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.     

Determination of the activity of diamine oxidases, urease and histidine ammonia-lyase by enzymatic assay of ammonia

Summary The activities of diamine oxidases (DAO) from submaxillary glands, parotid glands and kidneys, from human serum during the pregnancy and from pig serum and of DAO from pea seedlings and the activities of urease and histidine ammonia-lyase have been determined by measuring NH₄ ⁺ released from the corresponding substrates. Ammonia has been determined with the aid of glutamate dehydrogenase reaction in the coupled optic test. The specifity and sensitivity of the method, by which still 3×10^–9 Mol of NH₄ ⁺ could be measured, is excellent, the performance simple and rapid. The sensitivity could be enhanced by fluorometric determination of NAD⁺ in strong alkali solution. A method for the preparation of tissues for the spectrophotometric test of DAO is described. The importance of DAO determination in different diseases is briefly discussed.

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Zusammenfassung Die Aktivität von Diaminoxydasen aus Speicheldrüsen und Nieren, aus menschlichem Serum während der Schwangerschaft und Schweineserum und aus Erbsenkeimlingen sowie die Aktivität der Urease und Histidase wurden anhand der NH₃-Abspaltung aus ihren entsprechenden Substraten bestimmt. Das entstehende Ammoniak wurde dabei mit Hilfe der Glutamatdehydrogenasereaktion im gekoppelten optischen Test gemessen. Spezifität und Empfindlichkeit der Methode, mit der noch 3 · 10^–9 Mol NH₄ ⁺ bestimmt werden können, sind ausgezeichnet, die Durchführung einfach und rasch. Die Empfindlichkeit konnte außerdem noch durch die fluorimetrische Bestimmung von NAD⁺ gesteigert werden. Für die Bestimmung der Diaminoxydasen im Gewebe wird eine Methode der Aufarbeitung des Gewebes angegeben, die praktisch keinen Verlust an Gesamtaktivität gegenüber dem Ausgangshomogenat aufweist. Die Bedeutung der Diaminoxydasebestimmung für die Klinik wird kurz diskutiert.

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Supported by a grant from Deutsche Forschungsgemeinschaft.     

Synthese,EPR und Röntgenkristallstrukturanalyse von mer-Trichloro(2,2′-bipyridin)nitridotechnetium(VI), einem neuen Nitridokomplex des Technetium(VI)

Synthesis, EPR and X-Ray Structure of mer-Trichloro(2,2′-bipyridine)nitridotechnetium(VI) — a new Technetium(VI) Nitrido Complex mer-Trichloro(2,2′-bipyridine)nitridotechnetium(VI) has been prepared by the reaction of (NBu₄)[TcNCl₄] with 2,2′-bipyridine in acetonitrile, whereas the same procedure gives in methanol the technetium(V) cation [TcNCl(bipy)₂]⁺. The EPR spectrum of [TcNCl₃(bipy)] suggests a meridional coordination of the three chloro ligands. [TcNCl₃(bipy)] crystallizes monoclinic in the space group P2₁/n; a = 8.572(1), b = 15.462(1), c = 10.110(1) Å, β = 104.21(1)°, Z = 4. The R value converged at 0.034 on the basis of 3 040 reflections. The technetium atom is distorted octahedrally coordinated with the chloro ligands meridionally cis with respect to the nitrido nitrogen. The Tc? N(1) bond length is 1.669(4) Å, and the Tc? N(3) bond (2.371(4) Å) is significantly lengthened due to the structural trans labilizing influence of the “N^3?” ligand.     

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.     

Thermoanalytische Untersuchungen psychotroper Substanzen vom Typ der Abwandlungsprodukte des Phenothiaztns und der Butyrophenone auf Isomorphie und Polymorphie. II

Zusammenfassung Aus der Gruppe der Dibenzoazepinderivate wurden die Hydrochloride von Clomipramin, Imipramin und Desipramin miteinander kombiniert und aus der Gruppe der Dibenzocykloheptadiene bzw.-triene die Hydrochloride von Amitriptylin, Nortriptylin, Noxiptilin und Protriptylin.Bei fünf der untersuchten binären Systeme liegt Mischkristallbildung aufgrund von Isomorphiebeziehungen mit instabilen Modifikationen vor: Imipraminhydrochlorid — Clomipraminhydrochlorid, Imipraminhydrochlorid — Desipraminhydrochlorid, Clomipraminhydrochlorid — Desipraminhydrochlorid, Nortriptylinhydrochlorid — Protriptylinhydrochlorid und Noxiptilinhydrochlorid-Amitriptylinhydrochlorid. Das Substanzpaar Protriptylinhydrochlorid — Noxiptilinhydrochlorid bildet eine Molekülverbindung im Verhältnis 11. In drei Fällen werden einfache Eutektika gebildet.

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Thermoanalytical investigations of psychotropic substances derived from phenothiazine and butyrophenones for isomorphism and polymorphism. II

Summary From the group of dibenzoazepine derivatives, the hydrochlorides of clomipramine, imipramine and desipramine were combined with each other and from the group of dibenzocycloheptadienes or -trienes the hydrochlorides of amitriptyline, nortriptyline, noxiptiline and protryptiline. In five of the binary systems investigated, there is formation of mixed crystals due to isomorphism with unstable modifications: imipramine hydrochloride — clomipramine hydrochloride, imipramine hydrochloride — desipramine hydrochloride, clomipramine hydrochloride 3- desipramine hydrochloride, nortriptyline hydrochloride — protriptyline hydrochloride and noxiptiline hydrochloride — amitriptyline hydrochloride. The substance pair protriptyline hydrochloride — noxiptiline hydrochloride forms a molecular compound in the ratio 11. In three cases, simple eutectics are formed.

     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

1-Ethyl-1,4-dihydro-4-oxo-7-(pyridinyl)-3-quinolinecarboxylic acids. I. Synthesis of 3- and 4-(3-aminophenyl)pyridine intermediates

A series of substituted 3- and 4-(3-aminophenyl)pyridines has been prepared as intermediates for the synthesis of some 1-alkyl-1,4-dihydro-4-oxo-7-pyridinyl-3-quinolinecarboxylic acids. The Hantzsch, Hauser and other pyridine syntheses were used. 4-(3-Aminophenyl)pyridine was prepared via 3-(4-pyridinyl)-2-cyclohexen-1-one using the Semmler-Wolff reaction.