Graphs corresponding to reference polynomial or to circuit characteristic polynomial

A vertex-weighted graphG ^* is studied which is obtained by deleting edgee _rs in a circuit of a graphG and giving two vertices _r and _s weightsh _r = 1 andh _s = -1, respectively. It is shown that if subgraphG - _r is identical with subgraphG - _s, then the reference polynomial ofG ^* is identical with that ofG and the characteristic polynomial ofG ^* contains the contributions due to only a certain part of the circuits found in the original graphG. This result gives a simple way to find a graph whose characteristic polynomial is equal to the reference polynomial in the topological resonance energy theory or to the circuit characteristic polynomial in the circuit resonance energy theory. This approach can be applied not only to Hilckel graphs but also to Möbius graphs, provided that they satisfy a certain condition. The significances of this new type of reference graph thus obtained are pointed out.     

On theC v toC p conversion for solid linear macromolecules

TheC _v toC _p conversion for solid linear macromolecules via the Nernst-Lindemann equationC _p -C _v =A ₀,C _p ² T/T_m is discussed on hand of data for 10 crystals and seven glasses. An average value ofA ₀=(5.11±2.41) · 10^–3 mol K J^–1 was calculated if the mole is assumed to refer to heavy atoms only. ThisA ₀ is numerically equal to the original Nernst—Lindemann constant.

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Zusammenfassung An Hand von sich auf 10 Kristalle und 7 Gläser beziehenden Daten wird die Umrechnung vonC _v -inC _p -Werte für feste lineare Makromoleküle mittels der Nernst-Lindemann-GleichungC _p -C _v =A ₀ C _p ² T/T _m diskutiert. Ein Durchschnittswert vonA ₀=(5.11±2.41) · 10^–3 mol K J^–1 wurde unter der Annahme berechnet, daß sich das Mol nur auf schwere Atome bezieht. DieserA ₀-Wert ist numerisch gleich der ursprünglichen Nerns-Lindemann-Konstanten.

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10 , - C _v C _p , —C _p –C _v = _{0 p} ² / . , , ₀ (5.11±2.41) · 10^–3 · ^–1. ₀ — .

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Support by the National Science Foundation, Polymers Program (Grant No. DMR 83-17097) is gratefully acknowledged.     

Zum Verhalten von Ketenen gegenüber P−N-Yliden Reaktionen mit phosphororganischen verbindungen, 39. Mitt.

1,3-Skeletal rearrangement of N-substituted ketimines via a possible intimate ion pair is discussed. (CH₃)₃SiCH=C=O (1) reacts with N-(aziridinyl)-triphenylphosphinimine (2) to give N-(1-aziridinyl)-2-trimethylsilylketen-1-imines (3). The compounds3 b, c are thermally labile and do not undergo 1,3-rearrangement but a retro-ene type reaction to yield (CH₃)₃SiCH₂CN and 2,3-diphenyl-2H-azirine (4). Diphenylketene (5) reacts with N-(N, N-dialkylamino)-triphenylphosphinimines (6) to yield -(N-disubstituted-amino)-nitriles (7). , -Dimethyl--(triphenylphosphinimino)-acetonitrile (9) reacts with (5) at room temperature to form , -dimethyl--(2, 2-diphenylketen-1-imino)-acetonitrile (10) which rearranges at 80° to dimethyl diphenylsuccinonitrile (11). The reaction of5 with 7-(triphenylphosphinimino)-7-azabicyclo[4.1.0]heptane (12) gives tetraphenylsuccinonitrile13 and 7-(7-azabicyclo[4.1.0]heptane)-, -diphenylacetonitrile (14). Finally the synthesis of N-acylketenimines (16) from (5) and acyltriphenylphosphinimines (15) is reported.

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38. Mitt.:Chr. Ivancsics undE. Zbiral, Mh. Chem.106, 839 (1975).     

