The automorphism groups of the congruence group and of some of its subgroups in finite Euclidean planes

In the affine plane over a Galois field GF(q), q ; 3(4), q = p, of congruence transformations, of motions and of the generation of all point reflections respectively. Then we determine the groups AutC, AutM, AutM and obtain the following results: 1. Aut C is isomorphic to the product of the augmented group of similarities (generated by similarities, quasi reflections, quasi rotations 2) and the group of collineations which are induced by the automorphism of GF(q) operating on the coordinates. 2. AutM– AutC. 3. AutM– group of affinities of the affine space of dimension 2 over the prime field. 4. Moreover for any desarguesian affine plane Aut Dil (Dil = group of dilatations) is isomorphic to (the full collineation group).Lecture delivered at the Haifa Geometry conference 1983In my lecture I called these transformations semi-. To avoid confusion I follow here a suggestion of E. Schröder.     

Ebene algebraische Kurven vom Typ p,q

Let p,q be relatively prime integers with 2pr ^p,q be the numerical semigroup generated by p,q,{(p–1) (q–1)–1–(ip+jq)¦i+jr–2}. Then there exists a smooth projective curve X and a point x on X, such that H _r ^p,q is the set of orders of poles of the rational functions on X, which are regular on X\{x}; in other words: H _r ^p,q is a Weierstraß semigroup.     

Superstructures of temporarily stabilized nanocrystalline CaCO3 particles: morphological control via water surface tension variation

In this paper, the formation of different complex morphologies of nanocrystalline CaCO3 under the control of double hydrophilic block copolymers (DHBCs) carrying phosphate groups is described. The DHBCs consist of a poly(ethylene glycol) (PEG) block and a pendant poly[2-(2-hydroxy ethyl)ethylene] block with different degrees of phosphorylation up to 40%, some of which show surface activity. The polymers furthermore temporarily stabilize CaCO3 nanocrystals, which are formed by slow CO2 evaporation from a supersaturated Ca(HCO3)2 solution (Kitano method). The polymers are active down to concentrations of 10(-4) g/L. In dependence of the nature and concentration of the DHBC, tunable complex shuttlecock flowerlike and other superstructures are formed, which are aggregates of CaCO3 vaterite nanoparticles with an enhanced stability of at least 2 months. It is shown that the aggregation starts around template CO2 gas bubbles at the air/water interface. The size and morphology of the growing aggregates depends on the polymer concentration, phosphorylation degree, and water surface tension. The latter determines when the aggregate sinks to the bottom, interrupting the further growth process. Variation of the water surface tension by addition of the nonionic surfactant Antharox CO880 also allows a variation of the aggregate morphology, thus implying the described method as simple and versatile for the generation of complex CaCO3 morphologies.     

Chromatographie von Carbamat- und Phenylharnstoff-Pesticiden auf Dünnschichten von basischem Zinkcarbonat

Thin layers of basic zinc carbonate can be used with good results for separation and multiple identification of carbamate and phenylurea pesticides. Five important substances could be separated by one-dimension TLC. The best results were obtained by the following developing solvents: a) benzene, b) a mixture of benzene/petroleum ether/chloroform (6∶1∶1). The substances are either recognisable in short-wave UV-light, when a fluorescence indicator (F 254 nm) is added, or in day-light, after spraying a solution of 0.1 N AgNO₃ in 3 N HNO₃, followed by an UV-exposure for about 4 min.     

High-resolution/higher-order derivative spectrophotometry in microanalytical chemistry

Summary Examples are given of the application of higher-order derivative spectrophotometry to microanalytical problems, including the increase in sensitivity for estimation of Zn and Cd dithizonates and the quantitative detection of arenes, aniline and phenols. We also describe the estimation of saccharin in soft drinks, and the characterization and estimation of dyes in solution and after absorption on a thin layer of alumina. Only ng-g amounts of substance are needed.

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Hochauflösende UV/VIS-Derivativspektrophotometrie höherer Ordnung in der Mikroanalytik

Zusammenfassung Einige Beispiele für die Anwendung der Derivativspektrophotometrie höherer Ordnung in der Mikroanalyse wurden angegeben. Im besonderen wurden die Erhöhung der Empfindlichkeit der Zn- und Cd-Dithizonat-Bestimmung, die quantitative Bestimmung von Arenen, Anilin, Phenol, die Erfassung von Saccharin in Limonaden und sowohl die Charakterisierung als auch die quantitative Bestimmung von Farbstoffen in Lösung oder adsorbiert an einer dünnen Schicht Aluminiumoxid beschrieben. Es werden nur einige Mikrogramm bis Nanogramm Substanz für die Untersuchungen benötigt.

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Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

On the zeros of polynomials over arbitrary finite dimensional algebras

In [3] it was shown that a polynomial of degree n with coefficients in an associative division algebra, which is d-dimensional over its center, has either infinitely many or at most n^d zeros. In this paper we raise the same question for arbitrary m-ary F-algebras A which are d-dimensional over the algebraically closed field F. Our main result states that in the affine space of m-ary algebras of dimension d there is a non-empty Zariski-open set whose elements A have the following property: in the space of polynomial of precise degree n with coefficients in A there is a non-empty Zariski-open set whose elements have precisely n^d zeros. It is shown that all simple algebras, all semi-simple associative algebras, all semisimple Jordan algebras (char F2), all semi-simple Lie algebras (char F=0), and the generic algebra possess this property.     

