Note on non-separating and removable cycles in highly connected graphs

We combine two well-known results by Mader and Thomassen, respectively. Namely, we prove that for any k-connected graph G (k≥4), there is an induced cycle C such that G−V(C) is (k−3)-connected and G−E(C) is (k−2)-connected. Both “(k−3)-connected” and “(k−2)-connected” are best possible in a sense.     

Two-parameter families of uniquely extendable Diophantine triples

Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A~2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.     

Theoretical study on keto–enol tautomerisation of glutarimide for exploration of the isomerisation reaction pathway of glutamic acid in proteins using density functional theory

ABSTRACT

In order to elucidate the reason why glutamic acid residues have lesser racemisation reactivity than asparaginic acid, we investigated the racemisation energy barrier of piperidinedione, which is the presumed intermediate of the isomerisation reaction of L-Glu to D-Glu, by density functional theory calculations. In two-water-molecule-assisted racemisation, the activation barrier for keto–enol isomerisation was 28.1 kcal/mol. The result showed that the activation barrier for the racemisation of glutamic acid residues was not different from that for the racemisation of aspartic acid residues. Thus, glutamic acid residues can possibly cause the racemisation reaction if the cyclic intermediate stably exists.     

Peptide recognition: encapsulation and alpha-helical folding of a nine-residue peptide within a hydrophobic dimeric capsule of a bowl-shaped host

A dimeric capsule of coordination bowl 1 encapsulated a nine-residue peptide (Trp-Ala-Glu-Ala-Ala-Ala-Glu-Ala-Trp; 2) within the large hydrophobic cavity in water, and stabilized the alpha-helical conformation of bound 2. An NMR titration experiment revealed that monomeric bowl 1 recognized two Trp residues at the both terminals of 2 through 1/2 = 1:1 to 2:1 complexation. The 1:1 and 2:1 species exist in equilibrium even in the presence of excess 1. It was found that the formation of the 2:1 complex, in which two bowls of 1 wrapped the whole of 2, became dominant by the addition of NaNO3 due to the fact that the enhanced ion strength increased the hydrophobic interaction between Trp residues and the cavity of 1. The alpha-helical conformation of 2 within the dimeric capsule of 1 was elucidated from detailed NOESY analysis.     

Environmentally friendly one-pot synthesis of alpha-alkylated nitriles using hydrotalcite-supported metal species as multifunctional solid catalysts

A ruthenium-grafted hydrotalcite (Ru/HT) and hydrotalcite-supported palladium nanoparticles (Pd(nano)/HT) are easily prepared by treating basic layered double hydroxide, hydrotalcite (HT, Mg(6)Al(2)(OH)(16)CO(3)) with aqueous RuCl(3)n H(2)O and K(2)[PdCl(4)] solutions, respectively, using surface impregnation methods. Analysis by means of X-ray diffraction, and energy-dispersive X-ray, electron paramagnetic resonance, and X-ray absorption fine structure spectroscopies proves that a monomeric Ru(IV) species is grafted onto the surface of the HT. Meanwhile, after reduction of a surface-isolated Pd(II) species, highly dispersed Pd nanoclusters with a mean diameter of about 70 A is observed on the Pd(nano)/HT surface by transmission electron microscopy analysis. These hydrotalcite-supported metal catalysts can effectively promote alpha-alkylation reactions of various nitriles with primary alcohols or carbonyl compounds through tandem reactions consisting of metal-catalyzed oxidation and reduction, and an aldol reaction promoted by the base sites of the HT. In these catalytic alpha-alkylations, homogeneous bases are unnecessary and the only by-product is water. Additionally, these catalyst systems are applicable to one-pot syntheses of glutaronitrile derivatives.     

Rainbow Generalizations of Ramsey Theory: A Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.     

A Facile,Controlled Synthesis of Soluble Star Polymers Containing a Sugar Residue by Ring-Opening Metathesis Polymerization (ROMP)

Summary: Precise syntheses of soluble star polymers containing a sugar residue could be attained by adopting sequential ring-opening metathesis polymerizations of norbornene, 1,4,4a,5,8,8a-hexahydro-1,4,5,8-exo-endo-dimethanonaphtalene, and then 1,2:3,4-di-O-isopropylidene-α-D-galacto-pyranos-6-O-yl 5-norbornene-2-carboxylate using Mo(CHCMe₂Ph)(N-2,6-ⁱPr₂C₆H₃)(O^tBu)₂. The resultant polymers possessed uniform molecular weight distributions, and the M_n values could be varied by the monomer/Mo molar ratios; their spherical images were observed in the TEM micrographs.     

Transition‐Metal‐Mediated and ‐Catalyzed C−F Bond Activation by Fluorine Elimination

The activation of carbon–fluorine (C?F) bonds is an important topic in synthetic organic chemistry. Metal‐mediated and ‐catalyzed elimination of β‐ or α‐fluorine proceeds under milder conditions than oxidative addition to C?F bonds. The β‐ or α‐fluorine elimination is initiated from organometallic intermediates having fluorine substituents on carbon atoms β or α to metal centers, respectively. Transformations through these elimination processes (C?F bond cleavage), which are typically preceded by carbon–carbon (or carbon–heteroatom) bond formation, have been increasingly developed in the past five years as C?F bond activation methods. In this Minireview, we summarize the applications of transition‐metal‐mediated and ‐catalyzed fluorine elimination to synthetic organic chemistry from a historical perspective with early studies and from a systematic perspective with recent studies.     

Nucleophilic 5-endo-trig cyclization of 2-(trifluoromethyl)allylic metal enolates and enamides: Synthesis of tetrahydrofurans and pyrrolidines bearing exo-difluoromethylene units

Ketones and imines bearing a 2-(trifluoromethyl)allylic moiety successfully underwent nucleophilic 5-endo-trig cyclization via their metal enolates and enamides. O- or N-Cyclization proceeded exclusively in each case to afford the corresponding five-membered heterocycles with both exo-difluoromethylene and exo-alkylidene units. On treatment with potassium hexamethyldisilazide (KHMDS) or lithium diisopropylamide (LDA), 2-(trifluoromethyl)allylic ketones or imines provided the corresponding tetrahydrofurans or pyrrolidines bearing a Z-alkylidene group with perfect or substantial stereoselectivity, respectively.