Über die Primfunktionen in einer arithmetischen Progression

Ohne ZusammenfassungVerfasser, geboren in Wohlau am 23. August 1890, hatte vor dem Kriege selbständig die Entdeckung gemacht, daß Dirichlets klassischer Beweis des Satzes von den Primzahlen einer arithmetischen Progression (nebst den späteren elementaren Begründungen des Nichtvershwindens der bekannten Reihen) ein Analogon z. B. in der Theorie der Primfunktionen in Restklassen nach einem Doppelmodulp, M hat. Über dies selbstgewählte Thema hatte er seine Doktordissertation im wesentlichen schon fertiggestellt. Als Kriegsfreiwilliger fiel er im Oktober 1914 bei Poël-Capelle. Erst kürzlich erhielt ich aus seinem Nachlaß das (mir schon seit 1914 bekannte) Manuskript. Ich übergebe hiermit die schönsten und interessantesten Teile der Öffentlichkeit. Der Kornblumsche Ansatz zeichnet sich durch hohe Eleganz aus und zeigt, daß die Wissenschaft in ihm einen hoffnungsvollen Forscher verloren hat. Den Satz und Beweis des § 1 habe ich aus Kornblums Manuskript übernommen; einige Bemerkungen habe ich in Fußnoten angefügt. Den Satz und Beweis des § 2 hat er allerdings nur fürk=2 gehabt; doch wäre die von mir hinzugefügte Ausdehnung auf beliebigesk wohl ohnebin bei gemeinsamer Besprechung in seiner Dissertation hinzugekommen, da alles unmittelbar mit seiner Methode herauskommt.     

Turbulence modulation in two-phase jets

A simple model is presented which can be used to predict the modifying effect of a dispersed-phase on the turbulence structure of two-phase jets. It is based on Kolmogorov's concept of spectral energy transfer and takes into account the additional energy dissipation resulting from the inability of dispersed-phase particles to completely follow turbulent eddy fluctuations. According to the analysis presented, high-frequency eddies are attenuated preferentially and a reduction of the total rate of turbulent energy dissipation results. Turbulence intensities were also reduced. Good agreement between predictions and experimental findings were obtained.     

Phase Behavior of a Designed Cyclopropyl Analogue of Monoolein: Implications for Low‐Temperature Membrane Protein Crystallization

Lipidic cubic phases (LCPs) are used in areas ranging from membrane biology to biodevices. Because some membrane proteins are notoriously unstable at room temperature, and available LCPs undergo transformation to lamellar phases at low temperatures, development of stable low‐temperature LCPs for biophysical studies of membrane proteins is called for. Monodihydrosterculin (MDS) is a designer lipid based on monoolein (MO) with a configurationally restricted cyclopropyl ring replacing the olefin. Small‐angle X‐ray scattering (SAXS) analyses revealed a phase diagram for MDS lacking the high‐temperature, highly curved reverse hexagonal phase typical for MO, and extending the cubic phase boundary to lower temperature, thereby establishing the relationship between lipid molecular structure and mesophase behavior. The use of MDS as a new material for LCP‐based membrane protein crystallization at low temperature was demonstrated by crystallizing bacteriorhodopsin at 20 °C as well as 4 °C.     

A linearization technique for multi-species transport problems

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor’s series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.     

Inplace 2D matching in compressed images

The compressed matching problem is the problem of finding all occurrences of a pattern in a compressed text. In this paper we discuss the 2-dimensional compressed matching problem in Lempel–Ziv compressed images. Given a pattern P of (uncompressed) size m×m, and a text T of (uncompressed) size n×n, both in 2D-LZ compressed form, our algorithm finds all occurrences of P in T. The algorithm is strongly inplace, that is, the amount of extra space used is proportional to the best possible compression of a pattern of size m². The best compression that the 2D-LZ technique can obtain for a file of size m² is O(m). The time for performing the search is O(n²) and the preprocessing time is O(m³). Our algorithm is general in the sense that it can be used for any 2D compression which can be sequentially decompressed in small space.     

Structural characterization of nanocrystalline CrOOH·2H2O aerogel by X-ray diffraction

The nanostructured powder prepared by critical CO₂ extraction of the urea-assisted wet chromia gel mixture at 373 K in vacuum was studied by X-ray diffraction techniques. Thermoanalytical methods showed the presence of the lattice water molecules in the resulting phase corresponding to a chemical formula CrOOH·2H₂O. The CrOOH·2H₂O nanocrystals of 3-5 nm in diameter were observed in transmission electron microscopy and their structure was derived from the Rietveld analysis in which the disorder contribution to the X-ray scattering was implemented. The structural model shows that the hexagonal unit cell of α-CrOOH undergoes monoclinic distortion with half of the O⁻² anions and OH⁻ groups being replaced by bonded water molecules in the three-dimensional packing resulting in half of the sites in regular Cr⁺³ octahedra being vacant. Further examination of the quasi-crystalline disordered state of the CrOOH·2(H₂O) nanocrystals was performed by model independent method of Radial Distribution Function (RDF). This complementary technique is sensitive to the molecular composition and allows to assess the average atomic (or electron) density distribution and the spacings of the atomic arrangements in the nearest neighbor shells comprising the range of the crystalline order in the structure of this material.     

Prediction for two processes and the nehari problem

We exploit an analogy between the trigonometric moment problem and prediction theory for a stationary stochastic process. Extending this theory, we show how to use correlations between two processes to predict one from the other. In turn, this gives rise to a simple and unified treatment of the Caratheodory and Nehari moment problems.     

Über einen Valironschen Satz

Ohne Zusammenfassung