Parity of the weak Fréedericksz transition

The European Physical Journal E - Motivated by the recent experimental findings by Kumar et al. (Phys. Rev. E., 82, 011701 (2010)) in which the inverse Fréedericksz transition is observed, we...     

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ( monochromatic components in what follows) have order at most . Ban and Linial Conjectured that every bridgeless cubic graph admits a -bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph with has a -edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (ie, a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we provide evidence of a strong relation of the conjectures of Ban-Linial and Wormald with Ando's Conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above-mentioned conjectures. Moreover, we prove Ban-Linial's Conjecture for cubic-cycle permutation graphs. As a by-product of studying -edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Conformational and Electronic Interaction Studies of Some β-Ketosulfoxides

ABSTRACT.

The analysis of the carbonyl I.R. band and the U.V. phoelectron spectroscopic data along with the ab-initio calculations and X-ray diffraction of α-(methylsulfinyl)- and α-(phenylsulfinyl)-acetophenones indicated the predominance of the cis rotamers over the qauche ones.     

Regioselective cyclization of chloroacylaminobenzenesulfonamide derivatives

Chloroacylaminobenzensulfonamides regioselectively thermally cyclize under solvent free conditions to 1,2,4-benzothiadiazines with five- and six-membered rings fused on face b.