Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

Letq be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) and GF(q) is at mostn ². In this paper, we show that, with the exception ofn = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactlyn ² points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3).This research was partially supported by the National Science Foundation under Grants DMS-8521826 and DMS-8500494.     

Diffusion of HDO in pure and acid-doped ice films

In these experiments, a few bilayers of D(2)O were vapor-deposited on a pure crystalline H(2)O ice film or an ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the D(2)O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the HDO from the initial HDO mixture layer to HDO isolated in the H(2)O ice film. This was possible because isolated HDO in H(2)O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H(2)O ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations up to 1 x 10(-4) mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) x 10(-4) mole fraction HCl with a concentration-independent rate constant. The diffusion under these conditions followed Arrhenius behavior for T = 135-145 K yielding E(a) = 25 +/- 5 kJ/mol. The mechanism for the HDO diffusion involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop and orientational turn steps. While these spectroscopic results compare favorably with recent studies of molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A comparison and discussion of the various diffusion studies are included in this report.     

Fast detection of triacetone triperoxide (TATP) from headspace using planar solid-phase microextraction (PSPME) coupled to an IMS detector

Triacetone triperoxide (TATP) is a high explosive synthesized from easily available reactants making it accessible for illicit uses. In this study, fast detection of TATP is achieved using a novel planar solid-phase microextraction (PSPME) as a preconcentration and sampling device for headspace analysis offering improved sensitivity and reduced sampling time over the conventional fiber-based solid-phase microextraction (SPME) when followed by ion mobility spectrometer (IMS) detection. Quantitation and comparison of the retention capabilities of PSPME as compared to the commercially available SPME were determined using TATP standards and analyzed using gas chromatography–mass spectrometry for SPME analysis and a commercial IMS with no instrumental modification for PSPME. Static and dynamic headspace extractions were used and compared for PSPME extractions, in which low milligram quantities of TATP were detected within 30 s of static mode sampling and less than 5 s in the dynamic mode sampling for PSPME–IMS.     

Matroids and Graphs with Few Non-Essential Elements

An essential element of a 3-connected matroid M is one for which neither the deletion nor the contraction is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In an earlier paper, the authors showed that a 3-connected matroid with at least one non-essential element has at least two such elements. This paper completely determines all 3-connected matroids with exactly two non-essential elements. Furthermore, it is proved that every 3-connected matroid M for which no single-element contraction is 3-connected can be constructed from a similar such matroid whose rank equals the rank in M of the set of elements e for which the deletion M\e is 3-connected.     

On removable cycles through every edge

Mader and Jackson independently proved that every 2‐connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G/E(C) is 2‐connected. This paper considers the problem of determining when every edge of a 2‐connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of two edges from G remains 2‐connected, then, not only is every edge in a removable cycle but, for every two edges, there are edge‐disjoint removable cycles such that each contains one of the distinguished edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 155–164, 2003     

Aromatic nitration using nitroguanidine and EGDN

Acid catalyzed nitration has been examined using a variety of novel nitration agents: guanidine nitrate (GN) and nitroguanidine (NQ) as well as the simple nitrate ester, ethylene glycol dinitrate (EGDN). Reactions with either activated or deactivated aromatic substrates proceed rapidly and in high yield. Regioselectivity was similar for all nitrating agents examined. The synthetic advantages of liquid EGDN include high solubility in organic solvents, strong nitration activity and ease of preparation.     

Computational aberration correction for an arbitrary linear imaging system

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schr?dinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.     

Mass spectral fragmentation pathways in cyclic difluoramino and nitro compounds

The recently synthesized compounds 4, 4-bis(difluoramino)-1-nitropiperidine (I), 1,4,4-trinitropiperidine (II), 1,1,4,4-tetranitrocyclohexane (III), 1,1,4, 4-tetrakis(difluoramino)cyclohexane (IV) and 3,3,7, 7-tetrakis(difluora-mino)octahydro-1,5-dinitro-1,5-diazocine (HNFX, V) are being considered as potential energetic materials. The mass spectra of these compounds were studied using electron ionization (EI) mass spectrometry. A collision-induced dissociation (CID) study of the major EI peaks was carried out using a Finnigan TSQ 700 tandem mass spectrometer. The mass fragmentation pathways are constructed and discussed. The decomposition of HNFX (V), under EI, appeared to parallel the thermal decomposition of nitramines where N-NO(2) cleavage is often the first step. However, the two nitramines with a six-membered ring structure (I and II) underwent initial loss of a geminal substituent; loss of a nitramine nitro group was the secondary step. The two cyclohexane structures (III and IV) showed similar initial fragmentation pathways, featuring successive losses of nitro or difluoramino groups. Copyright 2000 John Wiley & Sons, Ltd.     

Phase diagram of RDX (hexahydro-1,3,5-trinitro-s-triazine) at high pressures and temperatures

Abstract

The phase diagram of RDX-h₆ (hexahydro-1,3,5-trinito-s-triazine) and RDX-d₆ has been studied by Raman spectroscopy to more than 13 GPa at 295 K and 7.5 GPa between 150 and 450 K. Two stable high pressure phases have been found. γ-RDX or RDX-III forms from α-RDX above 3.8 GPa below 380 K. β-RDX forms when α- or γ-RDX are heated, can be retained metastably at low temperatues, and may be related to a very unstable form occasionally recovered at ambient pressure. Deuterium isotopic substitution and shear increase the temperature where β-RDX begins to form on heating.