Thermochemical studies on the systems ACl/CeCl3 (A=Na-Cs)

The pseudobinary systems ACl/CeCl₃ (A=Na-Cs) were reinvestigated by means of DTA. The following compounds were found and identified through their X-ray patterns (primarily detected compounds in italics):NaCe _1.67 Cl ₆; K₃CeCl₆, K₂CeCl₅,KCe _1.67 Cl ₆;Rb ₃ CeCl ₆, Rb₂CeCl₅,RbCe ₂ Cl ₇; Cs₃CeCl₆, Cs₂CeCl₅,CsCe ₂ Cl ₇. The compounds A₂CeCl₅ crystallize with the K₂PrCl₅ structure. The high-temperature modifications of the compounds A₃CeCl₆ have the cubic elpasolite structure. The hexagonal unit cell of KCe_1.67Cl₆ is related to the CeCl₃ structure: 0.33 Ce³⁺ are substituted by one K^s+. The structure of CsCe₂Cl₇ can be described with a hexagonal subcellZ=4,a=9.72 andc=14.94 Å; however, small superstructure reflexions reduce the symmetry.The thermodynamic functions for the reactionsnACl+CeCl₃=A _n CeCl _n+3(A=K, Rb) were determined by means of e.m.f. measurements.Measurements of the e.m.f.E vs. T yielded the Gibbs enthalpiesG ^r . The temperature-dependence was found to be linear.The most important result is the formation of the elpasolites (A₃CeCl₆) and ACe₂Cl₇.

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Zusammenfassung Die pseudobinären Systeme ACl/CeCl₃ (A=Na-Cs) wurden mittels Differenzthermoanalyse (DTA) neu untersucht. Folgende Verbindungen wurden gefunden und durch ihre Röntgenbeugungsmuster charakterisiert (erstmalig nachgewiesene Verbindungen sind kursiv):NaCe _1.67 Cl ₆; K₃CeCl₆, K₂CeCl₅,KCe _1.67 Cl ₆;Rb ₃ CeCl ₆, Rb₂CeCl₅,RbCe ₂ Cl ₇; Cs₃CeCl₆, Cs₂CeCl₅,CsCe ₂ Cl ₇. Die Verbindungen A₂CeCl₅ kristallisieren im K₂PrCl₅-Typ. Die Hochtemperaturmodifikationen der Verbindungen A₃CeCl₆ liegen in der kubischen Elpasolith-Struktur vor. Die hexagonale Elementarzelle des KCe_1.67Cl₆ ist mit der CeCl₃-Struktur verwandt: 0,33 Ce³⁺ sind durch ein K⁺ ersetzt. Die Struktur des CsCe₂Cl₇ kann mit einer hexagonalen Pseudozelle beschrieben werden:a=9,72;c=14,94Å;Z=4; schwache Überstrukturreflexe reduzieren jedoch die Symmetrie. Die thermodynamischen Funktionen für die Reaktionen:n ACl + CeCl₃=A _n CeCl _n+3 (A=K, Rb) wurden durch EMK-Messungen bestimmt. Messungen der Abhängigkeit von e. m. f.E gegenT ergaben die Gibbs-EnthalpienG ^r . Es wurde eine lineare Temperaturabhängigkeit gefunden. Als wichtigstes Resultat ist die Bildung von Elpasoliten (A₃CeCl₆) und von Verbindungen (ACe₂Cl₇) anzusehen.

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ACl/CeCl₃, A . - ( ):NaCe _1.67 Cl ₆; K₃CeCl₆, K₂CeCl₅,KCe _1.67 Cl ₆;Rb ₃ CeCl ₆, Rb₂CeCl₅,RbCe ₂ Cl ₇; Cs₃CeCl₆, Cs₂CeCl₅ CsCe ₂Cl₇. A₂CeCl₅ K₂PrCl₅. A₃CeCl₆ . KCe_1.67Cl₆ CeCl₃, 0,33 Ce³⁺ . CsCe₂Cl₇ a=9,72 Å,c=14,94 Å Z=4. , . n ACl + CeCl₃=A _n CeCl _n+3(A=K, Rb) . . . . . .E , G ^r . ACe₂Cl₇.

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Presented as a poster at the 8th ICTA, Bratislava, 1985.

