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.     

On some contact problems for composite half-spaces PMM vol. 31, no. 6, 1967, pp. 1001–1008

Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.

1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.

2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.

In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.

Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.

The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].

The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials.     

Crystal Structures of Hydrochlorides of 2,3-Pentamethylene-3, 4-dihydroquinazolin-4-one

The crystal structures of hydrate (1) and anhydrate (2) forms of 2,3-pentamethylene-3,4-dihydroquinazolin-4-one hydrochloride have been determined by X-ray structure analysis. Crystal data of 1 are 2(C₁₃H₁₄N₂O)*3(HCl)*4.5 (H₂O), triclinic P?1, Z=2, a=8.004(5), b=13.129(7), c=15.725(7) Å, α=106.45(4), β=92.61(4), γ=97.98(5), R=0.0652 and 2 are C₁₃H₁₄N₂O*HCl, monoclinic C2/c, Z=8, a=21.360(4), b=5.954(1), c=21.263(4), β=117.89(3), R=0.0556. The crystal of the hydrate form 1is unstable. This form collapses easily with evaporation of H₂O and part of HCl molecules from crystals. By recrystallizing destroyed form has been obtained stable crystal form 2.     

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.

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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.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.