Über meromorphe Modifikationen

Ohne Zusammenfassung     

Application of compressed sensing to in vivo 3D ¹⁹F CSI

This study shows how applying compressed sensing (CS) to (19)F chemical shift imaging (CSI) makes highly accurate and reproducible reconstructions from undersampled datasets possible. The missing background signal in (19)F CSI provides the required sparsity needed for application of CS. Simulations were performed to test the influence of different CS-related parameters on reconstruction quality. To test the proposed method on a realistic signal distribution, the simulation results were validated by ex vivo experiments. Additionally, undersampled in vivo 3D CSI mouse datasets were successfully reconstructed using CS. The study results suggest that CS can be used to accurately and reproducibly reconstruct undersampled (19)F spectroscopic datasets. Thus, the scanning time of in vivo(19)F CSI experiments can be significantly reduced while preserving the ability to distinguish between different (19)F markers. The gain in scan time provides high flexibility in adjusting measurement parameters. These features make this technique a useful tool for multiple biological and medical applications.     

Nanoparticle adsorption on a weak polyelectrolyte. Stiffness, pH, charge mobility, and ionic concentration effects investigated by Monte Carlo simulations

Monte Carlo simulations have been used to study two different models for a weak linear polyelectrolyte in the presence of nanoparticles: (i) a rodlike and (ii) a flexible polyelectrolytes. The use of simulated annealing has made it possible to simulate a polyelectrolyte chain in the presence of several nanoparticles by improving conformation sampling and avoiding multiple minima problems when dense conformations are produced. Nanoparticle distributions along the polymer backbone were analyzed versus the ionic concentration, polyelectrolyte stiffness, and nanoparticle surface charge. Titration curves were calculated and the influences of the ionic concentration, solution pH, and number of adsorbed nanoparticles on the acid/base polyelectrolyte properties have been systematically investigated. The subtle balance of attractive and repulsive interactions has been discussed, and some characteristic conformations are presented. The comparison of the two limit models provides a good representation of the stiffness influence on the complex formation. In some conditions, overcharging was obtained and presented with respect to both the polyelectrolyte and nanoparticle as the central element. Finally, the charge mobility influence along the polyelectrolyte backbone was investigated by considering annealed and quenched polyelectrolyte chains.     

2. Internationale Konferenz iiber Methoden der Darstellung and Aufbewahrung markierter Verbindungen

Es wurde die Verteilung von ¹³¹J im Zeitraum von 1/2–24 h nach einer einmaligen Röntgenbestrahlung mit 0,21 C/kg verfolgt, wobei das Radiojod zu zwei verschiedenen Zeitpunkten nach der Exposition verabreicht wurde; 2 Stunden nach der Exposition bei der Gruppe T₂ und 18 Stunden bei der Gruppe T₁₈. Unterschiede in der Verteilung des Radiojods bei den Kontroll- und Versuchstieren weisen auf pathophysioloyische strahlenbedingte Organveränderungen hin.     

Combinatorial constructions for the Zeckendorf sum of digits of polynomial values

Let $p(X)\in\mathbb{Z}[X]$ with $p(\mathbb{N})\subset\mathbb{N}$ be of degree h≥2 and denote by s _F (n) the sum of digits in the Zeckendorf representation of n. We study by combinatorial means three analogues of problems of Gelfond (Acta Arith. 13:259–265, 1967/1968), Stolarsky (Proc. Am. Math. Soc. 71:1–5, 1978) and Lindström (J. Number Theory 65:321–324, 1997) concerning the distribution of s _F on polynomial sequences. First, we show that for m≥2 we have #{n<N:s _F (p(n))≡amodm}? _p,m N ^4/(6h+1) (Gelfond). Secondly, we find the extremal minimal and maximal orders of magnitude of the ratio s _F (p(n))/s _F (n) (Stolarsky). Third, we prove that lim?sup _n→∞ s _F (p(n))/log _φ (p(n))=1/2, where φ denotes the golden ratio (Lindström).     

