Colouring steiner quadruple systems

An algorithm is described which finds a proper 2-colouring of a Steiner quadruple system if one exists; the time required by this method is polynomial. By way of contrast, 2-colouring a partial Steiner quadruple system is shown to be NP-complete.     

Simple proof of the existence of restricted ramsey graphs by means of a partite construction

By means of a partite construction we present a short proof of the Galvin Ramsey property of the class of all finite graphs and of its strengthening proved in [5]. We also establish a generalization of those results. Further we show that for every positive integerm there exists a graphH which is Ramsey forK _m and does not contain two copies ofK _m with more than two vertices in common.     

Complexity of diagrams

A diagram is an undirected graph corresponding to the covering relation of a finite poset. We prove that three decision problems related to diagrams are NP-complete.     

Finite union theorem with restrictions

The aim of this paper is to prove the following extension of the Folkman-Rado-Sanders Finite Union Theorem: For every positive integersr andk there exists a familyL of sets having the following properties:

1. ifS ₁,S ₂, ...,S _{k + 1} are distinct pariwise disjoint elements ofL then there exists nonemptyI ? {1, 2, ...,k + 1} with ∪ _i∈I S _i ?L
2. ifL =L ₁ ?...?L _r is an arbitrary partition then there existsj ≤ r and pairwise disjoint setsS ₁,S ₂, ...,S _k ∈L _j , such thatL _i∈I S _i ∈L _j for every nonemptyI ? {1, 2, ...,k}.

     

Discrepancy and eigenvalues of Cayley graphs

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.     

Diatomics-in-molecules calculation of interaction of molecular hydrogen with a lithium metal cluster

Interaction of H₂ with a lithium metal surface simulated by eight Li atoms is studied using the DIM method. Two variables are examined, the distance of H₂ from the surface and the HH separation. The adsorption proceeds adiabatically. Associative chemisorption is predicted to be energetically more favourable than dissociative.     

Model study of the relaxation accompanying adsorption of atomic hydrogen on the Li(100) cluster surface

Relaxation effects in the (4, 1, 4) and (5, 4) Li₉ clusters induced by interaction with H are studied using the diatomics-in-molecules method. Total electronic energies for the clusters are determined as functions of the Li-Li bond lengths, both in the absence and in the presence of hydrogen adsorbed in a position of C_4v symmetry. Two models of cluster relaxation are considered, differing in which part of the cluster is allowed to relax. The calculations reveal that hydrogen adsorbed on the (100) cluster surface causes quite a significant contraction of the metal atoms. The effect of the cluster relaxation on the nonadiabatic coupling between the lowest two Born-Oppenheimer states of the hydrogen-cluster system is discussed.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Diatomics-in-molecules correlation diagrams for (BH2)+

The diatomics-in-molecules method is applied to calculate potential energy surfaces of the system B⁺(¹S, ³P) + H₂ (X¹ Σ_g⁺. Results are presented as correlation diagrams following the approximate minimum energy paths for C_∞v and C_2v geometries of the reactants. Two possible non-adiabatic mechanisms of complex formation are discussed.     

Sexual attraction in the silkworm moth. Nature of binding of bombykol in pheromone binding protein--an ab initio study

An analysis of the crystal structure of [BmPBP...bombykol] complex identified nine amino acid residues involved in a variety of intermolecular interactions binding the ligand. Using simple model fragments as the representatives of the residues, the interaction energies of their complexes with bombykol were calculated using high-level ab initio methods. The results were discussed in terms of the method and basis set dependence and were further corrected to account for their pair nonadditivities. This enabled us to describe quantitatively the nature and origin of the binding forces in terms of contribution of the individual amino acids and individual types of interaction to the overall stability. All of these interactions are well defined and cannot be considered as nonspecific hydrophobic interactions, one of the major conclusions of this work.     

Sorption of radiactive strontium on binary systems of some alkaline earth sulfates

Equilibrium and metastable solid solutions of binary mixtures of BaSO₄−CaSO₄ and SrSO₄−CaSO₄, and sorbents based on mixtures of compounds in the systems BaSO₄−MgSO₄ and SrSO₄−MgSO₄ were prepared by special heat treatments. The sorption properties of such systems were studied in relation to their structural characteristics. A positive effect of the dynamic reconstruction of the lattice on the sorption of strontium ions was found in all cases. Good sorption properties were found for the systems BaSO₄−CaSO₄ and BaSO₄−MgSO₄ An effort was made to explain the mechanism of sorption on such systems, using several independent methods.