Equivalence of the Metaplectic Representation with Sums of Wavelet Representations for a Class of Subgroups of the Symplectic Group

Equivalence of the metaplectic representation with a sum of affine representations is discussed for a class of subgroups of the symplectic group. The paper begins with a study of sums of wavelet transforms, and it is shown that the usual admissibility conditions for the wavelet transform apply to transforms by sums of affine representations as well. A construction of admissible vectors, bandlimited admissible vectors and frames for sums of affine representations by means of transversals is given. A class of subgroups of the symplectic group which are compact extensions affine groups are identified, and it is shown how subrepresentations of the metaplectic representation can be equivalent to affine representations. This equivalence is illuminated by several examples.     

Neue massenspektrometrische Methoden in der analytischen Praxis

Ohne Zusammenfassung

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New mass-spectrometric methods in practical analysis

     

Chern Classes of Gauss–Manin Bundles of Weight 1 Vanish

We show that the Chern character of a variation of polarized Hodge structures of weight one with nilpotent residues at dies up to torsion in the Chow ring, except in codimension 0.     

Role of the Polymer Matrix on the Photoluminescence of Embedded CdSe Quantum Dots

The photoluminescence (PL) of CdSe quantum dots (QDs) that form stable nanocomposites with polymer liquid crystals (LCs) as smectic C hydrogen‐bonded homopolymers from a family of poly[4‐(n‐acryloyloxyalkyloxy)benzoic acids] is reported. The matrix that results from the combination of these units with methoxyphenyl benzoate and cholesterol‐containing units has a cholesteric structure. The exciton PL band of QDs in the smectic matrix is redshifted with respect to QDs in solution, whereas a blueshift is observed with the cholesteric matrix. The PL lifetimes and quantum yield in cholesteric nanocomposites are higher than those in smectic ones. This is interpreted in terms of a higher order of the smectic matrix in comparison to the cholesteric one. CdSe QDs in the ordered smectic matrix demonstrate a splitting of the exciton PL band and an enhancement of the photoinduced differential transmission. These results reveal the effects of the structure of polymer LC matrices on the optical properties of embedded QDs, which offer new possibilities for photonic applications of QD–LC polymer nanocomposites.     

Elastic light scattering from nanoparticles by monochromatic vacuum-ultraviolet radiation

Elastic light scattering is reported using monochromatic vacuum-ultraviolet radiation to study free, spherical silica nanoparticles prepared by approaches from colloidal chemistry, with diameters between 100 and 240 nm. The colloidal nanoparticles of defined size are transferred from an aqueous solution into the gas phase using a particle beam experiment. After focusing of the particle beam by an aerodynamic lens, the scattered light from monochromatic synchrotron radiation is measured. Angle-resolved elastically scattered light is detected, showing a strong forward-scattering component. Additional evidence for the detection of elastically scattered light comes from plotting the scattered light intensity as a function of the dimensionless parameter qR, where q is the magnitude of the scattering wave vector and R is the particle radius. This yields different power-law regimes that are assigned to scattering from the surface and the bulk of the nanoparticles. Furthermore, there is evidence for modulations in the scattered light intensity as a function of scattering angle, which is clearly distinguished from the forward-scattering component. The experimental results are compared to Mie scattering simulations for isolated particles, yielding general agreement with the experimental results. Deviations from Mie simulations are observed for samples consisting of significant amounts of aggregates. The present results indicate that the optical properties of free nanoparticles are sensitively probed by vacuum-ultraviolet radiation.     

Cavity ring-down spectroscopy of the torsional motions of 1,4-bis(phenylethynyl)benzene

The torsional motions of jet-cooled 1,4-bis(phenylethynyl)benzene (BPEB), a prototype molecular wire, were studied using cavity ring-down spectroscopy in the first UV absorption band (316-321 nm). The torsional spectrum of 1,4-bis(phenylethynyl)-2,3,5,6-tetradeuteriobenzene was also recorded in the gas phase. Both spectra were successfully simulated using simple cosine potentials to describe the torsional motions. The ground-state barrier to rotation was estimated to be 220-235 cm(-1), which is similar to that of diphenylacetylene (tolane). Complementary DFT calculations were found to overestimate the torsional barrier.     

Point configurations on the projective line over a finite field

We study n-point configurations in \({\mathbb{P}^1(\mathbb{F}_q)}\) modulo projective equivalence. For n = 4 and 5, a complete classification is given, along with the numbers of such configurations with a given symmetry group. Using Polya’s coloring theorem, we investigate the behavior of the numbers C(n, q) of classes of n-configurations resp. C ^spec(n, q) of classes with nontrivial symmetry group. Both are described by rational polynomials in q which depend on q modulo \({\lambda(n) = {\rm lcm} \{m \in \mathbb{N} | m \leq n\}}\) .     

Unforgettable film music: The role of emotion in episodic long-term memory for music

Background  

Specific pieces of music can elicit strong emotions in listeners and, possibly in connection with these emotions, can be remembered even years later. However, episodic memory for emotional music compared with less emotional music has not yet been examined. We investigated whether emotional music is remembered better than less emotional music. Also, we examined the influence of musical structure on memory performance.     

Exact gravitational field of the infinitely long rotating hollow cylinder

The vacuum line element inside an infinitely long rotating hollow cylinder is the usual flat space line element. It is fitted in a most general way to the general cylindrical vacuum field outside at the singular hypersurfaceR ₀=const, representing the infinitely thin hollow cylinder. With the use of the jump conditions atR ₀=const the surface densities , of which the energy-momentum-stress tensor of the shell consists, are calculated. The physical properties of the cylinder, as derived from the eigenvalues and -vectors of , and the generated gravitational field are discussed in full detail.