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This work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.     

Augmentation of the Generalised n×n Eigenvalue Equation to a Generalised (n+1)×(n+1) Eigenvalue Equation

Generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) where B and S ^b are n×n Hermitian matrices while S ^b is in addition positive definite is considered. This equation is augmented to a generalised (n+1)(n+1) eigenvalue equation H| _k = _k S| _k (k=1,...,n+1) where Hermitian matrices H and S represent matrices B and S ^b , respectively, augmented by one additional row and one additional column. It is shown how the eigenvalues _k and the eigenvectors | _k of the augmented eigenvalue equation can be expressed in terms of the eigenvalues _i and the eigenvectors | _i of the original eigenvalue equation. Operation count to obtain by this method all augmented eigenvalues and eigenvectors is of the order O(n ²). Unless matrices involved are of some special kind such as sparse matrices or alike, this operation count is one order of magnitude smaller than operation count required by other presently known methods. In many practical cases operation count to obtain a single selected eigenvalue and/or eigenvector by this method is of the order O(n). In the case of the generalised eigenvalue equation, all other methods usually require again O(n ³) operations, even if only a single eigenvalue and/or eigenvector is required. Thus in many cases of interest operation count to obtain a selected eigenvalue and/or eigenvector by this method is two orders of magnitude smaller than operation count required by other methods.     

Synthesen von Heterocyclen, 148. Mitt.: Zur Chemie der Biisochininone

Zusammenfassung Brombernsteinsäure reagiert mit Benzalanilin inDMF/POCl₃ zum 2,2-Diphenyl-4,4-biisochinolin-3,3 (2H, 2H)-dion (1a). Brombernsteinsäuredichlorid gibt mit dem Anil vorerst ein Addukt, welches beim Erhitzen in Nitrobenzol unter Abgabe von H₂O, HBr und H₂ ebenfalls in1 a übergeht. Analog können die Derivate1b-1k hergestellt werden, die in Lösung intensiv fluoreszieren.

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Syntheses of heterocycles, CXLVIII: concerning the chemistry of bi-isoquinolones

Bromosuccinic acid reacts with benzylidene aniline inDMF/POCl₃ yielding 2.2-diphenyl-4.4-biisoquinoline-3.3 (2H, 2H)-dione (1a). Bromosuccinyldichloride and benzylidene aniline give firstly an adduct, which loses H₂O, HBr and H₂ to yield1 a, if heated in nitrobenzene. The derivatives1b-1k are obtained in a similar way and show in solution an intensive fluorescence.

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J. R. Geigy AG, Basel, zum Patent angemeldet, CH 3-3253 am 3. Februar 1970.     

On the Permanental Polynomials of Some Graphs

Let G be a simple graph with adjacency matrix A(G) and (G,x) the permanental polynomial of G. Let G × H denotes the Cartesian product of graphs G and H. Inspired by Kleins idea to compute the permanent of some matrices (Mol. Phy. 31 (3) (1976) 811–823), in this paper in terms of some orientation of graphs we study the permanental polynomial of a type of graphs. Here are some of our main results.1.If G is a bipartite graph containing no subgraph which is an even subdivision of K _2,3, then G has an orientation G ^e such that (G,x) = det (xI-A(G ^e )), where A(G ^e ) denotes the skew adjacency matrix of G ^e.2.Let G be a 2-connected outerplanar bipartite graph with n vertices. Then there exists a 2-connected outerplanar bipartite graph with 2n+2 vertices such that (G,x) is a factor of .3.Let T be an arbitrary tree with n vertices. Then , where ₁ , ₂ , ..., _n are the eigenvalues of T.     

Unicyclic Graphs with Minimal Energy

If G is a graph and ₁,₂,..., _n are its eigenvalues, then the energy of G is defined as E(G)=|₁|+|₂|++| _n |. Let S _n ³ be the graph obtained from the star graph with n vertices by adding an edge. In this paper we prove that S _n ³ is the unique minimal energy graph among all unicyclic graphs with n vertices (n6).     

