Laboratory gas phase spectroscopy of carbon molecular structures in relation to diffuse interstellar bands

An experiment suitable for studying the carbon molecular structures which are the candidates for carriers of the diffuse interstellar bands (DIBs) in astrophysical spectra has been developed in the plasma-chemistry laboratory of the Masaryk University in Brno. The experimental arrangement including an apparatus for detecting the gas phase spectra of monopolar high-frequency discharge is described. The preliminary results involving a search for the ultraviolet, visible, and near-infrared well pronounced features of the carbon molecular structures are discussed. This work was supported by the Grant Agency of the Czech Republic, grant No. 205/94/0470.     

Towards a new measurement of the neutron electric dipole moment

Precision measurements of particle electric dipole moments (EDMs) provide extremely sensitive means to search for non-standard mechanisms of T (or CP) violation. For the neutron EDM, the upper limit has been reduced by eight orders of magnitude in 50 years thereby excluding several CP violation scenarios. We report here on a new effort aiming at improving the neutron EDM limit by two orders of magnitude, down to a level of 3 × 10⁻²⁸ e·cm. The two central elements of the approach are the use of the higher densities which will be available at the new dedicated spallation UCN source at the Paul Scherrer Institute, and the optimization of the in-vacuum Ramsey resonance technique, with storage chambers at room temperature, to reach new limits of sensitivity.     

Generalized spline wavelets

A generalized multiresolution of multiplicityr, generated byr linearly independent spline functions with multiple knots, is introduced. With the help of the autocorrelation symbol and the two-scale symbol of the scaling functions, spline wavelets with multiple knots can be completely characterized. New decomposition and reconstruction algorithms, based on the Fourier technique, are presented.     

Uniform spherical grids via equal area projection from the cube to the sphere

We construct an area preserving map from a cube to the unit sphere S², both centered at the origin. More precisely, each face F_i of the cube is first projected to a curved square S_i of the same area, and then each S_i is projected onto the sphere by inverse Lambert azimuthal equal area projection, with respect to the points situated at the intersection of the coordinate axes with S². This map is then used to construct uniform and refinable grids on a sphere, starting from any grid on a square.     

A new factorization technique of the matrix mask of univariate refinable functions

Summary. A univariate compactly supported refinable function can always be written as the convolution product , with the B-spline of order k,f a compactly supported distribution, and k the approximation orders provided by the underlying shift-invariant space . Factorizations of univariate refinable vectors were also studied and utilized in the literature. One of the by-products of this article is a rigorous analysis of that factorization notion, including, possibly, the first precise definition of that process. The main goal of this article is the introduction of a special factorization algorithm of refinable vectors that generalizes the scalar case as closely (and unexpectedly) as possible: the original vector is shown to be `almost' in the form , with F still compactly supported and refinable, andk the approximation order of . The algorithm guarantees F to retain the possible favorable properties of , such as the stability of the shifts of and/or the polynomiality of the mask symbol. At the same time, the theory and the algorithm are derived under relatively mild conditions and, in particular, apply to whose shifts are not stable, as well as to refinable vectors which are not compactly supported. The usefulness of this specific factorization for the study of the smoothness of FSI wavelets (known also as `multiwavelets' and `multiple wavelets') is explained. The analysis invokes in an essential way the theory of finitely generated shift-invariant (FSI) spaces, and, in particular, the tool of superfunction theory. Received June 10, 1998 / Revised version received June 14, 1999 / Published online August 2, 2000     

Stretched exponential survival statistics for microorganisms in radiation field

The so-called concave or tailed survival curves are reported both for multi and single species bacterial populations. Taking as an example Bacillus pumilus, frequently encountered in decontamination studies, it is shown that the tailed survival curves are adequately described by stretched (0<<1) exponential SF=exp[−(D/D₀)], where SF denotes the fraction of species surviving the irradiation dose D, D₀ is the effective dose, and is the dispersion parameter interpreted phenomenologically in terms of radiation sensivity distribution for single species population under the given experimental conditions.     

Directional Haar wavelet frames on triangles

Traditional wavelets are not very effective in dealing with images that contain orientated discontinuities (edges). To achieve a more efficient representation one has to use basis elements with much higher directional sensitivity. In recent years several approaches like curvelets and shearlets have been studied providing essentially optimal approximation properties for images that are piecewise smooth and have discontinuities along C²-curves. While curvelets and shearlets have compact support in frequency domain, we construct directional wavelet frames generated by functions with compact support in time domain. Our Haar wavelet constructions can be seen as special composite dilation wavelets, being based on a generalized multiresolution analysis (MRA) associated with a dilation matrix and a finite collection of ‘shear’ matrices. The complete system of constructed wavelet functions forms a Parseval frame. Based on this MRA structure we provide an efficient filter bank algorithm. The freedom obtained by the redundancy of the applied Haar functions will be used for an efficient sparse representation of piecewise constant images as well as for image denoising.     

Wavelet Shrinkage on Paths for Denoising of Scattered Data

We propose a new algorithm for denoising of multivariate function values given at scattered points in ${\mathbb{R}^{d}}$ . The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by Plonka (Multiscale Model Simul 7:1474–1496, 2009) to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take the distribution of the scattered points as well as the corresponding function values into account. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method.