Spectra of unicyclic graphs

Unicyclic graphs are discussed in the context of graph orderings related to eigenvalues. Several theorems involving lexicographical ordering by spectral moments as well as the ordering by the largest eigenvalue are proved. An appendix contains a table of the 89 unicyclic graphs on eight vertices together with their spectra, spectral moments and characteristic polynomials.Carnegie Research Fellow, University of Stirling, 1985–86.     

Left conjugacy closed loops of nilpotency class two

Every LCC loop Q with Inn Q abelian is nilpotent class two. A loop Q of nilpotency class two is LCC ? L(x, y) = L(y, x) for all x, y ∈ Q ? ?/Z(Mlt Q) is abelian ? [x, y, z] = [x,z,y] for all x, y, z ∈ Q ? [x, y, z] = [xy, z][x, z]^?1 for all x, y, z ∈ Q. All nilpotent LCC loops of order p² are described, and some of their multiplication groups are computed.     

PSPACE complexity of modal logic <Emphasis Type="Italic">K D</Emphasis>45<Subscript>n</Subscript>

We study sequent calculus for multi-modal logic K D45_n and its complexity. We introduce a loop-check free sequent calculus. Loop-check is eliminated by using the marked modal operator □_i^•, which is used as an alternative to sequents with histories ([8], [3], [5]). All inference rules are invertible or semi-invertible. To get this, we use or branches beside common and branches. We prove the equivalence between known sequent calculus and our newly introduced efficient sequent calculus. We concentrate on the complexity analysis of the introduced sequent calculus for multi-modal logic K D45_n. We prove that the space complexity of the given calculus is polynomial (O(l ³)). We show the maximum height of the constructed derivation tree that leads to the reduction of the time and space complexity. We present a decision algorithm for multi-modal logic K D45_n and some nontrivial examples to improve the introduced loop-check free sequent calculus.     

Renormalization of Wilson operators in the light-cone gauge

We test the renormalization of Wilson operators and the Mandelstam–Leibbrandt gauge in the case when the sides of the loop are parallel to the vectors used in the M–L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M–L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M–L gauge for loops containing spacelike lines. Received: 31 May 2000 / Published online: 23 January 2001     

Codimension one symplectic foliations and regular Poisson structures

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9].     

The synthesis and characterisation of an expansive additive for M-type cements

The expansion effect of laboratory-prepared expansive additives for M-type expansive cement was investigated at the early stage of hydration by the multicell isoperibolic calorimeter and volumetric technique based on Archimedes’ principle. The relative volume changes and heat released during hydration are strongly affected by the content of lime in the expansive additive due to the influence of CaO on the kinetics and mechanism of formation of ettringite. The increasing content of lime favours the formation of monosulphate and its later transformation to ettringite generating expansion stress. The effect of expansive additive on the behaviour of mortar samples was measured as linear elongation of test blocks using Graf-Kaufman dilatometer. Lower or higher content of lime in expansion additive slightly decreases the 7th-day compressive and flexural strength of samples while this effect is negligible for expansive additive with nominal composition of ettringite.     

Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.     

An integrated experimental and theoretical investigation of the vibrational modes and molecular structure of a new Cu(II)–phosphocreatine complex

A new complex of Cu(II) of stoichiometry [Cu(PCr)(H₂O)] was prepared from aqueous solution at pH 6. Its synthesis, characterization, thermogravimetric, vibrational spectroscopy, and electron paramagnetic resonance analyses were described and suggest that phosphocreatine (PCr) in solid state is acting as a tridentate ligand (the nitrogen atom of the guanidine group and the oxygen atoms of the phosphate group and the carboxylate group being the donor atoms). The fourth position is occupied by a water molecule. These results were confirmed through computational calculations (DFT/B3LYP:6-311G theoretical procedure). The tetra coordination of Cu(II) arranged in a quadratic planar geometry was found to be more stable in the DFT calculations. The calculated vibrational spectrum agrees well with the FT-IR experimental spectrum.