The classification of closed surfaces using colored graphs

A short graph theoretic proof of the classification of closed surfaces is given. The new proof has the feature that the symmetric canonical graphs for the surfaces do not correspond to the canonical polygons in the usual proof of the classification.     

Separation index of a graph

The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53–61, 2002     

Co-Orthogonal Codes

We define, construct and sketch possible applications of a new class of non-linear codes: co-orthogonal codes, with possible applications in cryptography and parallel processing. We also describe a fast and general method for generating (non-linear) codes with prescribed dot-products with the help of multi-linear polynomials.     

Balanced extensions of graphs and hypergraphs

For a hypergraphG withv vertices ande _i edges of sizei, the average vertex degree isd(G)= ∑ie ₁/v. Callbalanced ifd(H)≦d(G) for all subhypergraphsH ofG. Let $$m(G) = \mathop {\max }\limits_{H \subseteqq G} d(H).$$ A hypergraphF is said to be abalanced extension ofG ifG?F, F is balanced andd(F)=m(G), i.e.F is balanced and does not increase the maximum average degree. It is shown that for every hypergraphG there exists a balanced extensionF ofG. Moreover everyr-uniform hypergraph has anr-uniform balanced extension. For a graphG let ext (G) denote the minimum number of vertices in any graph that is a balanced extension ofG. IfG hasn vertices, then an upper bound of the form ext(G) ₁ n ² is proved. This is best possible in the sense that ext(G)>c ₂ n ² for an infinite family of graphs. However for sufficiently dense graphs an improved upper bound ext(G) ₃ n can be obtained, confirming a conjecture of P. Erdõs.     

The influence of the purine 2-amino group on DNA conformation and stability-II: Synthesis and physical characterization of d[CGT(2-NH2)ACG], d[CGU(2-NH2)ACG], and d[CGT(2-NH2)AT(2-NH2)ACG]

Synthesis of an N-protected derivative of 2-amino-2'-deoxyadenosine (dA') from 2'-deoxyguanosine is reported. The syntheses of several oligodeoxynucleotides containing this modified nucleoside are described, together with physical characterization via melting studies and CD conformational analysis. As expected, the 2-amino group is seen to add to the duplex stability. Although the sequence d(TA')₃ was found to undergo a salt-induced conformational transition, mixed sequences such as d(CGTA'CG) did not display this behavior. All guanine residues present in these sequences were O⁶ protected, either with the cyanoethyl group or the 4-nitrophenylethyl group, to eliminate guanine degradation during phosphorylation and condensation reactions. Procedures for the introduction and removal of these O⁶ protecting groups are described.     

Studies related to the head-maturation pathway of bacteriophages T4 And T2:II. nuclear disruption, protein synthesis and particle formation with the mutant 43-.30-.46-

We describe the aberrant phage multiplication of the triple conditional lethal mutant 43-(polymerase).30-(ligase).46-(exonuclease) of bacteriophage T4D in which phage DNA replication is arrested but some late protein synthesis occurs (33). The nuclear disruption is indistinguishable from wild type. Forty-five empty small and empty large particles are assembled per cell when the multiplicity of infection (m.o.i.) is 100. This number corresponds closely to the 38 phage equivalents of cleaved major head protein determined biochemically. By reducing the m.o.i. the number of observable particles decreases, reaching 1-5 per cell at an m.o.i. of 5(+5). The total synthesis of phage related proteins is not significantly dependant on the m.o.i. The synthesis of late proteins is about 10% of that of wild type at high m.o.i. and decreases with the m.o.i. The different early and late proteins do not show the same relative proportions as in wild type and respond differently to an increased m.o.i. These and other results are discussed with respect to the role of phage DNA in prehead assembly and head maturation.     

Differential binding of Mg2+, Zn2+, and Cd2+ at two sites in a hammerhead ribozyme motif, determined by 15N NMR

A decamer duplex model of Domain II of the hammerhead ribozyme was synthesized with [8-13C-1,7,NH2-15N3]-guanosine at the known metal binding site, G10.1 and, for comparison, [2-13C-1,7,NH2-15N3]-guanosine at G16.2. The 15N NMR chemical shifts of the labeled N7s monitored during addition of Mg2+, Cd2+, and Zn2+ showed the same preference for binding at G10.1 over G16.2 for each metal. These results demonstrate that 15N labeling can be used to evaluate the binding of different metals, including Mg2+, to a given nitrogen, as well as to compare the binding potential of different sites.     

Palladium-Catalyzed Allylic Coupling of 1,2,3-Triazolo[4,5-d]pyrimidines (8-Azapurines)

The palladium-catalyzed coupling of the sodium salt of 7-amino-1,2,3-triazolo[4,5-d]pyrimidine (8-azaadenine, 1) with allylic phosphates or carbonates resulted in mixtures of 2- and 3-substituted 1,2,3-triazolopyrimidines, which were separated by chromatography. 1-Substituted triazolopyrimidines were not isolated from these reactions. Regioselectivity (and stereoselectivity) was also observed for substitution of the allylic moiety when more than one isomer is possible from the reaction. The use of 5-amino-1,2,3-triazolo[4,5-d]pyrimidin-7-ones (8-azaguanine, 2), instead of 8-azaadenine, also resulted in mixtures. Alternate syntheses of the 3-allyl-1,2,3-triazolo[4,5-d]pyrimidines confirmed the structures of these compounds.     

Synthesis of O-6-alkylated deoxyguanosine nucleosides

A general route for synthesis of 6-$\text{O}$-alkyl-2∝deoxyguanosine nucleosides is described. The key step is conversion of the 6-$\text{O}$-TPS derivative $\text{2}$ to the 6-trimethylamino compound $\text{3}$. The trimethylamino group is readily displaced by alcohols in the presence of DBU. Using this route the 6-$\text{O}$-methyl, ethyl and n-butyl 2∝-deoxyguanosine derivatives $\text{5a-c}$ have been prepared in excellent overall yields.     

Mechanism of the oxidation of L-ascorbic acid by the bis(pyridine-2,6-dicarboxylate)cobaltate(III) ion in aqueous solution

A detailed investigation of the oxidation of L-ascorbic acid (H₂A) by the title complex has been carried out using conventional spectrophotometry at 510 nm, over the ranges: 0.010 [ascorbate] _T 0.045 mol dm^–3, 3.62 pH 5.34, and 12.0 30.0 °C, 0.50 I 1.00 mol dm^–3, and at ionic strength 0.60 mol dm^–3 (NaClO₄). The main reaction products are the bis(pyridine-2,6-dicarboxylate)cobaltate(II) ion and l-dehydroascorbic acid. The reaction rate is dependent on pH and the total ascorbate concentration in a complex manner, i.e., k _obs = (k ₁ K ₁)[ascorbate] _T /(K ₁ + [H⁺]). The second order rate constant, k ₁ [rate constant for the reaction of the cobalt(III) complex and HA^–] at 25.0 °C is 2.31 ± 0.13 mol^–1 dm³ s^–1. H = 30 ± 4 kJ mol^–1 and S = –138 ± 13 J mol^–1 K^–1. K ₁, the dissociation constant for H₂A, was determined as 1.58 × 10^–4 mol dm^–3 at an ionic strength of 0.60 mol dm^–3, while the self exchange rate constant, k ₁₁ for the title complex, was determined as 1.28 × 10^–5 dm³ mol^–1 s^–1. An outer-sphere electron transfer mechanism has been proposed.