Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

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Mit 2 Abbildungen

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Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.     

The Mitsunobu Reaction: Origin,Mechanism, Improvements,and Applications

The Mitsunobu reaction is a widely used and versatile method for the dehydrative oxidation–reduction condensation of an acid/pronucleophile usually with a primary or secondary alcohol that requires the combination of a reducing phosphine reagent together with an oxidizing azo reagent. The utility of this reaction stems from the fact that it is generally highly stereoselective and occurs with inversion of the stereochemical configuration of the alcohol starting material. Furthermore, as carboxylic acids, phenols, imides, sulfonamides, and other compounds can be used as the acid/pronucleophile, this reaction is useful for the preparation of a wide variety of functional groups. This Focus Review of the Mitsunobu reaction summarizes its origins, the current understanding of its mechanism, and recent improvements and applications.     

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐Molybdate(II) Anions: Synthesis,Spectroscopy, and Density Functional Theory Calculations

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐molybdate‐(II) anions, [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo), which are novel weakly coordinating anions that contain a metal carbonyl/nitrosyl moiety, have been generated in fluorosulfonic acid and completely characterized by multinuclear NMR, IR, and Raman spectroscopy as well as ESI mass spectrometry. ESI MS measurements performed for the first time on a superacidic solution system unambiguously reveal the formation of the monoanionic, mononuclear W and Mo complexes formulated as [M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo). Multinuclear NMR spectroscopic studies at natural abundance and ¹³C and ¹⁵N enrichment clearly indicate the presence of one CO ligand, two equivalent NO ligands, and two types of nonequivalent SO₃F^? groups in a 2:1 ratio. The IR and Raman spectra reveal that the two equivalent NO ligands have a cis conformation, thus indicating a fac structure. Density functional calculations at the B3LYP level of theory predict that these anions have a singlet ground state (¹A′) with a C_s symmetry along with C–O and N–O vibrational frequencies that are in agreement with the experimental observations. Mulliken population analysis shows that the monovalent negative charge is dispersed on the bulky sphere, the surface of which is covered by all the negatively charged O and F atoms with charge densities much lower than SO₃F^?, suggesting that [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo) are weakly nucleophilic and poorly coordinating anions.     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

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Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

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Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables     

Über 1-Alkyl-bzw. 1-Aryl-dihydro-6-methyl-2(1H)-pyrimidinthione

The title compounds7 are formed in a general reaction by heating β-isothiocyanoketones3 with primary amines in inert solvents, or by thermal elimination of water from tetrahydro-6-hydroxy-6-methyl-2(1H)-pyrimidinethiones5, also in inert solvents. The 1-alkyl compounds can also be prepared under similar conditions from α,β-unsaturated ketones by reaction with alkylammonium rhodanides. The NMR-spectra show that the 1-substituted dihydro-6-methyl-2(1H)-pyrimidinethiones are in tautomeric equilibrium with the tetrahydro-6-methylene-2(1H)-pyrimidinethiones13. The reactivity of 1-alkyl and 1-aryldihydro-6-methyl-2(1H)-pyrimidinethiones is similar to that of dihydro-4,4,6-trimethyl-2(1H)-pyrimidinethione7 j, although their ring stability is certainly less.     

Beiträge zur Chemie des Sulfamids, 1. Mitt.: Zur Konstitution des Disilber-sulfamids

According to spectroscopic (IR, broadline proton NMR) and chemical (alkylation) investigations of disilver sulphamide the following molecular structure is assumed: $$\begin{gathered} O \hfill \\ || \hfill \\ H_2 N\_\_S\_\_NAg| \hfill \\ OAg \hfill \\ \end{gathered}$$ From the IR and NMR data deduction concerning the nature of the chemical bonds in this compound is possible. The instability of the still unknown mono-and trisilver sulphamide is discussed with regard to the structure of disilver sulphamide.     