5- and 6-pulse electron spin echo envelope modulation (ESEEM) of multi-nuclear spin systems

In 3-pulse ESEEM and the original 4-pulse HYSCORE, nuclei with large modulation depth (k approximately 1) suppress spectral peaks from nuclei with weak modulations (k approximately 0). This cross suppression can impede the detection of the latter nuclei, which are often the ones of interest. We show that two extended pulse sequences, 5-pulse ESEEM and 6-pulse HYSCORE, can be used as experimental alternatives that suffer less strongly from the cross suppression and allow to recover signals of k approximately 0 nuclei in the presence of k approximately 1 nuclei. In the extended sequences, modulations from k approximately 0 nuclei are strongly enhanced. In addition, multi-quantum transitions are absent which simplifies the spectra. General analytical expressions for the modulation signals in these sequences are derived and discussed. Numerical simulations and experimental spectra that demonstrate the higher sensitivity of the extended pulse sequences are presented.     

Phase Cycling in Electron Spin Echo Envelope Modulation

We present a general way to devise efficient phase cycles for arbitrary electron spin echo envelope modulation (ESEEM) experiments. The method determines all coherence transfer pathways contributing to the measured signal, selects those of interest and then examines all possible nested phase cycles in order to find those that achieve the required selection. The procedure is used to find efficient nested phase cycles for ESEEM sequences containing up to nine pulses: two-pulse, three-pulse and five-pulse ESEEM, standard and six-pulse hyperfine sublevel correlation (HYSCORE) as well as their extensions including remote echo detection. In addition, it is shown that by shifting the last pulse by 90° three-pulse ESEEM and HYSCORE do not need phase cycling in the case of a symmetrically excited line. Authors' address: Stefan Stoll, Department of Chemistry, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA     

Boundary limits and non-integrability of )

In this paper we consider weighted non-tangential and tangential boundary limits of non-negative functions on the unit ball in that are subharmonic with respect to the Laplace-Beltrami operator on . Since the operator is invariant under the group of holomorphic automorphisms of , functions that are subharmonic with respect to are usually referred to as -subharmonic functions. Our main result is as follows: Let be a non-negative -subharmonic function on satisfying

for some and some , where is the -invariant measure on . Suppose . Then for a.e. ,

uniformly as in each , where for ( when )

We also prove that for the only non-negative -subharmonic function satisfying the above integrability criteria is the zero function.

     

Complete decomposition of Dickson-type polynomials and related Diophantine equations

We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)

     

Extracellular SH3 domain containing proteins--features of a new protein family

In the year 1994, the protein MIA (melanoma inhibitory activity) was found to be strongly expressed and secreted by malignant melanomas and subsequent studies revealed that MIA has an important function in melanoma development and invasion. Multidimensional NMR-spectroscopy and x-ray crystallography revealed that recombinant human MIA adopts a Src homology 3 (SH3) domain-like fold in solution, a structure with two perpendicular antiparallel three- and five-stranded beta-sheets. SH3 domains are protein modules that are found in many intracellular signalling proteins and mediate protein-protein interactions by binding to proline-rich peptide sequences. Unlike previously described protein structures with SH3 domain folds, MIA is a secreted single-domain protein of 12 kDa that contains an additional antiparallel beta-sheet and two disulfide bonds. Furthermore, the charge surrounding the canonical binding site differs from that of classical SH3 domains. The two disulfide bonds are crucial for correct folding and function as revealed by mutation analysis. Therefore, MIA appears to be the first extracellular protein adopting an SH3 domain-like fold. MIA was shown to interact with fibronectin, and MIA-interacting peptide ligands identified by phage display screening are similar to the consensus sequence of type III human fibronectin repeats, especially FN14. Interestingly, recent data revealed that MIA can also directly bind to integrin alpha 4 beta 1 and alpha 5 beta1 and that it modulates integrin activity negatively. These findings suggest an interesting role of the SH3-domain proteins in the extracellular compartment. Recently, MIA homologous proteins with a sequence identity of 44% and a sequence homology of approximately 80% were determined (TANGO, MIA-2, OTOR). This clearly suggests that this structural device is used more frequently, in processes ranging from developmental changes to the interference of cell attachment in the extracellular matrix. Detailed studies are necessary to determine the exact function of the MIA homologous proteins. It will be interesting to know whether additional protein families can be identified which are secreted and carry SH3 domain-like modules, in addition to elucidate what the specific physiological targets of this protein family are.