Surface crossing in interaction of atomic hydrogen with a lithium metal cluster

Interaction of atomic hydrogen with a (4,1,4) lithium cluster, simulating the (100) metal surface, is studied using the diatomics-in-molecules method. Ground-and excited-state potential curves for normal approach ofH to some attack positions on the surface intersect or pseudo-intersect. The results reveal possible non-adiabatic character of the absorption process.     

Sparse ramsey graphs

IfH is a Ramsey graph for a graphG thenH is rich in copies of the graphG. Here we prove theorems in the opposite direction. We find examples ofH such that copies ofG do not form short cycles inH. This provides a strenghtening also, of the following well-known result of Erdős: there exist graphs with high chromatic number and no short cycles. In particular, we solve a problem of J. Spencer. Dedicated to Paul Erdős on his seventieth birthday     

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvátal, Trotter and the two senior authors proved that for any Δ there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph KN with N?Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Δ. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and edges, with N=⌈B^′n⌉ for some constant B^′ that depends only on Δ. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Δ is . Our approach is based on random graphs; in fact, we show that the classical Erd?s–Rényi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Δ.The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed.     

On K s -free subgraphs in K s+k -free graphs and vertex Folkman numbers

Extending the problem of determining Ramsey numbers Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let f _s,t (n) = min{max{|S|: S ⊆ V (H) and H[S] contains no K _s }}, where the minimum is taken over all K _t -free graphs H of order n. This function attracted a considerable amount of attention but despite that, the gap between the lower and upper bounds is still fairly wide. For example, when t=s+1, the best bounds have been of the form Ω(n ^1/2+o(1)) ≤ f _s,s+1(n) ≤ O(n ^1−ɛ(s)), where ɛ(s) tends to zero as s tends to infinity. In this paper we improve the upper bound by showing that f _s,s+1(n) ≤ O(n ^2/3). Moreover, we show that for every ɛ > 0 and sufficiently large integers 1 ≪ k ≪ s, Ω(n ^1/2−ɛ ) ≤ f _s,s+k (n) ≤ O(n ^1/2+ɛ . In addition, we also discuss some connections between the function f _s,t and vertex Folkman numbers.     

Dissociation kinetics of Mn2+ complexes of NOTA and DOTA

The kinetics of transmetallation of [Mn(nota)](-) and [Mn(dota)](2-) was investigated in the presence of Zn(2+) (5-50-fold excess) at variable pH (3.5-5.6) by (1)H relaxometry. The dissociation is much faster for [Mn(nota)](-) than for [Mn(dota)](2-) under both experimental and physiologically relevant conditions (t(?) = 74 h and 1037 h for [Mn(nota)](-) and [Mn(dota)](2-), respectively, at pH 7.4, c(Zn(2+)) = 10(-5) M, 25 °C). The dissociation of the complexes proceeds mainly via spontaneous ([Mn(nota)](-)k(0) = (2.6 ± 0.5) × 10(-6) s(-1); [Mn(dota)](2-)k(0) = (1.8 ± 0.6) × 10(-7) s(-1)) and proton-assisted pathways ([Mn(nota)](-)k(1) = (7.8 ± 0.1) × 10(-1) M(-1) s(-1); [Mn(dota)](2-)k(1) = (4.0 ± 0.6) × 10(-2) M(-1) s(-1), k(2) = (1.6 ± 0.1) × 10(3) M(-2) s(-1)). The observed suppression of the reaction rates with increasing Zn(2+) concentration is explained by the formation of a dinuclear Mn(2+)-L-Zn(2+) complex which is about 20-times more stable for [Mn(dota)](2-) than for [Mn(nota)](-) (K(MnLZn) = 68 and 3.6, respectively), and which dissociates very slowly (k(3)～10(-5) M(-1) s(-1)). These data provide the first experimental proof that not all Mn(2+) complexes are kinetically labile. The absence of coordinated water makes both [Mn(nota)](-) and [Mn(dota)](2-) complexes inefficient for MRI applications. Nevertheless, the higher kinetic inertness of [Mn(dota)](2-) indicates a promising direction in designing ligands for Mn(2+) complexation.     

The number of Sidon sets and the maximum size of Sidon sets contained in a sparse random set of integers

A set A of non‐negative integers is called a Sidon set if all the sums , with and a₁, , are distinct. A well‐known problem on Sidon sets is the determination of the maximum possible size F(n) of a Sidon subset of . Results of Chowla, Erd?s, Singer and Turán from the 1940s give that . We study Sidon subsets of sparse random sets of integers, replacing the ‘dense environment’ by a sparse, random subset R of , and ask how large a subset can be, if we require that S should be a Sidon set. Let be a random subset of of cardinality , with all the subsets of equiprobable. We investigate the random variable , where the maximum is taken over all Sidon subsets , and obtain quite precise information on for the whole range of m, as illustrated by the following abridged version of our results. Let be a fixed constant and suppose . We show that there is a constant such that, almost surely, we have . As it turns out, the function is a continuous, piecewise linear function of a that is non‐differentiable at two ‘critical’ points: a = 1/3 and a = 2/3. Somewhat surprisingly, between those two points, the function is constant. Our approach is based on estimating the number of Sidon sets of a given cardinality contained in [n]. Our estimates also directly address a problem raised by Cameron and Erd?s (On the number of sets of integers with various properties, Number theory (Banff, AB, 1988), de Gruyter, Berlin, 1990, pp. 61–79). © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 1–25, 2015     

Local surrounding of Mn in LaMn1−xCoxO3 compounds by means of EXAFS on Mn–K

A systematic study of LaMn_1?xCo_xO₃ perovskite series by means of X-ray absorption spectroscopy in the extended X-ray absorption fine structure (EXAFS) range of the K-absorption edge of Mn is reported. The Mn–K edge absorption measurements in the EXAFS region were performed to study the local surrounding of Mn ions. Polycrystalline powder samples of LaMn_1?xCo_xO₃ (x=0, 0.02; 0.2; 0.4; 0.5; 0.6; 0.8) prepared by solid-state reaction were used. The EXAFS spectra were analyzed with the FEFF8 computer program. The Mn–O distances of Mn to the nearest oxygen surroundings were evaluated for the samples in the series and compared with the Co–O distances obtained by EXAFS in V. Procházka et al., JMMM 310 (2007) 197 and with results of X-ray powder diffraction in C. Autret, J. Phys. Condens. Matter 17 (2005) 1601.