Abhängigkeit der freien Enthalpie-Änderung von der Netzebenenzahl bei Bildung von Mikroparakristallen

Zusammenfassung Das anhand vieler sorgfältiger Reflexprofilanalysen abgeleitete ^*-Gesetz läßt sich auch thermodynamisch verstehen, wenn man die Fragilität der Valenzwinkel durch ein entsprechendes MuldenpotentialU einführt. Dies liefert in dem Ausdruck für die ÄnderungG der freien Enthalpie bei Teilchenbildung neben den bekannten, von der Teilchengröße unabhängigen zwei Termen für freie Oberflächenenergie und freie VolümenthalpieG _v einen dritten, mit der ZahlN der Netzebenen wachsenden Summanden. Diese sog. Volum-StörenthalpieA ₀g² N ist also auch abhängig von der relativen statistischen Varianzg der Abständed von Gitterbausteinen benachbarter Netzebenen. Durch Einführung des ^*-Gesetzes ergibt sich die Beziehung ¦G_v¦ /A ₀ K()=0.06 mitK()=356 g² /¯ d¦G_v¦=1–1–. Im Grenzfall=1 ist die kritische Keimgröße gleich der mittleren statistischen Größe der Mikroparakristalle. Dieser Fall wird für Metallschmelzen diskutiert.=0 stellt den anderen Grenzfall der Kristallbildung dar.Herrn Prof. Dr. K. Kobayashi zum 70. Geburtstag zugedacht.     

Differential thermal analysis studies on the crystallization of strontium tungstate from sodium tungstate melt. Nucleation mechanism and induction periods

The nucleation mechanism, kinetics and induction periods in strontium tungstate crystallization from sodium tungstate melt in platinum crucibles were investigated by differential thermal analysis. Heterogeneous nuclei first formed on the metal platinate particles within the solution during the induction periods (¯t); the main crystal growth started only after ¯t and few new nuclei were then formed. At any crystallization temperature, ¯t varied inversely with the cooling rate (R _T), and with the rate (R_C) of development of excess solute concentration according to the relation ¯t = 1/(k ₁ R _c ), wherek ₁ and are constants. The critical temperature (¯T), critical supersaturation(¯ S), k ₁ and were evaluated.

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Zusammenfassung Der Keimbildungsmechanismus, sowie die Kinetik und die Induktionsperioden wurden bei der Kristallisation von Strontiumwolframat aus Natriumwolframatschmelzen in Platintiegeln durch Differentialthermoanalyse untersucht. Die heterogenen Kristallkeime wurden zuerst während der Induktionsperiode () an den Metallplatinat-Teilchen in der Lösung gebildet: das Hauptkristallwachstum begann erst nach und nachfolgend wurden einige neue Keime gebildet. Bei jeder Kristallisationstemperatur änderte sich umgekehrt proportional zu den Abkühlungsgeschwindigkeiten (R _T) und den Geschwindigkeiten (R _c) der Bildung überschüssig gelösten Materials, entsprechend der Gleichung = 1/(k ₁ R _c , wobeik ₁ und Konstanten sind. Die kritische Temperatur (¯T), die kritische Übersättigung (¯S),k ₁ und wurden bewertet.

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Résumé On a étudié par analyse thermique différentielle le mécanisme de nucléation ainsi que la cinétique et les périodes d'induction de la cristallisation du tungstate de strontium, à partir des bains fondus de tungstate de sodium, dans des creusets de platine. Des noyaux hétérogènes se forment d'abord sur les particules de platinate métallique dans la solution, au cours des périodes d'induction (): la croissance principale des cristaux ne commence qu'après et il se forme alors quelques noyaux nouveaux. A une température quelconque de cristallisation, varie de façon inverse avec les vitesses de refroidissement (R _T) et les vitesses de développement (R _c ) de concentrations de sursaturation de la substance en solution, selon la relation = 1/(k ₁ R _c , oùk ₁ et sont des constantes. On a évalué la température critique (¯T), la sursaturation critiques (¯S),k ₁ et.

