An extension of regular supermagic graphs

A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we consider an extension of regular supermagic graphs and apply it to some constructions of supermagic graphs. Using the extension we prove that for any graph G there is a supermagic regular graph which contains an induced subgraph isomorphic to G.     

Dualities in full homomorphisms

In this paper we study dualities of graphs and, more generally, relational structures with respect to full homomorphisms, that is, mappings that are both edge- and non-edge-preserving. The research was motivated, a.o., by results from logic (concerning first order definability) and Constraint Satisfaction Problems. We prove that for any finite set of objects (finite relational structures) there is a finite duality with to the left. It appears that the surprising richness of these dualities leads to interesting problems of Ramsey type; this is what we explicitly analyze in the simplest case of graphs.     

Matrices related to interpolatory quadratures

Summary An explicit formula for the coefficients of interpolatory quadratures with knots of arbitrary multiplicity which uses the eigenvectors and principal vectors of certain matrices is derived. The construction and properties of such matrices are discussed, and applications for the evaluation of Gauss and generalized Gauss-Lobatto quadratures are indicated.     

A mathematical model of realistic constitutional chemistry. A synthon approach. I: An algebraic model of a synthon

A mathematical model of a synthon is suggested. The synthon is modelled by a special so-calledS-matrix. The notion of isomeric synthons on the set of atoms A and that of a Family of Isomeric SynthonsFIS (A) is introduced. The chemical reaction is represented by a matrix equation and it is modelled by the so-calledSR-matrix. The notion of the reaction distance (RD) between two isomeric synthons is defined. A mathematical theory of the S andSR-matrices is developed.     

Spectroscopic measurements in nitrogen arcs with respect to local thermodynamic equilibrium

A wall-stabilized nitrogen arc at atmospheric pressure was studied spectroscopically in the current range from 20 to 70 A with the aim of detecting departures from LTE. Measurements of the relative intensity of several N(I) lines showed that the populations of the upper excited states are in equilibrium for currents greater than approx. 25 A. Comparisons of the excitation temperatures obtained from relative intensities with the electron temperature and with the temperature curves calculated for different departures from LTE show that deviations from equilibrium are small at the arc center for electron densities above approx. 4 × 10¹⁶ cm^-3. Deviations between the radial profiles of the electron and excitation temperatures were observed for currents between 35 and 55 A.     

New analytical method for determination and speciation of forms of carbon

A new analytical method is presented, allowing the identification and determination of various forms of carbon (elemental and combined) present in materials. The method is based on temperature-controlled heating of the sample in oxygen or an inert atmosphere, with continuous recording of the amount of carbon oxides evolved, as a function of temperature. The application of the method is demonstrated with typical examples (cast iron, artificial diamond, carbides isolated from steel, electrographite).     

NMR study of the structure of poly(N-benzoyl-8-octanelactam)

The structure of a polymer prepared by the polymerization of N-benzoyl-8-octanelactam initiated with benzoic acid was studied by ¹H and ¹³C NMR, using S-INEPT, COSY, COLOC, and ROSEY methods, with the aid of model oligomers. Beside the expected N-benzoylated segments, the polymer also contained deacylated segments and about 50% of branching units. The polymer can be characterized as a statistical, highly branched copolymer of N-benzoyl-8-octanelactam and 8-octanelactam. © 1993 John Wiley & Sons, Inc.     

Theoretical investigation of the interaction between the hydrogen atom and Pd clusters

The chemisorption of hydrogen on small Pd_n clusters (n = 1–3) has been investigated using the pseudopotential procedure followed by configuration interaction (PP-CI). The interaction of H with the cluster modeling the three-fold hollow site of the Pd(111) surface is found to be stronger than that at the bridge and the top site models. When H occupies a top site the bonding has a partial ionic character as a consequence of charge transfer from the metal to H. At the bridge and hollow sites the bonding is essentially covalent. The MO energy spectrum of the Pd₃-H (hollow) cluster is characterized by the presence of a well separated MO level ～ 7 eV below the Fermi level which is consistent with the experimentally observed photoelectron spectra of H on Pd(111) surface. The bonding between H and Pd clusters occurs mainly via d-orbitals and seems to be of quite local nature.