Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004     

Primitive Groups with no Regular Orbits on the Set of Subsets

We determine all primitive groups which do not have a regularorbit on the power set of the permutation domain. As a corollary,we also determine all families of orbit equivalent primitivepermutation groups. 1991 Mathematics Subject Classification20B15.     

Maximal triangle-free graphs with restrictions on the degrees

We investigate the problem that at least how many edges must a maximal triangle-free graph on n vertices have if the maximal valency is ≤D. Denote this minimum value by F(n, D). For large enough n, we determine the exact value of F(n, D) if D ≥ (n ? 2)/2 and we prove that lim F(n, cn)/n = K(c) exists for all 0 < c with the possible exception of a sequence c_k → 0. The determination of K(c) is a finite problem on all intervals [γ, ∞). For D = cn^?, 1/2 < ? < 1, we give upper and lower bounds for F(n, D) differing only in a constant factor. (Clearly, D < (n - 1)^1/2 is impossible in a maximal triangle-free graph.)     

Modeling the cluster formation during infrared and ultraviolet matrix-assisted laser desorption ionization of oligonucleotides in succinic acid matrix with molecular mechanics

A large succinic acid (HOOC(CH₂)₂COOH) matrix containing 7 × 7 × 7 unit cells with guest oligonucleotide AGCAGCT was modeled with molecular dynamics simulation for infrared matrix-assisted laser desorption ionization. We simulated the laser heating of the succinic acid (this data is still missing from the literature) with λ=2.94 μm infrared laser pulses and compared it to ultraviolet excitation. We did this in order to elucidate the cluster formation of succinic acid in the gas phase in itself and around the analyte. At this wavelength, the laser energy is coupled into the matrix through the OH vibrations of the carboxyl groups. The most pronounced difference we observed at 1,500 K simulation is that infrared heating generates about 10–15 more succinic acid molecules bound to the analyte in noncovalent complex form than the ultraviolet mode, which generates about 2 molecules thus bound. We report energy redistribution within the matrix between the host and guest species as well as other dynamical properties. The parameter and topology data for succinic acid that we used are reported and ready for use in CHARMM computer code environment for simulation. Revised: 12 October 2001 / Accepted: 27 February 2002 / Published online: 13 June 2002     

Laser microprobe mass spectrometry of quaternary phosphonium salts: Direct versus matrix-assisted laser desorption

The use of laser microprobe mass spectrometry (LMMS) for the structural characterization of thermolabile quaternary phosphonium salts has been evaluated. A comparison has been made between LM mass spectra obtained by direct analysis of “neat” organic salts and the corresponding “matrix-assisted” LM mass spectra. Main limitations of LMMS for the direct analysis of neat organic salts (i.e., no matrix) result from (1) formation of artifact ions that originate from thermal degradation and surface recombination reactions and (2) poor shot-to-shot reproducibility of the spectra. Dilution of the organic salts in a suitable, UV-absorbing matrix (e.g., nicotinic acid) significantly enhances the quality of the LM mass spectra. Improvements are: (1) an increase of the ion yield of preformed cations, (2) reduction or elimination of thermal decomposition and other deleterious surface reactions, and (3) a much better shot-to-shot spectral reproducibility. An interesting analytical feature is that these LM mass spectra, which contain only a few matrix peaks, can be obtained for subnanogram amounts of sample. The results also show that triphenylphosphonium salts with polycyclic aromatic substituents can be used as “molecular thermometers” to probe both the temperatures experienced by the sample molecules during the laser-induced desorption ionization process and the internal energies of the desorbed ion species. In this way, quaternary phosphonium salts can be used for evaluating whether improvements have been achieved by applying different sample treatments. Comparison of four different matrices (i.e., nicotinic acid, ammonium chloride, glycerol, and 3-nitrobenzylalcohol) indicates that the effectiveness of a matrix to reduce thermal degradation and to decrease the internal energies of the ions depends on the UV-absorption characteristics and the volatilization/sublimation temperature of the matrix material.     

