Incomplete data problems in X-ray computerized tomography

Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4     

Stochastic control problems with delay

We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal consumption rate in a financial market with delay. Finally, we solve explicitly a deterministic fluid problem with delay which arises from admission control in ATM communication networks.     

Native ethylene glycol in wine: Application of a dead volume free,very fast “deans heart-cut” system on-line with multi-chromatography

Data about the existence of native HO? CH₂? CH₂? OH (MEG) in natural wines and champagne has led to delicate questions because of legal decisions already made to declare wine or champagne illegal for sale if the MEG concentrations found are above 10 mg/liter. Action has been taken because of the DEG (diethylene glycol) disaster in European wines of 1985…86. An incorrect legal decision was made due to the belief that MEG cannot be produced biochemically by grape vines. A further reason may be lack of correct data on native MEG trace concentrations, as a result of the special behavior of this diol. As first member of a homologous series whose higher members (C₄) are normally found in all wines at quite high concentration levels, MEG shows extremely adsorptive behavior. The solution of the chromatographic problems is summarized in this paper. MEG concentrations in Riesling as example are in the range of 2 to 6 mg/liter and can easily be increased by biotechnological steps to a level of around 10 to 60 mg/liter. This is again due to the specific adsorptive behavior of MEG, which can be enriched on filter surfaces and displaced when the wine acidity changes with changing types. In order to control and guarantee the qualitative and quantitative results of MEG analyses we used a combination of Deans heart cutting on-line with Multi-Chromatography. It was easy to produce false data by many otherwise useful single column or two-dimensional separation processes, etc.     

Configurationally and conformationally homogeneous cyclicN-aryl sulfimides. II.13C-and1H NMR spectra

The configuration and (in case of mobile ring systems) the preferred conformation in a series of thiane- and ofcis-andtrans-1-thiadecalin-1-N-4-chlorophenyl imides were assigned by means of¹³C- and¹H nmr spectroscopy.¹H nmr criteria known to be valid for determination of the stereochemistry of cyclic sulfoxides may be applied (with limitations) to cyclicN-aryl sulfimides, if both isomers (S–N bond equatorial and axial, respectively) are known. The assignments are easier, and unambiguous for single isomers, by comparison of¹³C nmr chemical shifts of ring carbon atoms of sulfimides and sulfides. The influence of equatorially and axially oriented sulfimide groups on the chemical shifts of neighbouring protons, and on the carbon atoms of the heterocyclic rings are discussed in detail.

---

Konfigurativ und konformationell einheitliche cyclische N-Aryl-sulfimide. II.¹³C- und¹H-NMR-Spektroskopie

Zusammenfassung Die Konfiguration und (bei beweglichen Ringsystemen) die bevorzugte Konformation einer Reihe von Thian- und voncis- undtrans-1-Thiadekalin-1-N-4-chlorophenylimiden wurde durch¹³C- und¹H-NMR-Spektroskopie bestimmt. Bekannte¹H-NMR-Kriterien zur Festlegung der Stereochemie cyclischer Sulfoxide sind (mit Einschränkungen) auch bei cyclischenN-Arylsulfimiden anwendbar, wenn beide Isomere (S–N-Bindung äquatorial bzw. axial) bekannt sind. Leichter, und auch bei Vorliegen von nur einem Isomeren eindeutig, gelingt die Zuordnung durch Vergleich der¹³C-NMR-Verschiebungen der Ringkohlenstoffatome von Sulfimiden und Sulfiden. Die Einflüsse äquatorial oder axial orientierter Sulfimidgruppen auf die chemischen Verschiebungen benachbarter Wasserstoffe und der Kohlenstoffe des Heterorings werden diskutiert.

     

Infrared and Raman study of Si2Te3

Results of ir and Raman investigations on trigonal layer-structured Si₂Te₃ single crystals are reported. The ir reflection spectrum withEc exhibits seven reststrahl-like bands, whereas the corresponding spectrum withEc shows only one very small bump. Values for ₀ and are given. The Raman spectra are very rich in structure and can only be interpreted qualitatively as being a mixture of single phonon lines and one- and two-phonon density-of-states contributions. One-phonon density-of-states effects are disorder-induced owing to the statistical occurrence of the Si atoms within the regular hexagonal Te sublattice.     

ON THE REARRANGEMENT OF N-ARYL SULFIMIDES

Abstract

N-Aryl-S,S-dialkylsulfimides, 1, with R¹ = alkyl other than CH₃, have been rearranged by heating in ethanol yielding o-alkylthiomethyl-anilines, 2, as main products. Isomeric o-methylthioalkyl-anilines, 14, are formed in minor amounts only. Reactions of sulfimides, 1, with R¹ = CH₃, with certain alkylating or acylating agents yielded o-methylthiomethylated, N-alkylated or -acylated products 9. Mechanistic considerations are discussed. The rearrangement of sulfimides 1 has been assumed to occur via [2,3]-sigmatropic reactions of intermediate azasulfonium ylids 3. Attempts to resolve (+)-camphor-10-sulfonates of N-aryl sulfimides failed, but optically active N-aryl sulfimides could be obtained by reaction of anilines with optically active sulfoxides and P₄O₁₀. Optically active 2,6-disubstituted sulfimides, 1, could be rearranged in ethanolic KOH to yield optically active cyclohexadienimines 12, indicating a transfer of asymmetry from sulfur to carbon and supporting the assumption of a sigmatropic rearrangement.     

Alkene–Tetrazine Ligation for Imaging Cellular DNA

5‐Vinyl‐2′‐deoxyuridine (VdU) is the first reported metabolic probe for cellular DNA synthesis that can be visualized by using an inverse electron demand Diels–Alder reaction with a fluorescent tetrazine. VdU is incorporated by endogenous enzymes into the genomes of replicating cells, where it exhibits reduced genotoxicity compared to 5‐ethynyl‐2′‐deoxyuridine (EdU). The VdU–tetrazine ligation reaction is rapid (k≈0.02 M ^?1 s^?1) and chemically orthogonal to the alkyne–azide “click” reaction of EdU‐modified DNA. Alkene–tetrazine ligation reactions provide the first alternative to azide–alkyne click reactions for the bioorthogonal chemical labeling of nucleic acids in cells and facilitate time‐resolved, multicolor labeling of DNA synthesis.     

Tubular Structures of Calcium Carbonate: Formation,Characterization, and Implications in Natural Mineral Environments

Chemical gardens are self-assembled tubular precipitates formed by a combination of osmosis, buoyancy, and chemical reaction, and thought to be capable of catalyzing prebiotic condensation reactions. In many cases, the tube wall is a bilayer structure with the properties of a diaphragm and/or a membrane. The interest in silica gardens as microreactors for materials science has increased over the past decade because of their ability to create long-lasting electrochemical potential. In this study, we have grown single macroscopic tubes based on calcium carbonate and monitored their time-dependent behavior by in situ measurements of pH, ionic concentrations inside and outside the tubular membranes, and electrochemical potential differences. Furthermore, we have characterized the composition and structure of the tubular membranes by using ex situ X-ray diffraction, infrared and Raman spectroscopy, as well as scanning electron microscopy. Based on the collected data, we propose a physicochemical mechanism for the formation and ripening of these peculiar CaCO₃ structures and compare the results to those of other chemical garden systems. We find that the wall of the macroscopic calcium carbonate tubes is a bilayer of texturally distinct but compositionally similar calcite showing high crystallinity. The resulting high density of the material prevents macroscopic calcium carbonate gardens from developing significant electrochemical potential differences. In the light of these observations, possible implications in materials science and prebiotic (geo)chemistry are discussed.