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, . - (¯ t). ¯t . - ,¯t (R _T), (R _c) ¯t=1/(K₁ R _c ), ₁ — . (¯), (_-S), K₁ .

     

Thermodynamic parameters characterizing adsorption of organic compounds from aqueous solutions on iron oxide α-Fe2O3

Adsorption of a series of organic compounds on the surface of -Fe₂O₃ is studied. The experimental data are analyzed using the Frumkin and Langmuir isotherms. The standard Gibbs energies of adsorption G _A ⁰ and G _ads ⁰ corresponding to different standard states are estimated.Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 9, 2004, pp. 1446–1451.Original Russian Text Copyright © 2004 by Afanasev, Aleksandrova, Akulova.     

The supramolecular structures and reactivities of some complexes of chiral crown ethers with borane ammonia

Whereas 1 1 crystalline complexes have been isolated between borane ammonia and methyl 4,6-O-benzylidene-2,3-dideoxy--d-galactopyranosido [2,3-b]-1,4,7,10,13,16-hexaoxacyclo-octadecane (1), methyl 4,6-O-benzylidene-2,3-dideoxy--d-mannopyranosido [2,3-b] (methyl 4,6-O-benzylidene-2,3-dideoxy--d-mannopyranosido [2,3-k]-1,4,7,10,13,16-hexaoxacyclo-octadecane (3), and (1R,2R,7R,24R)-3,5,8,11,14,17,20,23,26,28-decaoxatricyclo-[21.4.0.0^2,7]octacosane (4), the hosts, methyl, 4,6-O-benzylidene-2,3-dideoxy--d-mannopyranosido[2,3-b] 1,4,7,10,13,16-hexaoxacyclo-octadecane (2) and 1,4 1,4 3,6 3,6-tetra-anhydro-2,2 5,5-bis-O-oxydiethylenedi-d-mannitol (5) have yielded 2 1 (guest:host) crystalline complexes with borane ammonia as guest. X-ray analyses of the supramolecular structures of BH₃NH₃ ·1, (BH₃NH₃)₂ ·2, BH₃NH₃ ·3, BH₃NH₃ ·4, and (BH₃NH₃)₂ ·5 have been carried out and BH₃NH₃ ·1, BH₃NH₃ ·2, and (BH₃NH₃)₂ ·5 have been shown to reduce acetophenone with enantiomeric excesses of 5, 13, and 10% respectively. Supplementary Data relating to this article (atomic coordinates of the hydrogen atoms and thermal parameters) are deposited with the British Library as Supplementary Publication No. SUP 82017 (74 pages).Dedicated to Professor H. M. Powell.     

Characteristic Features of the Formation of Copper(I) π-Complexes with N-Allyl Derivatives of Piperazinium Sulfamate

The crystals of two copper(I) complexes and piperazinium sulfamate were synthesized by ac electrochemical technique from Cu(NH₂SO₃)₂· xH₂O and N,N-diallylpiperazine, N-allylpiperazine, or piperazine titrated by sulfamic acid in aqueous methanol to pH 4. The crystal structures of the complexes were determined (DARCh diffractometer, MoK radiation, /2 scan mode). The crystal data: [C₃H₅NH(CH₂)₄NHC₃H₅]_0.5[Cu(NH₂SO₃)₂] · H₂O (I), space group P1¯, a = 8.053(1) Å, b = 10.247(2) Å, c = 8.918(2) Å, = 113.03(1)°, = 107.14(2)°, = 95.15(1)°, Z = 2; [NH₂(CH₂)₄NH₂]_0.5NH₂SO₃ (II), space group P2₁/a, a = 8.468(7) Å, b = 5.92(1) Å, c = 10.890(9) Å, = 100.40(9)°, Z = 4; {[C₃H₅NH(CH₂)₄NHC₃H₅][NH₂(CH₂)₄NH₂]}_0.5[Cu(NH₂SO₃)₃] · H₂O (III), space group P1¯, a = 11.729(3) Å, b = 8.266(2) Å, c = 10.611(3) Å, = 82.13(2)°, = 65.73(2)°, = 74.86(2)°, Z = 2. Structure III is a hybrid of elements of structures I and II and contains the -coordinated Cu(I) atom surrounded by three -donor sulfamate nitrogen atoms, which was found for the first time.     

