear NMR spectroscopy and an X-ray structural determination.     

Effect of ligand on the synthesis of star polymers by resorcinarene‐based ATRP initiators

The effect of the steric hindrance on the initiating properties of two multifunctional resorcinarene‐based initiators in atom transfer radical polymerization (ATRP) was studied by using Cu(I)‐complexes of three multidentate amine ligands in the polymerization of tert‐butyl acrylate and methyl methacrylate. These ligands are less sterically hindered and have higher activities in the catalysis of ATRP of (meth)acrylates than 2,2′‐bipyridine. The polymerizations were faster and more controlled than with the 2,2′‐bipyridyl catalyst, but the tendency for bimolecular coupling increased. Even though the initiator was octafunctional, the resulting star polymers had only four arms. This indicates that the steric hindrance arising from the conformations of the initiators determines the structure of the polymer, but the ligand noticeably affects the controllability of the polymerization © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3349–3358, 2005     

Die oxydative Bromierung bei der Bestimmung der Äpfelsäure und der Asparaginsäure

Analytical and Bioanalytical Chemistry - Die Identität des aus Äpfelsäure — wahrscheinlich auch aus Asparaginsäure und Tyrosin — durch bromierende...     

On initial populations of a genetic algorithm for continuous optimization problems

Genetic algorithms are commonly used metaheuristics for global optimization, but there has been very little research done on the generation of their initial population. In this paper, we look for an answer to the question whether the initial population plays a role in the performance of genetic algorithms and if so, how it should be generated. We show with a simple example that initial populations may have an effect on the best objective function value found for several generations. Traditionally, initial populations are generated using pseudo random numbers, but there are many alternative ways. We study the properties of different point generators using four main criteria: the uniform coverage and the genetic diversity of the points as well as the speed and the usability of the generator. We use the point generators to generate initial populations for a genetic algorithm and study what effects the uniform coverage and the genetic diversity have on the convergence and on the final objective function values. For our tests, we have selected one pseudo and one quasi random sequence generator and two spatial point processes: simple sequential inhibition process and nonaligned systematic sampling. In numerical experiments, we solve a set of 52 continuous test functions from 16 different function families, and analyze and discuss the results.