Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Some time change representations of stable integrals, via predictable transformations of local martingales

From the predictable reduction of a marked point process to Poisson, we derive a similar reduction theorem for purely discontinuous martingales to processes with independent increments. Both results are then used to examine the existence of stochastic integrals with respect to stable Lévy processes, and to prove a variety of time change representations for such integrals. The Knight phenomenon, where possibly dependent but orthogonal processes become independent after individual time changes, emerges as a general principle.     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Determination of Samarium in rocks by epithermal neutron-activation analysis

Summary A non-destructive neutron-activation method for the determination of samarium in rocks, based on activation with epithermal neutrons, is described. By this means the formation of¹⁵³Sm, as compared to most interfering radionuclides, is considerably higher than by thermal neutron activation. The precision of the method is 2–3% in the range of 3–25 ppm, and the sensivity is about 0,1 ppm. Results are presented for some standard rocks. The influence of other rare earth nuclides on the measurement of the 41 KeV X-ray of¹⁵³Sm has been investigated.

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Zerstörungsfreie Bestimmung von Samarium in Gesteinen durch Aktivierungsanalyse mit epithermischen Neutronen

Zusammenfassung Die Bildung von¹⁵³Sm ist hierbei im Vergleich zu den meisten störenden Radionukliden beträchtlich größer als bei der Aktivierung mit thermischen Neutronen. Die Präzision des Verfahrens beträgt 2–3% im Bereich von 3–25 ppm, die Empfindlichkeit etwa 0,1 ppm. Für einige Standardgesteine werden die Ergebnisse angeführt. Der Einfluß anderer Nuklide Seltener Erden auf die Messung der 41 keV Röntgenstrahlung von¹⁵³Sm wurde untersucht.

     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday     

Determination of uranium in rocks by instrumental activation-analysis using epithermal neutrons

A rapid non-destructive neutron-activation method for the determination of uranium in rocks is described. The method is based on activation with epithermal neutrons and subsequent measurement of the 74 keV gamma-ray of (239)U. Results given for some standard rocks are in good agreement with literature data. The precision of the method is about 5 % and the limit of detection is of the order of 0.1 ppm in silicate rocks.     

Marine gradients of halogens in moss studies by epithermal neutron activation analysis

INAA is known to be a powerful technique for the simultaneous determination of chlorine, bromine and iodine. In this paper INAA using epithermal neutrons is shown to be particularly useful to elucidate marine gradients of these elements. Examples are from a transect study in northern Norway where samples of the feather moss Hylocomium splendens were collected at distances of 0-300 km from the coastline. All three elements decrease exponentially as a function of distance from the ocean in the moss samples, strongly indicating that the atmospheric supply from the marine environment is the predominant source of these elements to the terrestrial ecosystem. It is suggested that environmental studies of halogens in general and iodine in particular is a promising future area of application for INAA, when employing epithermal neutrons. This revised version was published online in July 2006 with corrections to the Cover Date.     

Feasibility of instrumental neutron activation analysis for trace element studies in natural soils

Fifty natural surface soils with strongly variable organic matter content and elemental composition were investigated to see to what extent INAA would prove useful for multi-element surveys. A conventional scheme of irradiations and decay intervals was used and 35 elements were investigated. Detection limits of the various trace elements were studied with respect to the influence of elements giving rise to major radionuclides in activated samples. For the 18 elements Na, Al, K, Sc, Cr, Mn, Fe, Co, Zn, Br, Sb, Cs, Ba, La, Sm, Hf, Th, the performance of INAA was very good. Useful results were also obtained for V, As, Se, Rb, Sr, I, Ta, and Au, while the technique appeared marginal for Cl, Zr, Mo, Ag, and Hg, and unsatisfactory for Mg, Ti, Ni, and Cd.     

From primary to dual affine variety codes over the Klein quartic

Designs, Codes and Cryptography - In Geil and Özbudak (Cryptogr Commun 11(2):237–257, 2019) a novel method was established to estimate the minimum distance of primary affine variety...