Synthesis of novel deuterium labelled derivatives of N-alkylated polyamines

Novel di-, tetra- and octadeuterated derivatives of mono-N-alkylated diaminopropanes, spermidines, spermines, symmetrically bis-N-alkylated spermines and unsymmetrically bis-N-alkylated spermines were synthesized. Deuterium labels were introduced into the RHNCH₂CH₂CN intermediate either by exchanging the protons next to the nitrile group under basic conditions with D₂O-EtOD mixture or/and by reducing the nitrile group to a CD₂-NH₂ fragment with LiAlD₄.     

Lebesgue type decompositions for nonnegative forms

A nonnegative form on a complex linear space is decomposed with respect to another nonnegative form : it has a Lebesgue decomposition into an almost dominated form and a singular form. The part which is almost dominated is the largest form majorized by which is almost dominated by . The construction of the Lebesgue decomposition only involves notions from the complex linear space. An important ingredient in the construction is the new concept of the parallel sum of forms. By means of Hilbert space techniques the almost dominated and the singular parts are identified with the regular and a singular parts of the form. This decomposition addresses a problem posed by B. Simon. The Lebesgue decomposition of a pair of finite measures corresponds to the present decomposition of the forms which are induced by the measures. T. Ando's decomposition of a nonnegative bounded linear operator in a Hilbert space with respect to another nonnegative bounded linear operator is a consequence. It is shown that the decomposition of positive definite kernels involving families of forms also belongs to the present context. The Lebesgue decomposition is an example of a Lebesgue type decomposition, i.e., any decomposition into an almost dominated and a singular part. There is a necessary and sufficient condition for a Lebesgue type decomposition to be unique. This condition is inspired by the work of Ando concerning uniqueness questions.     

Solid-state shifts in the L3M4,5M4,5 Auger spectra of the elements Cu TO Se

The kinetic-energy shifts between atomic and solid-state L₃M_4,5M_4,5 Auger electron spectra of Cu, Zn, Ga, Ge, As, and Se are determined with the aid of semiempirically calculated atomic and experimental solid-state Auger energies. The shift values are calculated by applying the thermochemical model to the Auger process. Good agreement is found between the calculated and experimental values.     

Taylor expansion of the accumulated rounding error

The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.     

Melt‐compounded nanocomposites of titanium dioxide atomic‐layer‐deposition‐coated polyamide and polystyrene powders

Polyamide and polystyrene particles were coated with titanium dioxide films by atomic layer deposition (ALD) and then melt‐compounded to form polymer nanocomposites. The rheological properties of the ALD‐created nanocomposite materials were characterized with a melt flow indexer, a melt flow spiral mould, and a rotational rheometer. The results suggest that the melt flow properties of polyamide nanocomposites were markedly better than those of pure polyamide and polystyrene nanocomposites. Such behavior was shown to originate in an uncontrollable decrease in the polyamide molecular weight, likely affected by a high thin‐film impurity content, as shown in gel permeation chromatography (GPC) and scanning electron microscope (SEM) equipped with an energy‐dispersive spectrometer. Transmission electron microscope image showed that a thin film grew on both studied polymer particles, and that subsequent melt‐compounding was successful, producing well dispersed ribbon‐like titanium dioxide with the titanium dioxide filler content ranging from 0.06 to 1.12 wt%. Even though we used nanofillers with a high aspect ratio, they had only a minor effect on the tensile and flexural properties of the polystyrene nanocomposites. The mechanical behavior of polyamide nanocomposites was more complex because of the molecular weight degradation. Our approach here to form polymeric nanocomposites is one way to tailor ceramic nanofillers and form homogenous polymer nanocomposites with minimal work‐related risks in handling powder form nanofillers. However, further research is needed to gauge the commercial potential of ALD‐created nanocomposite materials. Copyright © 2011 John Wiley & Sons, Ltd.     

A physico-chemical characterisation of new raw materials for microcrystalline cellulose manufacturing

A detailed physico-chemical characterisation of potential new cellulose sources (rice husk, hemp stalk, and coniferous needles), and microcrystalline cellulose (MCC) manufactured from them, was made in this work. The length and the width of the cellulose crystallites were determined by wide-angle X-ray scattering (WAXS), crystallinities were studied by means of WAXS and solid state cross polarisation magic angle spinning ¹³C nuclear magnetic resonance (NMR) spectroscopy, and the packing and the cross-sectional shape of the microfibrils were determined by small-angle X-ray scattering. When MCC was prepared from rice husks and hemp stalks an acceptable yield was obtained. Crystallinities obtained with solid state NMR spectroscopy and WAXS were highest for MCC prepared from hemp stalks, and lowest for rice husk MCC. The crystallite sizes of MCC samples studied in this work varied more than in those MCC samples which were prepared from conventional plant sources, and crystallite size and cellulose crystallinity were related. When taking into account rather high values of specific surface, hemp stalks and rice husks appear as a promising raw materials for MCC production.     

Limit properties of monotone matrix functions

The basic objects in this paper are monotonically nondecreasing $n\times n$ matrix functions $D(·)$ defined on some open interval $?=(a\text{,}b)$ of $\mathbb{R}$ and their limit values $D(a)$ and $D(b)$ at the endpoints a and b which are, in general, selfadjoint relations in ${\mathbb{C}}^n$. Certain space decompositions induced by the matrix function $D(·)$ are made explicit by means of the limit values $D(a)$ and $D(b)$. They are a consequence of operator inequalities involving these limit values and the notion of strictness (or definiteness) of monotonically nondecreasing matrix functions. This treatment provides a geometric approach to the square-integrability of solutions of definite canonical systems of differential equations.     

Equations containing locally Henstock-Kurzweil integrable functions

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.     

On a frequency function approach to the unique continuation principle

In this survey we discuss the frequency function method so as to study the problem of unique continuation for elliptic partial differential equations. The methods used in the note were mainly introduced by Garofalo and Lin.