Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Spectroscopy of light nuclei with skyrme-type interactions

Deformed Hartree-Fock calculations are performed for some light nuclei in a large configuration space consisting of first four major shells. The interaction employed is the modified Skyrme interaction in which the deformed density is replaced by the band averaged scalar density that makes the Hamiltonian rotationally invariant rendering the spectroscopic calculations feasible. It is shown that the introduction of density dependence spreads out the energy spectra and that the Skyrme variant SIV which has a weak density dependence gives best overall agreement for energy spectra and the available data for the electromagnetic properties of the nuclei studied. It is found that the maximum contribution to the energy of any state in the low lying spectrum comes from thes-state attractive ands-state repulsive parts of the Skyrme interaction. It is also shown that when two-body density dependent version of Skyrme interaction is used, the Koopmans theorem no longer holds.     

Efficient synthesis of the C/D rings of atisine-type C20-diterpenoid alkaloids

A bicyclo[2.2.2]octane C/D ring system,with a lactonic ring at C-8 and C-9,of the atisine-type C₂₀-diterpenoid alkaloids,was successfully synthesized,using an oxidative dearomatization/intramolecular Diels-Alder reaction.     

Lie-admissible structures on Witt type algebras

In this paper we study Lie-admissible structures on Witt type algebras. Witt type algebras are Γ$\Gamma$-graded Lie algebras (where Γ$\Gamma$ is an abelian group) which generalize the Witt algebra. We give all third power-associative and flexible Lie-admissible structures on these algebras. In particular we generalize some results on the Witt algebra. After describing the second scalar cohomology group of Witt type algebras, we investigate third power-associative and flexible Lie-admissible structures on the central extension of some Witt type algebras. Finally we study a left-symmetric structure induced by a symplectic form for some Witt type algebras.     

The secondary X-ray fluorescence and absorption near the interface of multi-material: Case of EDS microanalysis

A simple model is proposed to take into account secondary X-ray fluorescence and absorption effects near the interface. This model is based on the investigation of the shape change of the first derivative equation that can fit the sigmoidal EDS profile obtained when a high vacuum electron beam passes through the interface of two adjacent materials. The contribution of the photoelectric absorption of primary X-rays (characteristic and Bremsstrahlung) and the secondary fluorescence on the degradation of the X-ray spatial resolution can be easily quantified. The close agreement between the simulated (Monte Carlo simulation using the Casino software) and the experimental data serves to assess the reliability of this developed model.     

Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollary 2.3, Corollary 2.4 and Corollary 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen’s conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.     

TOF-SIMS investigation of Streptomyces coelicolor, a mycelial bacterium

Streptomyces coelicolor is a mycelial microorganism that produces several secondary metabolites, including antibiotics. The physiology of the organism has largely been investigated in liquid cultures due to ease of monitoring different physiological parameters and more homogeneous culture conditions. However, solid cultures reflect the natural physiology of the microorganism better, given that in its natural state it grows in the soil. Imaging mass spectrometry with TOF-SIMS and C₆₀⁺ primary ion beams offers a potential route to studying chemical changes at the molecular level, both intracellular and extracellular that can help in understanding the natural physiology of the microorganism. Here, we report the application of the technique for studying the lateral distribution of the chemical species detected in a population, grown in both liquid and solid cultures. The capability of the technique for studying biological systems with minimal system intervention is demonstrated.     

C*-dynamical systems that are asymptotically highly anticommutative

It is shown that with probability 1 on , resp. ongx the irrational rotation algebra with respect to the CAT map and the generalized Price-Powers shiftA _X are asymptotically highly anticommutative.     

On the topological theory of self-dual connections over noncompact Riemann surfaces

A topological action for self-dual connections over noncompact Riemann surfaces is proposed. TheJ formulation and the associated linear system are obtained. A new connection is constructed, depending on a Kac-Moody parameter such that its flatness condition is theJ-equation associated to the self-dual problem. The algebra of infinitesimal Bäcklund transformations depending on this Kac-Moody parameter is constructed.