Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Investigations of precipitates in heat treated AgPd30/CuSn6 layers

The subject of the investigations are precipitation zones, which grew as a result of chemical diffusion in AgPd30/CuSn6 bimetals. These precipitation zones have been characterized by metallography, electron probe microanalysis and x-ray diffraction. The growth of precipitation zones in the plating layer and in the substrate layer in dependence on time have been determined. The use of x-ray diffraction alone for the identification of the precipitates could not supply satisfying results in every case. This problem was solved by the application of electron probe microanalysis using a correction method, which allows the estimation of the chemical composition of small particles.Dedicated to Professor Dr. rer. nat. Dr. h. c. Hubertus Nickel on the occasion of his 65th birthday     

Thermische Analyse eines chloridhaltigen basischen Cobaltcarbonates

The thermal decomposition of a chloride and water-containing basic cobalt carbonate was studied. As a first step, crystal water is lost without change of structure. The following decomposition steps overlap and proceed in different ways, depending on the atmosphere over the sample: under nitrogen, chloride volatilizes as HCl and CoCl₂; in air, oxidation occurs. CoO and Co₃O₄, respectively, are the final solid products at 700–800°.     

Charge transfer in the Cl-CO cluster induced by core ionization

Ab initio calculations of core-ionization spectra of the anion-molecule Cl-CO cluster are performed. Particular attention is paid to the investigation of charge-transfer screening processes accompanying core ionization of the CO molecule in the cluster. The charge-transfer processes are very efficient and favored by the presence of a low-lying unoccupied pi* orbital in CO capable of accepting an electron from Cl-. The O1s(-1) and C1s(-1) core-ionization spectra are calculated and compared. Both reveal a breakdown of the quasiparticle picture of core ionization caused by the charge-transfer processes. Remarkable differences between these two spectra are found which manifest themselves in distinct intensity distributions in the prominent low-energy spectral bands. The underlying reason for these differences is elucidated and linked with the preference of the pi* orbital to localize mainly on carbon. Core-ionization spectra of anion-molecule clusters are very sensitive to the type of the molecule involved as the comparative analysis of the O1s(-1) core-ionization spectra of the Cl-CO and Cl-H(2)O clusters show.     

Asymptotic expansions for the truncation error in Ramanujan-type series

The Ramanujan Journal - Many of the fastest known algorithms to compute $$\pi $$ involve generalized hypergeometric series, such as the Ramanujan–Sato series. In this paper, we investigate...     

Reaktivität von Monophosphan-Platin(0)-Verbindungen gegenüber Schwefeldioxid

Reactivity of Monophosphine Platinum(0) Complexes with SO₂ . The addition reaction of (PPh₃)Pt(ViSi) (ViSi = {η²-H₂C?CHSiMe₂}₂O) ( 1 ) with SO₂ gives within 30 min the red SO₂ complex (PPh₃)Pt(η²-H₂C?CHSiMe₂- OSiMe₂CH?CH₂)(SO₂) ( 2 ). A reaction time of 24 h with SO₂ leads to the elimination of the ViSi ligand, and the unstable monomeric intermediate (PPh₃)Pt(SO₂) cyclo- trimerizes to the stable cluster [Pt(PPh₃)(SO₂)]₃ ( 3 ). 3 is also obtained within 30 min by the reaction of (PPh₃)Pt(C₂H₄)₂ ( 4 ) with SO₂. The crystal structure of 3 has been determined; space group P2₁/n, Z = 4, a = 1 606.1(3), b = 1 019.3(1), c = 3 624.6(5) pm, β = 93.67°, R/R_w = 0.102/0.121.     