Ab initio Computational Modeling of Glyphosate Analogs: Conformational Perspective

A historical perspective on the application of conformational analysis to structure-based ligand design approach is presented. The application of isodensity molecular electrostatic potential surfaces with the conformational energy surfaces (CES) have allowed us to reach pertinent conclusions for aiding synthetic and biochemical studies. Here we illustrate such an application on the modeling of the potent analogs of an important, environmentally stringent herbicidal compound glyphosate by constructing conformational energy surfaces. The systems were modeled by substituting F, Cl, and NH— OH moiety to the position of pharmacophoric nitrogen center in glyphosate structure. All the calculations were thoroughly performed with ab initio MO theory at Hartree–Fock method using 3-21G(d) basis functions. On the basis of the results, we identified the bioactive conformations for N-fluoro-glyphosate, N-chloro-glyphosate, and N-hydroxyamino-glyphosate as (−38^∘, 77^∘), (−61^∘, 111^∘), and (−167^∘, −169^∘), respectively. Geometry optimization of certain selected conformations of these compounds using hybrid DFT method with 6–31+G(d) basis functions provides nearly equal values of φ and ψ. Moreover, the results indicate that the global minimum structures of N-fluoro and N-chloro analogs of glyphosate show cyclic conformation whereas the N-hydroxyamino-glyphosate global minimum structure shows spyrocyclic and zig-zag conformation. Also, the predicted bioactive conformation of N-hydroxyamino analog optimally overlaps with glyphosate backbone in EPSPS complex with 0.1 Å RMSD value. However, the other two compounds slightly deviate from the backbone of glyphosate with RMSD of 0.92 Å for N-fluoro-glyphosate and 0.83 Å for N-chloro-glyphosate. The linear N-hydroxyamino-glyphosate exhibits relatively more number of intermolecular hydrogen bond interactions as compared to the other two analogs. Further, comparison of CES of previously studied glyphosate analogs such as N-hydroxy-glyphosate (2.2 μM) and N-amino-glyphosate (0.61 μM) with the present systems reveals the order of activity as: N-hydroxyamino-glyphosate > N-fluoro-glyphosate > N-chloro-glyphosate based on CES flexibility. Also, the calculated heats of formation of N-fluoro-glyphosate, N-chloro-glyphosate, and N-hydroxyamino-glyphosate are −288, −209, and −288 kcal/mol, respectively, which clearly indicate that the N-hydroxyamino and N-fluoro analogs of glyphosate are thermodynamically more stable than N-amino-glyphosate (−278 kcal/mol).     

Über die Konfiguration des Prolins im Ergotamin

It is well known that in the ergot alkaloids of the peptide type the proline appears in thel-configuration. Different methods of acid hydrolysis may lead to various cleavage products; hydrolysis by HCl yieldsd-proline, on the other hand hydrolytic cleavage by means of strongly acid cation exchange resin preserved the orginall-configuration.

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Teilveröffentlichung der Dissertation vonH. Kolassa, Univ. Wien, 1973.     

Thermische Polymerisation von Acenaphthylen

Zusammenfassung Acenaphthylen wurde durch Anpolymerisation und zweifache Hochvakuumsublimation gereinigt. Die Reinigungsmethode wird ausführlich beschrieben.Bei verschiedenen Temperaturen wurde mit einer dilatometrischen Methode die thermische Bruttogeschwindigkeit gemessen. Zwischen 95 und 105 °C giltk _br=7,0₈·10¹⁰ exp (– 30,9 kcal/RT).Die beträchtliche Aktivierungsenergie der Bruttoreaktion ist sowohl auf eine große Aktivierungsenergie der thermischen Startreaktion als auch auf eine relativ hohe Wachstumsaktivierungsenergie zurückzuführen.Das Polymerisationsverhalten von Acenaphthylen kann vermutlich aufgrund seiner sterischen Eigenschaften erklärt werden.

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Summary Acenaphthylene was purified by partial polymerisation, followed by double stage high vacuum sublimation. The method of purification is described in detail.The thermal overall rate was measured at different temperatures by a dilatometric method. Between 95 and 105 °C the following relation holds:k _th=7,0₈ · 10¹⁰ exp (– 30,9 kcal/RT).The considerable energy of activation of the overall reaction depends on a relatively high energy of activation of both the thermal initiation and the propagation reaction.It is supposed, that the polymerisation behaviour of acenaphthylene depends mainly on its steric properties.