Multi‐Pathway Excited State Relaxation of Adenine Oligomers in Aqueous Solution: A Joint Theoretical and Experimental Study

The singlet excited states of adenine oligomers, model systems widely used for the understanding of the interaction of ultraviolet radiation with DNA, are investigated by fluorescence spectroscopy and time‐dependent (TD) DFT calculations. Fluorescence decays, fluorescence anisotropy decays, and time‐resolved fluorescence spectra are recorded from the femtosecond to the nanosecond timescales for single strand (dA)₂₀ in aqueous solution. These experimental observations and, in particular, the comparison of the fluorescence behavior upon UVC and UVA excitation allow the identification of various types of electronic transitions with different energy and polarization. Calculations performed for up to five stacked 9‐methyladenines, taking into account the solvent, show that different excited states are responsible for the absorption in the UVC and UVA spectral domains. Independently of the number of bases, bright excitons may evolve toward two types of excited dimers having π–π* or charge‐transfer character, each one distinguished by its own geometry and spectroscopic signature. According to the picture arising from the joint experimental and theoretical investigation, UVC‐induced fluorescence contains contribution from 1) exciton states with a different degree of localization, decaying within a few ps, 2) “neutral” excited dimers decaying on the sub‐nanosecond timescale, being the dominant species, and 3) charge‐transfer states decaying on the nanosecond timescale. The majority of the photons emitted upon UVA excitation are related to charge‐transfer states.     

The Molecular Composition of Soot

Soot (sometimes referred to as black carbon) is produced when hydrocarbon fuels are burned. Our hypothesis is that polynuclear aromatic hydrocarbon (PAH) molecules are the dominant component of soot, with individual PAH molecules forming ordered stacks that agglomerate into primary particles (PP). Here we show that the PAH composition of soot can be exactly determined and spatially resolved by low‐fluence laser desorption ionization, coupled with high‐resolution mass spectrometry imaging. This analysis revealed that PAHs of 239–838 Da, containing few oxygenated species, comprise the soot observed in an ethylene diffusion flame. As informed by chemical graph theory (CGT), the vast majority of species observed in the sampled particulate matter may be described as benzenoids, consisting of only fused 6‐membered rings. Within that limit, there is clear evidence for the presence of radical PAH in the particulate samples. Further, for benzenoid structures the observed empirical formulae limit the observed isomers to those which are nearly circular with high aromatic conjugation lengths for a given aromatic ring count. These results stand in contrast to recent reports that suggest higher aliphatic composition of primary particles.     

Assessment of laser-induced thermal load on silicon nanostructures based on ion desorption yields

Experimental assessment of the thermal load induced by fast laser pulses on micro- and nanostructures through IR imaging is currently too slow and lacks the spatial resolution to be useful. In this paper, we introduce a method based on measuring the laser-induced yields of ions to compare the thermal loads on nanofabricated silicon structures, when exposed to nanosecond laser pulses. The laser fluences at which the ion yields of, for example, sodiated and potassiated peptides ions are equal for two different structures correspond to equivalent thermal loads. Using alkalinated peptides is a convenient choice because the corresponding ion intensities are easily measured up to the melting point of silicon. As an example, we compare the nanosecond laser heating of silicon nanopost arrays with diverse post diameters and periodicities. Assessment of the thermal load through ion yield measurements can also be used to verify model assumptions for heat transport regimes in nanostructures.     

Nearly Linear Time Algorithms for Permutation Groups: An Interplay Between Theory and Practice

We survey polynomial time algorithms (both deterministic and random) for computations with permutation groups. Particular emphasis is given to algorithms with running time of the form O(n log ^c |G|), where G is a permutation group of degree n. In the case of small-base groups, i.e., when log |G| is polylogarithmic as a function of n, such algorithms run in nearly linear, O(n log^c' n) time. Important classes of groups, including all permutation representations of simple groups except the alternating ones, as well as most primitive groups, belong to this category. For large n, the majority of practical computations is carried out on small-base groups.In the last section, we present some new nearly linear time algorithms, culminating in the computation of the upper central series in nilpotent groups.