Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

On the use of surfaces of section in the N-body ring problem

In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.     

How Constant Momentum Acceleration Decouples Energy and Space Focusing in Distance–of–Flight and Time–of–Flight Mass Spectrometries

Resolution in time–of–flight mass spectrometry (TOFMS) is ordinarily limited by the initial energy and space distributions within an instrument’s acceleration region and by the length of the field–free flight zone. With gaseous ion sources, these distributions lead to systematic flight–time errors that cannot be simultaneously corrected with conventional static–field ion–focusing devices (i.e., an ion mirror). It is known that initial energy and space distributions produce non–linearly correlated errors in both ion velocity and exit time from the acceleration region. Here we reinvestigate an old acceleration technique, constant–momentum acceleration (CMA), to decouple the effects of initial energy and space distributions. In CMA, only initial ion energies (and not their positions) affect the velocity ions gain. Therefore, with CMA, the spatial distribution within the acceleration region can be manipulated without creating ion–velocity error. The velocity differences caused by a spread in initial ion energy can be corrected with an ion mirror. We discuss here the use of CMA and independent focusing of energy and space distributions for both distance–of–flight mass spectrometry (DOFMS) and TOFMS. Performance characteristics of our CMA–DOFMS and CMA–TOFMS instrument, fitted with a glow–discharge ionization source, are described. In CMA–DOFMS, resolving powers (FWHM) of greater than 1000 are achieved for atomic ions with a flight length of 285 mm. In CMA–TOFMS, only ions over a narrow range of m/z values can be energy–focused; however, the technique offers improved resolution for these focused ions, with resolving powers of greater than 2000 for a separation distance of 350 mm.      

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

Synthesis and properties of macrocyclic diazene switch with binaphthalene unit attached via acrylamide linkers

2,2′-Diiodo-1,1′-binaphthalene undergoes a tandem Heck reaction with methyl acrylate to afford methyl 2-(7H-dibenzo[c,g]fluoren-7-ylidene)acetate. As a consequence, the target macrocyclic diazene with binaphthalene unit attached via acrylamide linker was prepared by the stepwise building of acrylamide at a binaphthalene moiety, including the Doebner modification of the Knoevenagel condensation, and completed by oxidative macrocyclisation of aniline end-groups. Despite being an equimolar mixture of monomer and dimer, it exhibited remarkable changes in CD spectra due to reversible (E/Z) isomerisation of N=N diazene bonds upon irradiation at 365/465 nm. Although the dimer isomerises from (E) to (Z) isomer 7.4 times faster than the monomer, the latter’s contribution to the change in ellipticity at 307 nm in the photostationary state is 2.4 times greater.     

Theranostic Approach for the Protein Corona of Polysaccharide Nanoparticles

Polysaccharide nanoparticles are promising materials in the wide range of disciplines such as medicine, nutrition, food production, agriculture, material science and others. They excel not only in their non‐toxicity and biodegradability but also in their easy preparation. As well as inorganic particles, a protein corona (PC) around polysaccharide nanoparticles is formed in biofluids. Moreover, it has been considered that the overall response of the organism to nanoparticles presence depends on the PC. This review summarises scientific publications about the structural chemistry of polysaccharide nanoparticles and their impact on theranostic applications. Three strategies of implementation of the PC in theranostics have been discussed: I) Utilisation of the PC in therapy; II) How the composition of the PC is analysed for specific disease markers; III) How the formed PC can interact with the immune system and enhances the immunomodulation or immunoelimination. Thus, the findings from this review can contribute to improve the design of drug delivery systems. However, it is still necessary to elucidate the mechanisms of nano‐bio interactions and discover new connections in nanoscale research.     

Entropic uncertainty relation

Shannon's entropy is used for the formulation of the uncertainty relation. Two concrete examples are solved: the case of dynamically commuting continuous observables, and the case of theh/2 spin projections.