Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.Comment: LaTeX 4 pages, 3 EPS included, to appear in Europhysics Letter

Primitive points in rational polygons

Let $\mathcal A$ be a star-shaped polygon in the plane, with rational vertices, containing the origin. The number of primitive lattice points in the dilate $t\mathcal A$ is asymptotically $\frac6{\pi^2}$ Area$(t\mathcal A)$ as $t\to \infty$. We show that the error term is both $\Omega_\pm\big( t\sqrt{\log\log t} \big)$ and $O(t(\log t)^{2/3}(\log\log t)^{4/3})$. Both bounds extend (to the above class of polygons) known results for the isosceles right triangle, which appear in the literature as bounds for the error term in the summatory function for Euler's $\phi(n)$.Comment: 17 page

Classification of Two-Person Ordinal Bimatrix Games

The set of possible outcomes of a strongly ordinal bimatrix game is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto optimal sets of each cardinality; we establish asymptotic bounds for the number of different convex hulls of the point sets, for the average shape of the set of points dominated by the Pareto optimal set, and for the average shape of the convex hull of the point set. We also indicate the effect of individual rationality considerations on our results. As most of our results are asymptotic, the appendix includes a careful examination of the important case of 2 x 2 games.Game theory, rationality, preferences

Syntheses of 4′-thioribonucleosides and thermodynamic stability and crystal structure of RNA oligomers with incorporated 4′-thiocytosine

A facile synthetic route for the 4′-thioribonucleoside building block 4′SN (N = U, C, A and G) with the ribose O4′ replaced by sulfur is presented. Conversion of l-lyxose to 1,5-di-O-acetyl-2,3-di-O-benzoyl-4-thio-d-ribofuranose was achieved via an efficient four-step synthesis with high yield. Conversion of the thiosugar into the four ribonucleoside phosphoramidite building blocks was accomplished with additional four steps in each case. Incorporation of 4′-thiocytidines into oligoribonucleotides improved the thermal stability of the corresponding duplexes by ∼1°C per modification, irrespective of whether the strand contained a single modification or a consecutive stretch of 4′SC residues. The gain in thermodynamic stability is comparable to that observed with oligoribonucleotides containing 2′-O-methylated residues. To establish potential conformational changes in RNA as a result of the 4′-thio modification and to better understand the origins of the observed stability changes, the crystal structure of the oligonucleotide 5′-r(CC4′SCCGGGG) was determined and analyzed using the previously solved structure of the native RNA octamer as a reference. The two 4′-thioriboses adopt conformations that are very similar to the C3′-endo pucker observed for the corresponding sugars in the native duplex. Subtle changes in the local geometry of the modified duplex are mostly due to the larger radius of sulfur compared to oxygen or appear to be lattice-induced. The significantly increased RNA affinity of 4′-thio-modified RNA relative to RNA, and the relatively minor conformational changes caused by the modification render this nucleic acid analog an interesting candidate for in vitro and in vivo applications, including use in RNA interference (RNAi), antisense, ribozyme, decoy and aptamer technologie

Kaali raudmeteoriidi petrograafiline ja geokeemiline kirjeldus

Käesolevas töös uuriti 2017. aasta suvel leitud Kaali meteoriidifragmenti „Maria“. Eesmärgiks oli kirjeldada metoriidi petrograafiat ja geokeemiat ning saadud tulemusi võrrelda varasemalt saadud tulemustega. Domineerivaks faasiks on kamasiit, mis esines massiivsete kristalliitidena, mida liigestab taeniidi ja šreibersiidi erineva suurusega suletised. Kirjeldati erineva kujuga šreibersiidi kristalle, mis varieerusid mitmesaja mikroni pikkustest ja mõne mikroni laiustest kepikestest paari mikroniliste ümarate kristallideni. Kohati täitis šreibersiit kamasiidi kristalliitide vahelist ruumi, viidates šreibersiidi hilisemale kristallisatsioonile. Meteoriidis leiti erineva morfoloogiaga plessiite ja sfaleriidi ning hetkel klassifitseerimata kroomi-tsingi sulfiidi suletisi, millede detailne kirjeldus nõuab edasisi uuringuid. Uurimustulemused kinnitasid eelnevat Kaali meteoriidi klassifikatsiooni. Meteoriit on tekstuurse klassifikatsiooni järgi jäme oktaedriit (Og). Keemilise klassifikatsiooni alusel kuulub Kaali meteoriit IAB kompleksi ning pearühma (MG)

Syntheses of 4′-thioribonucleosides and thermodynamic stability and crystal structure of RNA oligomers with incorporated 4′-thiocytosine

