Kinetics of the substitution reactions of some Pt(II) complexes with 5′‐GMP and L‐histidine

The reactions of platinum(II) complexes, [PtCl₂(dach)] (dach = (1R,2R)‐1,2‐diaminocyclohexane) and [PtCl₂(en)] (en = ethylenediamine) with biologically relevant ligands such as 5′‐GMP (guanosine‐5′‐monophosphate) and l ‐His (l ‐histidine) were studied by UV–vis spectrophotometry, ¹H NMR spectroscopy, and high‐performance liquid chromatography (HPLC). Spectrophotometrically, these reactions were investigated under pseudo‐first‐order conditions at 310 K in 25 mM Hepes buffer (pH 7.2) and 10 mM NaCl to prevent the hydrolysis of the complexes. The [PtCl₂(en)] complex reacts faster than [PtCl₂(dach)] in the reaction with studied nucleophiles. This confirms the fact that the reactivity of studied Pt(II) complexes depends on the structure of the inert bidentate ligand. Also, the substitution reactions with l ‐His are always faster than the reactions with nucleotide 5′‐GMP. The reactions of [PtCl₂(dach)] and [PtCl₂(en)] complexes with l ‐histidine are studied by ¹H NMR spectroscopy. The obtained rate constants are in agreement with those obtained by UV–vis. The same reactions were studied by HPLC comparing the obtained chromatograms during the reaction. The changes in intensity of signals of the free and coordinated ligand show that after a few days there is only one dominant product in the system. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 99–106, 2011     

Synthesis and study on oxidative coupling products of 3-alkyl-2-hydroxynaphthazarins

The resulting products of oxidative coupling of substituted 3-alkyl-2-hydroxynaphthazarins in the presence of lead dioxide are the compounds with 7,14-dibenzo[a,i]oxanthrene skeleton.     

Fluorescence-based Broad Dynamic Range Viscosity Probes

We introduce two new fluorescent viscosity probes, SYBR Green (SG) and PicoGreen (PG), that we have studied over a broad range of viscosity and in collagen solutions. In water, both dyes have low quantum yields and excited state lifetimes, while in viscous solvents or in complex with DNA both parameters dramatically (300–1000-fold) increase. We show that in log-log scale the dependence of the dyes’ quantum yield vs. viscosity is linear, the slope of which is sensitive to temperature. Application of SG and PG, as a fluorescence-based broad dynamic range viscosity probes, to the life sciences is discussed.     

Fixed point and common fixed point theorems on ordered cone metric spaces

In the present work, some fixed point and common fixed point theorems for self-maps on ordered cone metric spaces, where the cone is not necessarily normal, are proved.     

Vertex-transitive expansions of (1, 3)-trees

A nonidentity automorphism of a graph is said to be semiregular if all of its orbits are of the same length. Given a graph X with a semiregular automorphism γ, the quotient of X relative to γ is the multigraph X/γ whose vertices are the orbits of γ and two vertices are adjacent by an edge with multiplicity r if every vertex of one orbit is adjacent to r vertices of the other orbit. We say that X is an expansion of X/γ. In [J.D. Horton, I.Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Combin. Theory Ser. B 53 (1991) 114-129], Horton and Bouwer considered a restricted sort of expansions (which we will call ‘strong’ in this paper) where every leaf of X/γ expands to a single cycle in X. They determined all cubic arc-transitive strong expansions of simple (1, 3)-trees, that is, trees with all of their vertices having valency 1 or 3, thus extending the classical result of Frucht, Graver and Watkins (see [R. Frucht, J.E. Graver, M.E. Watkins, The groups of the generalized Petersen graphs, Proc. Cambridge Philos. Soc. 70 (1971) 211-218]) about arc-transitive strong expansions of K₂ (also known as the generalized Petersen graphs). In this paper another step is taken further by considering the possible structure of cubic vertex-transitive expansions of general (1,3)-multitrees (where vertices with double edges are also allowed); thus the restriction on every leaf to be expanded to a single cycle is dropped.     

A note on the Poisson boundary of lamplighter random walks

The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich (Ann. Math. 152:659–692, 2000). A geometrical method for constructing the strip as a subset of the lamplighter group \mathbb Z₂\wr G{\mathbb {Z}_{2}\wr \Gamma} starting with a “smaller” strip in the group Γ is developed. Then, this method is applied to several classes of base groups Γ: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices. We show that under suitable hypothesis the Poisson boundary for a class of random walks on lamplighter groups is the space of infinite limit configurations.     

Random walks on Baumslag–Solitar groups

We consider random walks on non-amenable Baumslag–Solitar groups BS(p, q) and describe their Poisson–Furstenberg boundary. The latter is a probabilistic model for the long-time behaviour of the random walk. In our situation, we identify it in terms of the space of ends of the Bass–Serre tree and the real line using Kaimanovich’s strip criterion.