Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

Dirichletsche Reihen auf arithmetischen Progressionen

A characterisation of all real Δ≠0 is given, such that $$\overline {f(\sigma + i\Delta \mathbb{N})} = \overline {f(\sigma + i\mathbb{R})} $$ holds for all Dirichlet seriesf(s)=Σa _n n ^?s and all σ greater than the abscissa of absolute convergence off. For only countably many Δ relation (*) is not valid. By using transcendental results it is shown, that (*) holds in the special case, Δ=1.     

On a classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

Sur les séries de Taylor et les transformations de Möbius

Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero.     

Ein Algorithmus zur Lösung eines Verteilungsproblems

Zusammenfassung Bei der Lastverteilung eines Elektrizitätsversorgungsunternehmens besteht die Möglichkeit, durch eine Tonfrequenzrundsteueranlage die Last optimal aufzuteilen. Eine Zielsetzung besteht darin, durch Zu- und Wegschalten von Verbrauchergruppen die Lastspitze möglichst klein zu halten. Dabei muß allerdings jedem Verbraucher in einem gewissen Zeitraum eine gewisse Einschaltdauer garantiert sein. Der zur Lösung herangezogene Algorithmus basiert im wesentlichen auf dem Prinzip der dynamischen Optimierung und der Idee von Branch- and-Bound-Verfahren.

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Summary One aim of electric load management is to keep load peaks low by switching on and off water heaters of different groups of customers. There is a restriction that those heaters have to be switched on within a certain period of time for some fixed time. The optimal switching strategy for this distribution problem is computed using dynamic programming and the idea of branch and bound methods.

     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

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Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

Interactions of different heterocyclic compounds with monoionic forms of montmorillonite

Interactions of 3-R-and 2-R pyridine (R=CH₃, Cl, NH₂) with Ni(II)-exchanged montmorillonite have been studied. Thermal and X-ray analyses indicate that pyridine derivatives are intercalated into the interlayer spaces of montmorillonite. Infrared spectral data shown that the Lewis and/or Brönsted type of interactions of pyridine derivatives is connected with different steric and inductive effects of the substituents (R) on the pyridine ring. The alkylpyridines increase the electron density on the donor nitrogen atom and support the coordination to the central atom. The halogen substituents have a negative inductive effect (–I), so that those ligands show a lower basicity and weaker σ-bonding properties than pyridine and also the lower possibility of the coordination.     

Die IR-Spektren von NH4UO2AsO4·3H2O und NH4UO2PO4·3H2O

The infrared spectra of the title compounds, as well as that of the structurally related mineral meta-autunite, [Ca(UO₂)₂(PO₄)₂·n H₂O], are reported and discussed using the available crystallographic data. The results can be considered as representative for the full group of the so-called torbernite-minerals.     

Untersuchungen an Kristallhydraten anorganischer Salze, 8. Mitt. Interpretation der Schwingungsspektren vonM(BF4)2·6H2O fürM=Fe2+, Co2+, Ni2+

The infrared and Raman spectra were recorded in the range 4000–160 cm^–1 forM(BF₄)₂·6 H₂O whereM=Fe²⁺, Co²⁺, Ni²⁺. The spectroscopic data support the X-ray structural data in showing that in the crystal hydrates studied two kinds of hydrogen bonds are present: H₂O...H₂O and OH₂... F₄B^–. The energies and molecular force constants (f _OH and fH₂O) andr _OH for OH₂...F₄B^– were calculated for the three crystal hydrates. It was found that the bond OH₂... F₄B^– is comparatively weak, with mean energy 3.7–3.3 kcal/mol. Two types of water molecule with different structures are existing as the first are participating in H₂O...H–O–H...F₄B^– and the second in BF₄ ^–...H–O–H...F₄B^–.     

Strong Structural and Electronic Binding of Bovine Serum Albumin to ZnO via Specific Amino Acid Residues and Zinc Atoms

ZnO biointerfaces with serum albumin have attracted noticeable attention due to the increasing interest in developing ZnO-based materials for biomedical applications. ZnO surface morphology and chemistry are expected to play a critical role on the structural, optical, and electronic properties of albumin-ZnO complexes. Yet there are still large gaps in the understanding of these biological interfaces. Herein we comprehensively elucidate the interactions at such interfaces by using atomic force microscopy and nanoshaving experiments to determine roughness, thickness, and adhesion properties of BSA layers adsorbed on the most typical polar and non-polar ZnO single-crystal facets. These experiments are corroborated by force field (FF) and density-functional tight-binding (DFTB) calculations on ZnO-BSA interfaces. We show that BSA adsorbs on all the studied ZnO surfaces while interactions of BSA with ZnO are found to be considerably affected by the atomic surface structure of ZnO. BSA layers on the surface have the highest roughness and thickness, hinting at a specific upright BSA arrangement. BSA layers on surface have the strongest binding, which is well correlated with DFTB simulations showing atomic rearrangement and bonding between specific amino acids (AAs) and ZnO. Besides the structural properties, the ZnO interaction with these AAs also controls the charge transfer and HOMO-LUMO energy positions in the BSA-ZnO complexes. This ZnO facet-specific protein binding and related structural and electronic effects can be useful for improving the design and functionality of ZnO-based materials and devices.