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PURPOSE To visualize by direct fluorescent in situ hybridization the entire human visual pigment gene array on single X-chromosome fibers and to compare the results with values obtained by other molecular techniques. METHODS The size of the opsin gene array on the X-chromosome in eight male subjects was investigated by (i) direct visual in situ… (More)
Molecular genetic studies demonstrate that the human cone opsin gene array on the q-arm of the X-chromosome typically consists of one long-wave-sensitive (L) cone opsin gene and from one to several middle-wave-sensitive (M) cone opsin genes. Although the presence of the single L-cone opsin gene and at least one M-cone opsin gene is essential for normal… (More)
We define under which circumstances two multi-warped product spacetimes can be considered equivalent and then we classify the spaces of constant curvature in the Euclidean and Lorentzian signature. For dimension D = 2, we get essentially twelve representations, for D = 3 exactly eighteen. More general, for every even D, 5D + 2 cases exist, whereas for every… (More)
For the diagonalization of the Hamilton matrix in the Heisenberg model relevant dimensions are determined depending on the applicable symmetries. Results are presented, both, by general formulae in closed form and by the respective numbers for a variety of special systems. In the case of cyclic symmetry, diagonalizations for Heisenberg spin rings are… (More)
We present the history of fourth order metric theories of gravitation from its beginning in 1918 until 1988.
A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to negative temperatures, and vice versa.
We systematically investigate the possible transitions between classical homogeneous Riemannian 3-hypersurfaces of cosmological models on one hand, and between homogeneous Lorentzian minisuperspace 3-geometries on the other hand. For the Riemannian case, in contrast to our earlier approaches where we only evaluated the three scalar invariants from the Ricci… (More)
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to… (More)
For a class of frustrated spin lattices including e.g. the 1D sawtooth chain, the 2D kagomé and checkerboard, as well as the 3D pyrochlore lattices we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being… (More)
The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches , the conformal properties of gravitation plays the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometro-dynamics are of a more… (More)