Etude des residus d'evaporation de solutions d'hydrogenocarbonates de calcium et de magnesium

Résumé Des résidus d'évaporation de solutions pures ou mixtes de Ca(HCO₃)₂ et Mg(HCO₃)₂ ont été étudiés par ATD (atmosphère N₂ ou CO₂), ATG, AGE, rayons X et analyse classique. La valeur du rapport atomique Ca/Mg a une influence considérable sur la manifestation des accidents thermiques compris entre 400 et 500°. Pour 1.2 3 est sous forme d'aragonite. Pour Ca/Mg > 1.25, la calcite se substitue progressivement à l'aragonite, mais pas totalement. L'étude se poursuit afin de dégager d'autres conclusions.

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Residues from the evaporation of pure or mixed solutions of Ca(HCO₃)₂ and Mg(HCO₃)₂ were subjected to investigation by DTA (N₂ or CO₂ atmosphere), TG, EGA, X-ray and classical chemical analysis. The Ca/Mg atomic ratio exerted a great effect on EGA and DTA peaks between 400 and 500°. Peak temperatures were the lowest when 1.2 < Ca/Mg < 1.33. When Ca/Mg < 1.25, CaCO₃ exists only as aragonite. When Ca/Mg > 1.25, calcite progressively replaces aragonite, but never entirely. Investigations are continuing.

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Zusammenfassung Die Verdampfungsrückstände reiner Lösungen bzw. Gemische von Ca(HCO₃)₂ und Mg(HCO₃)₂ wurden mittels DTA (in N₂- oder CO₂-Atmosphäre), TGA, EGA, Röntgenstrahlung und klassischer Analyse untersucht. Der Wert des Atomverhältnisses Ca/Mg hat einen bedeutenden Einfluß auf die thermischen Vorgänge zwischen 400° und 500°. Bei 1.2 < Ca/Mg < 1.33 werden die Spitzen in Richtung der niederen Temperaturen verschoben. Bei Ca/Mg < 1.25 befindet sich das CaCO₃ in der Aragonitform. Bei Ca/Mg > 1.25 wird Aragonit fortschreitend, jedoch nicht vollständig durch Calcit ersetzt. Die Versuche werden fortgesetzt, um weitere Aussagen zu ermöglichen.

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, C(₃)₂ Mg (₃)₂, ( N_{2 2}) , , () . Ca/Mg 400–500°. 1.2 < Ca/Mg < 1.33. Ca/Mg < 1,25, ₃ . Ca/Mg > 1.25, , . .

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Nos remerciements vont à Monsieur le Professeur A. Beugnies, pour nous avoir accordé Ja permission d'utiliser son installation de rayons X avec le concours de son personnel spécialisé.     

Studies of supported catalysts for ethylene polymerization, prepared using organovanadium compounds

Catalysts containing trimethylsilyl complexes of V(IV) and (III) supported on SiO₂ and Al₂O₃, have been synthesized and examined for ethylene polymerization. The state of vanadium in solution and on the support and catalysts interaction with C₂H₄, CO, H₂ and pyridine have been studied using ESR and IR spectroscopy.

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, (IV) (III), SiO₂ Al₂O₃. , C₂H₄, CO, H₂ .

     

Quantitative DTA of epoxy adhesives of technological interest

The glass transition temperatures,T _g, and thermal effects of polymerization,H, have been determined for five epoxy adhesives of unknown composition. From the trendsH vs./t _cure it has been possible to attain a phenomenological kinetic order of the polymerization rate at 100° through an iterative calculation procedure. For most of the investigated adhesives there are reasons (double peak of polymerization and doubleT _g signal) to assume that they are graft copolymers.

