Hypercyclic sequences of PDE-preserving operators

A sequence of continuous linear operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that {T_nx:n0} is dense. A continuous linear operator, acting on some suitable function space, is PDE-preserving for a given set of convolution operators, when it map every kernel set for these operators invariantly. We establish hypercyclic sequences of PDE-preserving operators on , and study closed infinite-dimensional subspaces of, except for zero, hypercyclic vectors for these sequences.     

Photoionization assessment of C3-C5 alkadienes and alkenes in urban air.

Hydrocarbons from samples of traffic-polluted urban air were separated by gas chromatography on an aluminium oxide column and assessed simultaneously by photoionization detection (PID) and flame ionization detection (FID) after effluent splitting. The 10.2 eV photoionization detector selectively detects alkadienes and alkenes but not alkanes and alkynes in the C3-C5 region. The maximum PID/FID response ratio for alkadienes and alkenes is also obtained in this region. The analytical system as a whole is particularly favourable for the C3-C5 alkenes. Analytical data are given for propadiene, 1,3-butadiene, propene, butenes and pentenes.     

Chromatographic classification and comparison of commercially available reversed-phase liquid chromatographic columns using principal component analysis

A total of 135 commercially available alkyl, cyano, phenyl, perfluorinated, polar embedded, enhanced polar selectivity (i.e., polar/hydrophilic endcapped), "Aqua type" and a variety of novel phases including some non-silica based stationary phases have been characterised in terms of their surface coverage, hydrophobic selectivity, shape selectivity, hydrogen bonding capacity and ion-exchange capacity at pH 2.7 and 7.6. Principal component analysis has been used to provide a simple graphical comparison of the differences/similarities between columns in the entire database and differing subsets such as "Aqua type"/enhanced polar selectivity phases. The PCA has been correlated to the phase's ability to analyse a range of hydrophilic bases.     

A McLafferty-type rearrangement of a trimethylsilyl group in silylated hydroxy carbonyl compounds

A McLafferty-type rearrangement of a trimethylsilyl group is demonstrated. Abundant rearrangement ions are formed for trimethylsilyl derivatives of α,β-dihydroxy carbonyl compounds. Data are given for a large number of hydroxy acids and hydroxy ketones including aldonic acids, aldaric acids, acyclic ketoses and hydroxy keto acids. A few branched lactones are also shown to rearrange. The positive charge and the unpaired electron are extensively delocalized in the odd-electron rearrangement ions. Those substituents at the α-carbon atom which offer a favourable delocalization promote the rearrangement. Spectra of specifically methylated species reveal that migration over larger than six-membered rings occurs to some extent. An observed dependence of abundance on configuration is associated with steric strains in the transition state. The rearrangement ions are of great diagnostic value in structural analysis. They are relatively more abundant at low electron energies and give rise to the base peak at 20 eV for many compounds. Ions produced by the competing conventional McLafferty rearrangement are less abundant.     

Chiral phase transition in lattice QCD with dynamical quarks

The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 6³ × 2 lattice. The variation in the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory.     

The Number of Nonisomorphic Two-dimensional Algebras over a Finite Field

In this paper, we derive explicit formulas for the number of nonisomorphic two-dimensional nonassociative algebras, possibly without a unit, over a finite field. The proof combines the first author’s general classification theory of two-dimensional nonassociative algebras over arbitrary base fields with elementary counting arguments which are primarily addressed to the problem of determining the number of orbits of a finite set acted upon by the group of integers mod 2. The number of nonisomorphic two-dimensional division algebras will also be determined.     

A truncated Kv1.1 protein in the brain of the <Emphasis Type="Italic">megencephaly</Emphasis>mouse: expression and interaction

Background  

The megencephaly mouse, mceph/mceph, is epileptic and displays a dramatically increased brain volume and neuronal count. The responsible mutation was recently revealed to be an eleven base pair deletion, leading to a frame shift, in the gene encoding the potassium channel Kv1.1. The predicted MCEPH protein is truncated at amino acid 230 out of 495. Truncated proteins are usually not expressed since nonsense mRNAs are most often degraded. However, high Kv1.1 mRNA levels in mceph/mceph brain indicated that it escaped this control mechanism. Therefore, we hypothesized that the truncated Kv1.1 would be expressed and dysregulate other Kv1 subunits in the mceph/mceph mice.     

Birefringence-induced splitting of the zero-dispersion wavelength in nonlinear photonic crystal fibers

We investigate how the strongly wavelength-dependent birefringence in nonlinear photonic crystal fibers leads to a splitting in the zero-dispersion wavelength for the two polarizations. We translate the requirements for the maximum splitting of the zero-dispersion wavelength to requirements for transverse structural uniformity by adopting a simple effective-index approach in which the birefringence is calculated in a step-index fiber with an elliptical core. We find that to reduce the splitting to less than 1 nm the birefringence should be less than 2 x 10(-5), resulting in a transverse uniformity requirement of 1-3%, depending on the index step from the core to the cladding.