f-Element disiloxanediolates: novel Si-O-based inorganic heterocycles

The preparation and structural characterization of scandium and f-element complexes derived from the disiloxanediolate dianion, [(Ph2SiO)2O]2-, are reported. Reactions of in situ prepared Ln[N(SiMe3)2]3 (Ln = Eu, Sm, Gd) with (Ph2SiOH)2O in different stoichiometries afforded the lanthanide disiloxanediolates [Eu[[(Ph2SiO)2O]Li(Et2O)]3] (1), [[[(Ph2SiO)2O]Li(dme)]2SmCl(dme)] (2), and [[[((Ph2SiO)2O]Li(thf)2]2GdN(SiMe3)2] (3). In situ formed (Ph2SiOLi)2O reacted with anhydrous NdBr3 (molar ratio 3:1) to give polymeric [[Nd[(Ph2SiO)2O]3[mu-Li(thf)]2[mu2LiBrLi(thf)(Et2O)]]n] (4). Treatment of 3 with Ph2Si(OH)2 in the presence of acetonitrile yielded the dilithium trisiloxanediolate derivative [[Ph2Si(OSiPh2O)2][Li(MeCN)]2]2 (5), which according to an X-ray analysis displays an Li4O4 heterocubane structure. The trinuclear scandium complex [[[(Ph2SiO)2O]Sc(acac)2]2Sc(acac)] (6) was obtained by reaction of [(C5Me5)Sc(acac)2] (C5Me5 = eta5-pentamethylcyclopentadienyl) with (Ph2SiOH)2O in a 3:2 molar ratio. Selective formation of the colorless uranium(VI) derivative [U[Ph2Si(OSiPh20)2]2[(Ph2SiO)2O]] (7) was observed when uranocene, U(eta8-C8H8)2, was allowed to react with (Ph2SiOH)2O. An X-ray diffraction study of the solvated derivative [U[Ph2Si(OSiPh2O)2]2[(Ph2SiO)2O]].Et2O.TMEDA (TMEDA= N,N,N',N'-tetramethyl-ethylenediamine) (7a) revealed the presence of both the original [(Ph2SiO)2O]2- dianion as well as the ring-enlarged [Ph2Si(OSiPh2O)2]2- ligand in the same molecule.     

Coordination Chemistry of Acrylamide: 1. Cobalt(II) Chloride Complexes with Acrylamide – Synthesis and Crystal Structures

The molecular structures of blue dichloro‐tetrakis(acrylamide) cobalt(II), [Co{O‐OC(NH₂)CH=CH₂}₄Cl₂] ( 1 ) and pink hexakis(acrylamide)cobalt(II) tetrachlorocobaltate(II), [Co{O‐OC‐(NH₂)CH=CH₂}₆][CoCl₄] ( 2 ), characterized by single X‐ray diffraction, IR spectroscopy and elemental analyses, are described. The coordination of Co^II in 1 involves a tetragonally distorted octahedral structure with four O‐donor atoms of acrylamide in the equatorial positions and two chloride ions in the apical positions. The second complex 2 in ionic form contains Co^II cations surrounded by an octahedral array of O‐coordinated acrylamide ligands, accompanied by a [CoCl₄]^2? anion.     

Small-angle static light scattering of concentrated silica suspensions during in situ destabilization

The aggregation of concentrated aqueous silica suspensions is characterized by means of static light scattering. We use an in situ destabilization mechanism based on the enzyme-catalyzed hydrolysis of urea. This method enables us to continuously and homogeneously change the interparticle potential from repulsive to attractive without disturbing the aggregation process. Moreover, our electrostatically stabilized suspensions can be destabilized by two different methods. In the first method, the pH is shifted toward the isoelectric point of the particles ( Delta pH method), thereby leading to a decrease of their surface charge. In the second method, the ionic strength is continuously increased at constant pH ( Delta I method), leading to a compression of the electrical double layer around the charged particles. A laboratory-built flat-cell light-scattering instrument is used, which allows fast data acquisition and an adjustment of the sample cell thickness. To circumvent multiple scattering effects, we use a very small sample thickness ( approximately 13 microm). In addition, the refractive index difference between the aqueous phase and the particles is reduced by adding sucrose to the liquid phase of our suspensions. We are able to characterize the structural changes at the very early stages of the destabilization process, where no significant effects are yet detected in macroscopic rheological measurements. While during the Delta pH destabilization, the scattering curve shows significant changes only after some characteristic delay time, it changes continuously during the Delta I destabilization. The latter is attributed to the formation of a weak pre-gel structure in the suspensions, as a shallow secondary minimum appears in the interparticle potential. Data are evaluated by using a HMSA square-well structure factor model. Results are in good agreement with those predicted from DLVO theory.