The T(4) property of families of unit disks

For a family of n mutually disjoint unit disks in the plane, we show that if any four disks are intersected by a line then there is a line that intersects at least n − 1 disks of . Supported by an NSERC Discovery Grant. Supported by OTKA Grant F042959. Supported by CONACYT CCDG 50151.     

Alkane isomers: presence in petroleum ether and complexity

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine 'complexity'. Mass spectrometry and infrared spectroscopy in combination with gas chromatography were used to identify the various structural isomers of alkanes in petroleum ether. The isomers were categorised in quantitative terms by using topological indices and linear discriminant analysis. It was found that alkanes possessing a more complex, highly branched structure are less probable to be detected in petroleum ether than isomers with a simpler backbone structure. It was proposed that the experimental 'measure' of the complexity of isomer(i) should be proportional to 1/C(i), where C(i), denotes the concentration of isomer(i) in a (primary) petroleum derivative.     

Can the nearly conformal sextet gauge model hide the Higgs impostor?

New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β-function (DeGrand et al. [3]). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β-function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.     

Alternating Diene Metathesis Polycondensation (ALTMET) – A Versatile Tool for the Preparation of Perfectly Alternating AB Copolymers

Perfectly alternating copolymers can be synthesised by reacting diacrylates with terminal dienes using alternating diene metathesis polycondensation (ALTMET). This novel method is very versatile and allows preparation of diverse structures of polymers, including main‐chain liquid crystalline polymers.

Main‐chain liquid crystalline polymer obtained by ALTMET.