Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

Chemo- and regioselectivity in the reactions between highly electrophilic fluorine containing dicarbonyl compounds and amines. Improved synthesis of the corresponding imines/enamines

Chemo- and regioselectivity in the reactions between highly electrophilic fluorine containing dicarbonyl compounds (ethyl 4,4,4-trifluoroacetoacetate, 3,3,3-trifluoropyruvate and 1,1,1,5,5,5-hexafluoropentane-2,4-dione) and various benzylamines were systematically studied. The results obtained lead to the development of a generalized and practical method for large-scale synthesis of the corresponding imines/enamines, useful starting materials for preparation fluorinated amines and amino acid.     

Facile one-pot synthesis of BINOL- and H8-BINOL-based aryl phosphites and their use in palladium catalysed asymmetric allylation

Novel P-monodentate aryl phosphite ligands have been synthesised in one step from (R)-BINOL, (R)-H₈-BINOL and (R)-H₈-3,3′-dibromo-BINOL. With the new aryl phosphites, up to 86% ee was observed in the asymmetric Pd-catalysed amination of 1,3-diphenyl-2-propenyl acetate with sodium diformylamide. In the enantioselective alkylation of 1,3-diphenyl-2-propenyl acetate with dimethyl malonate, up to 97% enantioselectivity was achieved.     

Recovery of 177Lu from Irradiated HfO2 Targets for Nuclear Medicine Purposes

A new method of production of one of the most widely used isotopes in nuclear medicine, ¹⁷⁷Lu, with high chemical purity was developed; this method includes irradiation of the HfO₂ target with bremsstrahlung photons. The irradiated target was dissolved in HF and then diluted and placed onto a column filled with LN resin. Quantitative sorption of ¹⁷⁷Lu could be observed during this process. The column later was rinsed with the mixture of 0.1 M HF and 1 M HNO₃ and then 2 M HNO₃ to remove impurities. Quantitative desorption of ¹⁷⁷Lu was achieved by using 6 M HNO₃. The developed method of ¹⁷⁷Lu production ensures high purification of this isotope from macroquantities of hafnium and zirconium and radioactive impurities of carrier-free yttrium. The content of ^177mLu in ¹⁷⁷Lu in photonuclear production was determined. Due to high chemical and radionuclide purity, ¹⁷⁷Lu obtained by the developed method can be used in nuclear medicine.     

Equivariant quantization on quotients of simple Lie groups by reductive subgroups of maximal rank

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation quantizations equivariant under the action ofG and the corresponding quantum group. We also classify Poisson brackets relating to such quantizations. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Scanning paraxial optical tomography

We present a solution to this problem in the form of a fast algorithm with computational complexity that scales as N log N , where N is the number of spatial measurements of the scattered field.     

Parallel MRI at microtesla fields

Parallel imaging techniques have been widely used in high-field magnetic resonance imaging (MRI). Multiple receiver coils have been shown to improve image quality and allow accelerated image acquisition. Magnetic resonance imaging at ultra-low fields (ULF MRI) is a new imaging approach that uses SQUID (superconducting quantum interference device) sensors to measure the spatially encoded precession of pre-polarized nuclear spin populations at microtesla-range measurement fields. In this work, parallel imaging at microtesla fields is systematically studied for the first time. A seven-channel SQUID system, designed for both ULF MRI and magnetoencephalography (MEG), is used to acquire 3D images of a human hand, as well as 2D images of a large water phantom. The imaging is performed at 46 mu T measurement field with pre-polarization at 40 mT. It is shown how the use of seven channels increases imaging field of view and improves signal-to-noise ratio for the hand images. A simple procedure for approximate correction of concomitant gradient artifacts is described. Noise propagation is analyzed experimentally, and the main source of correlated noise is identified. Accelerated imaging based on one-dimensional undersampling and 1D SENSE (sensitivity encoding) image reconstruction is studied in the case of the 2D phantom. Actual threefold imaging acceleration in comparison to single-average fully encoded Fourier imaging is demonstrated. These results show that parallel imaging methods are efficient in ULF MRI, and that imaging performance of SQUID-based instruments improves substantially as the number of channels is increased.     

A beam summation algorithm for wave radiation and guidance in stratified media

A Gaussian beams summation (GBS) algorithm for tracking source excited wave fields in plane stratified media is presented. In the present application the medium is described by layers with constant gradient of the wave speed, and the GB propagators are calculated recursively in a closed form. The algorithm is calibrated for numerical efficacy and accuracy by defining simple physical criteria for choosing the expansion parameters (the beam collimation and the spectral discretization and truncation) that allow for sparse representation of the source-excited angular spectrum of beams. It is validated for a source-excited example in layered media, where it provides a smooth and physically meaningful solution under multipath and caustic conditions and remains accurate for long propagation ranges where phase error tends to accumulate.