Some Multiply Derived Translation Planes with SL(2,5) as an Inherited Collineation Group in the Translation Complement

Finite translation planes having a collineation group isomorphic to SL(2,5) occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2,5). The Hall plane and some of the planes discovered by Prohaska [10], see also [1], are translation planes of this kind of order q ²;, provided that q is odd and either q ²; 1 mod 5 or q is a power of 5. In this paper the case q ² -1 mod 5 is considered and some examples are constructed under the further hypothesis that either q 2 mod 3, or q 1 mod 3 and q 1 mod 4, or q -1 mod 4, 3 q and q 3,5 or 6 mod 7. One might expect that examples exist for each odd prime power q. But this is not always true according to Theorem 2.     

ASYMPTOTIC AND BIFURCATION ANALYSIS OF WAVE-PINNING IN A REACTION-DIFFUSION MODEL FOR CELL POLARIZATION

We describe and analyze a bistable reaction-diffusion (RD) model for two interconverting chemical species that exhibits a phenomenon of wave-pinning: a wave of activation of one of the species is initiated at one end of the domain, moves into the domain, decelerates, and eventually stops inside the domain, forming a stationary front. The second ("inactive") species is depleted in this process. This behavior arises in a model for chemical polarization of a cell by Rho GTPases in response to stimulation. The initially spatially homogeneous concentration profile (representative of a resting cell) develops into an asymmetric stationary front profile (typical of a polarized cell). Wave-pinning here is based on three properties: (1) mass conservation in a finite domain, (2) nonlinear reaction kinetics allowing for multiple stable steady states, and (3) a sufficiently large difference in diffusion of the two species. Using matched asymptotic analysis, we explain the mathematical basis of wave-pinning, and predict the speed and pinned position of the wave. An analysis of the bifurcation of the pinned front solution reveals how the wave-pinning regime depends on parameters such as rates of diffusion and total mass of the species. We describe two ways in which the pinned solution can be lost depending on the details of the reaction kinetics: a saddle-node or a pitchfork bifurcation.     

Resonance and localization effects at a dipolar organic semiconductor interface

The image state manifold of the dipolar organic semiconductor vanadyl naphthalocyanine (VONc) on highly oriented pyrolytic graphite is investigated by angle-resolved two-photon photoemission (AR-TPPE) spectroscopy in the 0-1 monolayer regimes. Interfacial charge-transfer from the image potential state of clean graphite populates a near-resonant VONc anion level, identifiable by the graphite image potential state by its distinct momentum dispersion obtained from AR-TPPE. This affinity level is subject to depolarization by the neighboring molecules, resulting in stabilization of this state with coverage. Near a coverage of one monolayer, a hybrid image potential/anion state is also formed, showing progressive localization with coverage. Intensities for all these features develop rather differently with molecular coverage, pointing towards the different types of charge-transfer interactions at play at this interface.     

Group divisible designs in MOLS of order ten

The maximum number of mutually orthogonal latin squares (MOLS) of order 10 is known to be between 2 and 6. A hypothetical set of four MOLS must contain at least one of the types of group divisible designs (GDDs) classified here. The proof is based on a dimension argument modified from work by Dougherty. The argument has recently led to the discovery of a counterexample to Moorhouse’s conjecture on the rank of nets, found by Howard and Myrvold. Although it is known that even three MOLS can admit no nontrivial symmetry group, we are hopeful this classification via GDDs and dimension can offer some structure to aid the eventual goal of exhausting the search for four MOLS of order 10.     

Linear astral configurations with dihedral symmetry

A linear astral (n_k) configuration is a collection of points and straight lines, so that each point lies on k lines and each line passes through k points, with symmetry (transitivity) classes of points and lines under rotations and reflections mapping the configuration to itself. We discuss the possible structures of astral (n₅) configurations with dihedral symmetry group D_m in the Euclidean plane, and we provide methods to investigate the existence of such configurations. In doing so, we introduce a new class of astral (n₃) configurations.     

Denitration of nitroaromatic compounds by arylnitrile radical cations

Substituted nitrobenzenes react with substituted benzonitrile radical cations in an ion trap mass spectrometer by a novel ion/molecule reaction involving NO2 elimination. Formation of an arylated nitrile, Ar1+N identical to CAr2 (where Ar1, Ar2 = aryl), is indicated by collision induced dissociation and comparison with the behavior of the authentic ion. Ab initio calculations (MP2/6-31G*/ /HF/6-31G*) show the reaction of the unsubstituted compounds (Ar1, Ar2 = phenyl) to be exothermic by 48 kcal/mol, consistent with the experimental observation that the reaction rate decreases as the collision energy is increased. Electron withdrawing and donating substituents on either the ionic or the neutral reagent have little effect on the relative amount of product observed, pointing to a radical mechanism. Related denitration reactions were found to occur, between nitrobenzene and its radical cation and between phenylisonitrile and ionized nitrobenzene. These reactions are suggested to yield Ar1+N(= O)OAr2 and Ar2+N identical to CAr1, respectively. The denitration reaction was applied to trinitrotoluene (TNT) as a possible diagnostic reaction for the presence of nitroaromatic explosives.     

Naphthyl-l-α-amino acids via chemo-enzymatic dynamic kinetic resolution

A double catalyst system (protease + base) was applied to the dynamic kinetic resolution (DKR) of isomeric 1- and 2-α-naphthyl-glycines and -alanines exploiting the in situ racemization of their thioesters. Due to the different C-acidity of the two sets of compounds, different experimental conditions have been devised to perform the simultaneous resolution/racemization process.In all cases, the racemic N-Boc-thioesters were converted into the aminoacids with an l-configuration almost quantitatively and with complete enantioselectivity.     

Gas-phase reactions for selective detection of the explosives TNT and RDX

Highly selective gas-phase reactions with ethyl vinyl ether (EVE) of major electron (EI) and chemical ionization (CI) fragment ions of the explosives TNT and RDX have been uncovered. The fragment ion of m/z 210 from TNT undergoes [4(+)+ 2] cycloaddition with EVE to form an oxo-iminium ion of m/z 282, which dissociates by acetaldehyde loss after a [1,5-H] shift to form a quinolynium ion of m/z 238. The fragment ion of m/z 149 from RDX reacts with EVE by a formal vinylation reaction, that is, the elusive cyclic adduct loses ethanol to yield a nitro-iminium ion of m/z 175, which reacts further with EVE to form a second cyclic product ion of m/z 247. Calculations and MS/MS experiments support the proposed structures. These highly characteristic reactions of diagnostic EI and CI fragment ions improve selectivity for TNT and RDX detection.     

Solvent-free Mukaiyama and Mukaiyama-Michael vinylogous reactions of a dioxinone-derived silyl enol ether promoted by Lewis bases

The vinylogous aldol-type addition of a dienolsilyl ether, derived from 2,2,6-trimethyl-4H-1,3-dioxin-4-one, showed to occur with complete γ-selectivity by enolate activation promoted by neutral Lewis bases under solvent-free conditions. Moderate to high yields were obtained with aromatic, hetero-aromatic, and aliphatic aldehydes, as well as activated ketones. Under the same conditions and in the absence of catalyst, the first Mukaiyama-Michael addition of the masked acetoacetate ester to α,β-unsaturated aldehydes took place in satisfactory way.