Symmetrische Permutationsmengen

A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and ^–1 (x) = ^–1 (x) implies ^–1 = ^–1 , andsharply 3-transitive, if for any two triples (x ₁,x ₂,x ₃), (y ₁,y ₂,y ₃) M ³ with|{x ₁,x ₂,x ₃ }| = |{y ₁,y ₂,y ₃ }| = 3 there is exactly one permutation with(x ₁) =y ₁,(x ₂) =y ₂,(x ₃) =y ₃. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic.     

Gasförmige Acetate

Gaseous Acetates Thermoanalytical and mass-spectrometrical observations are undertaken with some acetates and oxiacetates. The volatilization of copper(I) acetate takes place like that of the silver acetate as M₂Ac₂⁺ (besides the deposition of Ag). On the volatilization of the anhydrous compounds Cu₂Ac₄, Cr₂Ac₄, Rh₂Ac₄, and Mo₂Ac₄ in the vacuum of a mass spectrometer is observed that Cu₂Ac₄ vaporizes dissociative as Cu₂Ac₂⁺ (+ 2 “Ac”), while the other compounds vaporize as M₂Ac₄⁺ and simultaneously is formed an oxidic (e.g. Cr₂O₄) or metallic residue. PdAc₂ vaporizes in the mass spectrometer as a trimeric molecule Pd₃Ac₆. M₄OAc₆, which is formed from the dihydrates, vaporizes in a mass spectrometer with M ? Co, Mn as M₄OAc₆⁺. Other complexes of the same type appear as Be₄OAc₅⁺, Mg₄OAc₅⁺, and Zn₄OAc₅⁺.     

Insertion reactions of hydridonitrosyltetrakis(trimethylphosphine) tungsten(0)

[W(H)(NO)(PMe3)4] (1) was prepared by the reaction of [W(Cl)(NO)(PMe3)4] with NaBH4 in the presence of PMe3. The insertion of acetophenone, benzophenone and acetone into the W-H bond of 1 afforded the corresponding alkoxide complexes [W(NO)(PMe3)4(OCHR1R2)](R1 = R2 = Me (2); R1 = Me, R2 = Ph (3); R1 = R2 = Ph (4)), which were however thermally unstable. Insertion of CO2 into the W-H bond of yields the formato-O complex trans-W(NO)(OCHO)(PMe3)4 (5). Reaction of trans-W(NO)(H)(PMe3)4 with CO led to the formation of mer-W(CO)(NO)(H)(PMe3)3 (6) and not the formyl complex W(NO)(CHO)(PMe3)4. Insertion of Fe(CO)(5), Re2(CO)10 and Mn2(CO)10 into trans-W(NO)(H)(PMe3)4 resulted in the formation of trans-W(NO)(PMe3)4(mu-OCH)Fe(CO)4 (7), trans-W(NO)(PMe3)4(mu-OCH)Re2(CO)9 (8) and trans-W(NO)(PMe3)4(mu-OCH)Mn2(CO)9 (9). For Re2(CO)10, an equilibrium was established and the thermodynamic data of the equilibrium reaction have been determined by a variable-temperature NMR experiments (K(298K)= 104 L mol(-1), DeltaH=-37 kJ mol(-1), DeltaS =-86 J K(-1) mol(-1)). Both compounds 7 and 8 were separated in analytically pure form. Complex 9 decomposed slowly into some yet unidentified compounds at room temperature. Insertion of imines into the W-H bond of 1 was also additionally studied. For the reactions of the imines PhCH=NPh, Ph(Me)C=NPh, C6H5CH=NCH2C6H5, and (C6H5)2C=NH with only decomposition products were observed. However, the insertion of C10H7N=CHC6H5 into the W-H bond of led to loss of one PMe3 ligand and at the same time a strong agostic interaction (C17-H...W), which was followed by an oxidative addition of the C-H bond to the tungsten center giving the complex [W(NO)(H)(PMe3)3(C10H6NCH2Ph)] (10). The structures of compounds 1, 4, 7, 8 and 10 were studied by single-crystal X-ray diffraction.     

Stereoselective synthesis of pyrrolo[2,3-d]pyrimidine α- and β-D-ribonucleosides from anomerically pure D-ribofuranosyl chlorides: Solid-Liquid Phase-Transfer Glycosylation and 15N-NMR Spectra

Solid-liquid phase-transfer glycosylation (KOH, tris[2-(2-methoxyethoxy)ethye]amine ( = TDA-1), MeCN) of pyrrolo[2,3-d]pyrimidines such as 3a and 3b with an equimolar amount of 5-O-[(1,1 -dimethylethyl)dimethylsilyl]-2,3-O-(1-methylethylidene)-α-D -ribofuranosyl chloride (1) [6] gave the protected β-D -nucleosides 4a and 4b , respectively, stereoselectively (Scheme). The β-D -anomer 2 [6] yielded the corresponding α-D -nucleosides 5a and 5b with traces of the β-D -compounds. The 6-substituted 7-deazapurine nucleosides 6a , 7a , and 8 were converted into tubercidin (10) or its α-D -anomer (11) . Spin-lattice relaxation measurements of anomeric ribonucleosides revealed that T₁ values of H? C(8) in the α-D -series are significantly increased compared to H? C(8) in the β-D -series while the opposite is true for T₁ of H? C(1′). ¹⁵N-NMR data of 6-substituted 7-deazapurine D -ribofuranosides were assigned and compared with those of 2′-deoxy compounds. Furthermore, it was shown that 7-deaza-2′deoxyadenosine ( = 2′-deoxytubercidin; 12 ) is protonated at N(1), whereas the protonation site of 7-deaza-2′-deoxyguanosine ( 20 ) is N(3).