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Zusammenfassung Die Glas-Übergangstemperaturen (T _g) und dieH thermische Effekte der Polymerisation wurden für fünf Epoxy-Klebstoffe unbekannter Zusammensetzung bestimmt.Aus den TrendsH gegenübert _cure war es möglich eine phenomenologische kinetische Ordnung der Polymerisationsgeschwindigkeit bei 100° durch ein iteratives Berechnungsverfahren zu ermitteln.Für die meisten untersuchten Klebstoffe besteht der Grund — Doppelpeak der Polymerisation und doppeltesT _g-Signal — sie als Pfropfcopolymere zu betrachten.

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Résumé On a déterminé, pour cinq adhésifs époxy de composition inconnue, les températures de transition vitreuseT _g et les effets thermiques de polymérisationH.A partir de la variation deH en fonction du temps de recuit et par une méthode de calcul itératif, un ordre cinétique phénoménologique de la vitesse de polymérisation à 100° a pu être obtenu.Pour la plupart des adhésifs étudiés l'existence d'un pic double de polymérisation et d'une double transition vitreuseT _g permet de supposer qu'il s'agit de copolymères greffés.

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T _g H. H.-t. 100° . T _g , - .

     

Quantum chemical calculations on the catalytic dehydration of 2-propanol

The charge on atoms and the bond strengths in CH₃CHOHCH₃, CH₃ CH₃, CH₃CHOHCH ₂ ^– , CH₃ CH ₂ ^– and CH₃ CH₃...O(H)CH(CH₃)₂ have been calculated by the CNDO/2 method. The results are in agreement with published experimental observations on catalytic dehydration. A modified mechanism of anti-elimination on solid catalysts is proposed.

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CH₃CHOHCH₃, CH₃ CH₃, CH₃CHOHCH ₂ ^– , CH₃ CH ₂ ^– CH₃ CH₃...O(H)CH(CH₃)₂, CNDO/2. . .

     

Complex polarizability as used to analyze dielectric relaxation measurements

The effect of representing dielectric properties in terms of the complex polarizability ^c = – i is examined. Loss curves ( and tan ) are shifted towards higher frequencies, revealing the existence of new relaxations and allowing the clarifications of ones already known. We have calculated the shift ratios (at maximum or tan )/ (at maximum or tan ) from the more conventional empirical equations representing the dielectric behavior. Some examples are given.     

Ein einfacher Zugang zu (R)-γ-Amino-β-hydroxybuttersäure (GABOB) aus natürlichem (2S, 4R)-4-Hydroxyprolin

The oxidative decarboxylation sequence (1a 2a 3a 4a 5a) affording -aminobutanoic acid (5a) is adapted to the synthesis of its hydroxy derivative5b. A facile high yield conversion of (2S, 4R)-4-hydroxyproline-methylester-hydrochloride (7) to (R)-GABOB (5b) on a preparative scale is reported with the hydroxypyrrolidone8 as the intermediate.

     

NMR Spectral Assignment of Per-substituted Key-Intermediates of β-Cyclodextrin and Implications in the Structures of the Derivatives

The compounds, 6-per-O-(t-butyldimethylsilyl)--cyclodextrin(1), 2,3-per-O-benzyl-6-per-O-(t-butyldimethylsilyl)--cyclodextrin(2), 2,3-per-O-benzyl--cyclodextrin (3),2,3,6-per-O-benzyl--cyclodextrin (4),2,3,6-per-O-benzoyl--cyclodextrin (5), are used as keyintermediates in the synthesis of selectively substituted -CD derivatives. Simple and assignable ¹H and ¹³C NMR spectra (chemical shifts and coupling constants) were obtained for compounds1–4 indicating C₇ symmetry, ⁴C₁ glucose conformation and major arrangement of H6, H6' atoms at the primary side. The derivative 5, however, gave very broad peaksat room temperature. The peaks could partially be assigned at 270 K, but the broadening was still present at 220 K. This implies that there exist several conformers of similar energyand C₁ symmetry that continuously interchange, since there is not a single type of stabilizing interaction thatpredominates. We attributed this phenomenon to the presence of the carbonyl group, which probablydisfavors - stacking and induces random arrangements of the aromatic rings.