Ramadanov conjecture and line bundles over compact Hermitian symmetric spaces

We compute the Szegö kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in ${\mathbb C^n}We compute the Szeg? kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in \mathbb Cⁿ{\mathbb C^n} for Grassmannian manifolds of higher ranks. In particular, they provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds for which the logarithmic term in the Fefferman expansion of the Szeg? kernel vanishes but whose boundary is not diffeomorphic to the sphere (in fact, it is not even locally spherical). The analogous results for the Bergman kernel are also obtained.     

Error bounds of certain Gaussian quadrature formulae

We study the kernel of the remainder term of Gauss quadrature rules for analytic functions with respect to one class of Bernstein-Szegö weight functions. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective error bounds of the corresponding Gauss quadratures.     

An Exchange Mechanism for the Magnetic Behavior of Er3+ Complexes

We study the magnetic properties of the erbium based compounds, Na9[Er(W5O18)2] and [(Pc)Er{Pc{N(C4H9)2}8}]·/−, in the framework of an effective spin exchange model involving delocalized electrons occupying molecular orbitals. The calculations successfully reproduce the experimental data available in the literature for the magnetic spectrum, magnetization and molar susceptibility in dc and ac fields. Owing to their similar molecular geometry, the compounds’ magnetic behaviors are interpreted in terms of the same set of active orbitals and thus the same effective spin coupling scheme. For all three complexes, the model predicts a prompt change in the ground state from a Kramer’s doublet at zero fields to a fully polarized quartet one brought about by the action of an external magnetic field without Zeeman splitting. This alteration is attributed to the enhancement of the effect of orbital interactions over the spin exchange as the magnitude of the external magnetic field increases.     

Study of the island morphology at the early stages of Fe/Mo(110) MBE growth

We present theoretical study of morphology of Fe islands grown at Mo(110) surface in submonolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500 K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluate qualitatively morphological changes, we measured average aspect ratio of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.      

A short proof of an inequality of Littlewood and Paley

A very short proof is given of the inequality

where and is the Poisson integral of

     

Tolterodinium (+)‐(2R,3R)‐hydrogen tartrate

In the crystal structure of (R)‐N,N‐diisopropyl‐3‐(2‐hydroxy‐5‐methyl­phenyl)‐3‐phenyl­propyl­aminium (2R,3R)‐hydrogen tartrate, C₂₂H₃₂NO⁺·C₄H₅O₆⁻, the hydrogen tartrate anions are linked by O—H⋯O hydrogen bonds to form helical chains built from (9) rings. These chains are linked by the tolterodine molecules via N—H⋯O and O—H⋯O hydrogen bonds to form separate sheets parallel to the (101) plane.     

Label‐free Voltammetric Detection of Products of Terminal Deoxynucleotidyl Transferase Tailing Reaction

A label‐free approach that takes advantage of intrinsic electrochemical activity of nucleobases has been applied to study the products of terminal deoxynucleotidyl transferase (TdT) tailing reaction. DNA homooligonucleotides A₃₀, C₃₀ and T₃₀ were used as primers for the tailing reaction to which a dNTP – or a mixture of dNTPs – and TdT were added to form the tails. Electrochemical detection enabled study of the tailing reaction products created by various combinations of primers and dNTPs, with pyrolytic graphite electrode (PGE) being suitable for remarkably precise analysis of the length of tailing reaction products. Furthermore, the hanging mercury drop electrode (HMDE) was able to reveal formation of various DNA structures, such as DNA hairpins and G‐quadruplexes, which influence the behavior of DNA molecules at the negatively charged surface of HMDE. Thus, the described approach proves to be an excellent tool for studying the TdT tailing reactions and for exploring how various DNA structures affect both the tailing reactions and electrochemical behavior of DNA oligonucleotides at electrode surfaces.     

On Mechanism of Intermediate-Sized Circular DNA Compaction Mediated by Spermine: Contribution of Fluorescence Lifetime Correlation Spectroscopy

The compaction of DNA plays a role in the nuclei of several types of cells and becomes important in the non-viral gene therapy. Thus, it is in the scope of research interest. It was shown, that spermine-induced compaction of large DNA molecules occurs in a discrete "all-or-non" regime, where the coexistence of free and folded DNA molecules was observed. In the case of intermediate-sized DNA molecules (approximately 10 kbp), so far, it was stated that the mechanism of folding is continuous. Here, we show, that neither a standard benchmark technique-dynamic light scattering, nor a single molecule technique such as fluorescence correlation spectroscopy, can decide what kind of mechanism is undertaken in the compaction process. Besides, we introduce an application of a new approach-fluorescence lifetime correlation spectroscopy. The method takes an advantage of a subtle lifetime change of an intercalating dye PicoGreen during the titration with spermine and based on that, it reveals the discrete mechanism of the process. Furthermore, we show that it allows for observation of the equilibrium state transition dynamics.     

Über Isomorphismen gewisser Kardinalpotenzen

Zusammenfassung Es sei k eine lückenlose Kette ohne Sprünge und ohne gr?sstes Element, g, G geordnete Mengen. In der Bemerkung wird die geordnete Menge aller Isomorphismen der Kardinalpotenz k^G auf die Kardinalpotenz k^g beschrieben. Enrico Bompiani zu seinem wissenschaftlichen Jubil?um