A facile synthetic route for the 4′-thioribonucleoside building block (4′S)N (N = U, C, A and G) with the ribose O4′ replaced by sulfur is presented. Conversion of l-lyxose to 1,5-di-O-acetyl-2,3-di-O-benzoyl-4-thio-d-ribofuranose was achieved via an efficient four-step synthesis with high yield. Conversion of the thiosugar into the four ribonucleoside phosphoramidite building blocks was accomplished with additional four steps in each case. Incorporation of 4′-thiocytidines into oligoribonucleotides improved the thermal stability of the corresponding duplexes by ∼1°C per modification, irrespective of whether the strand contained a single modification or a consecutive stretch of (4′S)C residues. The gain in thermodynamic stability is comparable to that observed with oligoribonucleotides containing 2′-O-methylated residues. To establish potential conformational changes in RNA as a result of the 4′-thio modification and to better understand the origins of the observed stability changes, the crystal structure of the oligonucleotide 5′-r(CC(4′S)CCGGGG) was determined and analyzed using the previously solved structure of the native RNA octamer as a reference. The two 4′-thioriboses adopt conformations that are very similar to the C3′-endo pucker observed for the corresponding sugars in the native duplex. Subtle changes in the local geometry of the modified duplex are mostly due to the larger radius of sulfur compared to oxygen or appear to be lattice-induced. The significantly increased RNA affinity of 4′-thio-modified RNA relative to RNA, and the relatively minor conformational changes caused by the modification render this nucleic acid analog an interesting candidate for in vitro and in vivo applications, including use in RNA interference (RNAi), antisense, ribozyme, decoy and aptamer technologies

Metal-Free C-H Borylation of N-Heteroarenes by Boron Trifluoride

Organoboron compounds are essential reagents in modern C-C coupling reactions. Their synthesis via catalytic C-H borylation by main group elements is emerging as a powerful tool alternative to transition metal based catalysis. Herein, a straightforward metal-free synthesis of aryldifluoroboranes from BF(3)and heteroarenes is reported. The reaction is assisted by sterically hindered amines and catalytic amounts of thioureas. According to computational studies the reaction proceeds via frustrated Lewis pair (FLP) mechanism. The obtained aryldifluoroboranes are further stabilized against destructive protodeborylation by converting them to the corresponding air stable tetramethylammonium organotrifluoroborates.Peer reviewe

Palaeozoic carbon isotope excursions and carbonate component analysis

Palaeozoic carbonate δ13C studies have mainly focused on bulk rock analysis in chemostratigraphic correlations and palaeoenvironmental interpretations, assuming limited isotopic heterogeneity of samples. Particular attention has been paid to positive δ13C excursions, which likely reflect climatic events. However, several studies have provided isotope data from different rock components demonstrating significant sample-scale variation of δ13C values. We describe the isotopic and elemental composition of individual components in carbonate rocks and analyse which components carry the primary depositional isotopic signatures and which components have been isotopically reset by diagenetic processes. The comparison of bulk rock and component-specific data allows us to assess the reliability of isotopic data used in environmental reconstructions and offers an opportunity to better reconstruct magnitudes of δ13C excursions and related dynamics of seawater dissolved inorganic carbon. Here we focus on the Hirnantian Isotopic Carbon Excursion (HICE) at the end of the Ordovician period and the Mid-Ludfordian Carbon Isotope Excursion (MLCIE) during the late Silurian period. Previous bulk rock studies have demonstrated the occurrence of the HICE in multiple Estonian drill cores corresponding to the Porkuni Regional Stage. The HICE samples from the Kamariku, Karinu, and Otepää drill cores were subsampled by micro-drilling, and isotope analysis of individual components was done by isotope-ratio mass spectroscopy (IRMS). Limited sample-scale heterogeneity and good correspondence with bulk rock δ13C values are seen in micritic carbonate samples, whereas different bioclastic and cement components in wackestone and grainstone samples exhibit up to 4Ⱐrange of δ13C values with some components having δ13C values up to 3Ⱐhigher than the bulk rock values. Lithologically heterogeneous grainstone from the Otepää core shows δ18O variability as much as 3Ⱐand ooids carrying the lowest, most overprinted values. Isotope results obtained by the Secondary Ion Mass Spectrometry (SIMS) on MLCIE samples from Lithuanian Vidukle drill core show up to 5Ⱐrange of δ13C values, and some values are up to 4Ⱐhigher than the bulk rock values. A similar range can also be seen in δ18O values. Our results demonstrate that multi-component wackestone and grainstone samples from HICE and MLCIE intervals are isotopically heterogeneous and that heterogeneity needs to be accounted for in reconstructions of the past carbon cycle and δ13C curves