On quantum iterated function systems

A Quantum Iterated Function System on a complex projective space is defined through a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.     

Fundamental Geometric Structures for the Dirac Equation in General Relativity

We present an axiomatic approach to Dirac's equation in General Relativity based on intrinsically covariant geometric structures. Structure groups and the related principal bundle formulation can be recovered by studying the automorphisms of the theory. Various aspects can be most neatly understood within this context, and a number of questions can be most properly addressed (specifically in view of the formulation of QFT on a curved background). In particular, we clarify the fact that the usual spinor structure can be weakened while retaining all essential physical aspects of the theory.     

Transition to chaos in the self-excited system with a cubic double well potential and parametric forcing

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self-excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.     

Reaction of 3,3′,4,4′-tetramethyl-1,1′-diphosphaferrocene with [Re2(CO)8(CH3CN)2]: Novel coordination modes of the 1,1′-diphosphaferrocene ligand

Reaction of 3,3′,4,4′-tetramethyl-1,1′-diphosphaferrocene (1) with [Re₂(CO)₈(CH₃CN)₂] afforded two trimetallic complexes in which the heterometallocene is ligated across the Re-Re bond. The structure of the complex having 1 bridging the Re₂(CO)₈ moiety through two P atoms was determined by X-ray diffraction and compared with those of analogous complexes with organic bridging bis-phosphines. The second complex obtained in this reaction presumably contains 1 acting as a (P,Fe) bridging ligand.     

Why are the kinked polyacenes more stable than the straight ones? A topological study and introduction of a new topological index of aromaticity

A topological model for estimating the stability of benzenoid hydrocarbons (BHs) is presented showing an acceptable linear dependence on Hess-Schaad resonance energy per pi-electron values. The topological measure of stability is accessible by use of pencil calculation and is based on counting cis-type fragments of double bonds in all canonical structures of a given BH. Evidence is given that infinite chains of straight linear polyacenes are always less stable than the kinked ones.     

Circular dichroism and conformational dynamics of cephams and their carba and oxa analogues

The biological activity of bicyclic beta-lactam antibiotics depends strongly on the absolute configuration of the bridgehead carbon atom. Frelek and co-workers proposed an empirical helicity rule relating the configuration of the bridgehead carbon atom to the sign of the 220 nm band in the electronic circular dichroism (CD) spectrum of beta-lactams. Here we use synthetic organic chemistry, CD spectroscopy, and time-dependent density functional theory (TDDFT) to investigate the validity of this structure-property relationship for eight model compounds. For conformationally flexible beta-lactams, substantial thermal effects are found which must be included in calculations. To this end, we combine TDDFT calculations of CD with full quantum-mechanical Born-Oppenheimer molecular dynamics (MD) simulations for the first time. The CD spectra are sampled with ground-state density functional trajectories of up to 60 ps. The MD simulations show a surprisingly high sensitivity of the CD to the molecular conformation. On the other hand, the relation between CD and thermally averaged structural parameters is much less complex. While the helicity rule does not seem to hold for individual conformers, it is confirmed by the calculations for seven out of eight systems studied if thermally averaged CD spectra and structures are considered. Since thermal effects on CD can be larger than typical inherent inaccuracies of TDDFT, our results emphasize the need for a systematic treatment of conformational dynamics in CD calculations even for moderately flexible systems. Temperature-dependent CD measurements are very useful for this purpose. Our results also suggest that CD spectroscopy may be used as a sensitive probe of conformational dynamics if combined with electronic structure calculations.     

Determination of neptunium in plutonium and mixed uranium-plutonium samples by isotope dilution gamma-spectrometry with243Am as a spike

A method was developed for isolating neptunium from Pu, U or mixed oxide (MOX) samples and its determination by isotope dilution -spectrometry (IDGS) using²³⁹Np (²⁴³Am) as a spike. Extraction chromatography with trilaurylamine fixed on a SGX-C18 support was used for the isolation of Np. The decontamination factors for U, Pu, Am and Pa vary between 1000–2000 and 100, respectively. The average separation yield of Np is (95±3)%. The amount of²⁴³Am required for spiking is about 0.2–0.3 g. It is recommended to use the pair of -rays 86.53 keV (²³⁷Np)-106.13 keV (²³⁹Np) for the assay of neptunium. A relative uncertainty of 4% or better is achievable in the analysis of plutonium samples, containing 0.4–80 g neptunium. The detection limit, under the proposed experimental conditions, is about 0.05 g Np. The results were compared with the results obtained by using high resolution -spectrometry (HRGS).     

On-line capillary separations/tandem mass spectrometry for protein digest analysis by using an ion trap storage/reflectron time-of flight mass detector

Capillary separations interfaced to tandem mass spectrometry provide a very powerful tool for the characterization of biological macromolecules such as proteins and peptides. The development of real time data-dependent data acquisition has further enhanced the capability of this method. However, the application of this technique to fast capillary separations has been limited by the relatively slow spectral acquisition speed available on scanning mass spectrometers. In this work, an ion trap storage/reflectron time-of-flight mass spectrometer (IT/reTOF-MS) has been used as an on-line tandem mass detector for capillary high-performance liquid chromatography (HPLC) and capillary electrophoresis (CE) separations of peptide mixtures including a protein digest. By taking advantage of the nonscanning property of the time-of-flight mass spectrometer, a fast spectral acquisition rate has been achieved. This fast spectral acquisition rate, combined with a new protocol that speeds up tickle voltage optimization, has provided MS/MS spectra for multiple components in a hemoglobin digest during one liquid chromatography/mass spectrometry/mass spectrometry (LC/MS/MS) run. Further, the IT/reTOF-MS has the speed to provide MS/MS spectra for multiple components in a CE separation of a synthetic peptide mixture within one CE/MS/MS run.     

Determination of iron and titanium in kaolins by the method of non-dispersive X-ray fluorescence

The possibility of application of the radioactive source excited X-ray fluorescence analysis for titanium and iron determination in kaolins to the routine test of the refinement process has been studied. The iron content can be determined with a simple counting system using a single-channel pulse height analyser, argon filled proportional counter and¹⁰⁹Cd source of 3 mCi for the excitation of K Fe rays. The samples were analysed both as pellets and powders. The iron content ranged from 0.2–2.5% and titanium from 0.1–0.64%. For simultaneous determination of titanium and iron a Si(Li) spectrometer has been used. The²³⁸Pu source has been used for K Fe and K Ti excitation. It is the most convenient source for simultaneous determination of titanium and iron.⁵⁵Fe is the most efficient source for the determination of titanium alone. The best values of precision and determination limit have been achieved for iron with²³⁸Pu and for titanium with⁵⁵Fe.