Mural inspection by vibration measurements with TV-holography

A commonly encountered problem in the conservation of historical murals is the identification of sections in the plaster that have detached from the wall and thus threaten to fall off. Commonly, walls are inspected by the acoustic response to a gentle finger-tapping (percussion method). Since this is a costly and cumbersome technique, means for a more automatic inspection are searched for. A TV-holography system of increased sensitivity in combination with acoustic excitation of the object is shown to be a new and powerful tool for monitoring of loose areas. It has the advantage of non-contact and remote operation which, for example, is extremely useful in large buildings. Principles of the method, experimental results obtained at an artificial wall in the laboratory, and a thorough comparison of results from historical sites gained by the traditional percussion method and the new technique are presented. The latter shows very good agreement in the assessment of wall quality and thus is evidence of the suitability of the optical equipment for tasks in conservation.     

New Cyclic and Polycyclic Ring Systems Containing Group 14 (Si,Ge, Sn) and 16 (S,Se, Te) Elements

The reactions of Me₂MCl₂ (M = Si, Ge, Sn), Si₂Me₄Cl₂, Si₂Me₂Cl₃, Si₂Me₂Cl₄ and CH₂(SiCl₂Me)₂, and suitable mixtures thereof, with H₂S / NEt₃ and Li₂E (E = Se, Te) have been investigated and lead to a variety of new group 14 chalcogenide systems.     

Insights into LiAlH4 Catalyzed Imine Hydrogenation

Commercial LiAlH₄ can be used in catalytic quantities in the hydrogenation of imines to amines with H₂. Combined experimental and theoretical investigations give deeper insight in the mechanism and identifies the most likely catalytic cycle. Activity is lost when Li in LiAlH₄ is exchanged for Na or K. Exchanging Al for B or Ga also led to dramatically reduced activities. This indicates a heterobimetallic mechanism in which cooperation between Li and Al is crucial. Potential intermediates on the catalytic pathway have been isolated from reactions of MAlH₄ (M=Li, Na, K) and different imines. Depending on the imine, double, triple or quadruple imine insertion has been observed. Prolonged reaction of LiAlH₄ with PhC(H)=NtBu led to a side-reaction and gave the double insertion product LiAlH₂[N]₂ ([N]=N(tBu)CH₂Ph) which at higher temperature reacts further by ortho-metallation of the Ph ring. A DFT study led to a number of conclusions. The most likely catalyst for hydrogenation of PhC(H)=NtBu with LiAlH₄ is LiAlH₂[N]₂. Insertion of a third imine via a heterobimetallic transition state has a barrier of +23.2 kcal mol⁻¹ (ΔH). The rate-determining step is hydrogenolysis of LiAlH[N]₃ with H₂ with a barrier of +29.2 kcal mol⁻¹. In agreement with experiment, replacing Li for Na (or K) and Al for B (or Ga) led to higher calculated barriers. Also, the AlH₄⁻ anion showed very high barriers. Calculations support the experimentally observed effects of the imine substituents at C and N: the lowest barriers are calculated for imines with aryl-substituents at C and alkyl-substituents at N.     

Crystal and Molecular Structure of 3-Methoxy-estra-1,3,5(10)-trien-17β-ol

The crystal structure determination of the title compound was undertaken to determine the conformational flexibility of the steroid skeleton. 3-Methoxy-estra-1,3,5(10)-trien-17β-ol (C₁₉H₂₆O₂) crystallizes in the space group P2₁2₁2₁ with Z = 12, a = 12.589(2), b = 16.274(5), and c = 23.535(6) Å. The structure was solved by direct methods and refined to R = 0.056. Three symmetry independent molecules having different molecular conformations were observed in the crystal. The most flexible region of the molecules is the B ring which adopts following conformations: 7α,8β-half-chair, 8β-sofa, and an intermediate form between half-chair and sofa.     

A Representation of Quantum Measurement in Order-Unit Spaces

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.     

Different Faces of the Shearlet Group

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups.