Methyl chloride and the U.S. cigarette.

Various brands and types of cigarettes were purchased at retail locations in southern California. Volatile gas samples were analyzed using multicolumn/multidetector gas chromatography. Results showed methyl chloride (CH(3)Cl) levels as much as four orders of magnitude higher than typical urban levels, about 30-500 ppmv (1.5-5.3 mg/cigarette), compared with about 500 pptv in urban air. The concentration of CH(3)Cl correlated well with the levels of both CO (r (2) = 0.63) and CO(2) (r (2) = 0.77), showing the link between CH(3)Cl and combustion. In some brands, CH(3)Cl levels were well above the U.S. Environmental Protection Agency's maximum exposure limit of 200 ppmv. Light branded cigarettes tended to have higher CH(3)Cl levels than the heavier and filtered brands, possibly showing the dependence of cigarette packing on CH(3)Cl production. In addition, CH(3)Cl emitted from cigarette smoke may prove to be an important anthropogenic source of CH(3)Cl in the United States, at about 5%

New ferrocene-derived hydroxymethylphosphines: FcP(CH₂OH)₂ [Fc=(η⁵-C₅H₅)Fe(η⁵-C₅H₄)] and the dppf analogue 1,1′-Fc′[P(CH₂OH)₂]₂ [Fc′=Fe(η⁵-C₅H₄)₂]

Reactions of the ferrocene-phosphines FcPH₂ and 1,1′-Fc′(PH₂)₂ with excess formaldehyde gives the new hydroxymethylphosphines FcP(CH₂OH)₂ 1 and 1,1′-Fc′[P(CH₂OH)₂]₂ 2, respectively. Phosphine 1 is an air-stable crystalline solid, whereas 2 is isolated as an oil. Reaction of 1 with H₂O₂, S₈ or Se gives the chalcogenide derivatives FcP(E)(CH₂OH)₂ (E=O, S or Se), whilst reaction of 2 with S8 gives 1,1′-Fc′[P(S)(CH₂OH)₂]₂, which were fully characterised. Phosphine 1 was also characterised by an X-ray crystal structure determination

A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions

An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.Comment: 15 pages, 16 figures, some typos correcte

Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem

Consider a finite dimensional complex Hilbert space \cH, with dim(\cH) \geq 3, define \bS(\cH):= \{x\in \cH \:|\: ||x||=1\}, and let \nu_\cH be the unique regular Borel positive measure invariant under the action of the unitary operators in \cH, with \nu_\cH(\bS(\cH))=1. We prove that if a complex frame function f : \bS(\cH)\to \bC satisfies f \in \cL^2(\bS(\cH), \nu_\cH), then it verifies Gleason's statement: There is a unique linear operator A: \cH \to \cH such that $f(u) =$ for every u \in \bS(\cH). $A$ is Hermitean when $f$ is real. No boundedness requirement is thus assumed on $f$ {\em a priori}.Comment: 9 pages, Accepted for publication in Ann. H. Poincar\'

A Jost-Pais-type reduction of Fredholm determinants and some applications

We study the analog of semi-separable integral kernels in \cH of the type {equation*} K(x,x')={cases} F_1(x)G_1(x'), & a<x'< x< b, \\ F_2(x)G_2(x'), & a<x<x'<b, {cases} {equation*} where $-\infty\leq a<b\leq \infty$, and for a.e.\ $x \in (a,b)$, F_j (x) \in \cB_2(\cH_j,\cH) and G_j(x) \in \cB_2(\cH,\cH_j) such that $F_j(\cdot)$ and $G_j(\cdot)$ are uniformly measurable, and {equation*} \|F_j(\cdot)\|_{\cB_2(\cH_j,\cH)} \in L^2((a,b)), \; \|G_j (\cdot)\|_{\cB_2(\cH,\cH_j)} \in L^2((a,b)), \quad j=1,2, {equation*} with \cH and \cH_j, $j=1,2$, complex, separable Hilbert spaces. Assuming that $K(\cdot, \cdot)$ generates a trace class operator \bsK in L^2((a,b);\cH), we derive the analog of the Jost-Pais reduction theory that succeeds in proving that the Fredholm determinant {\det}_{L^2((a,b);\cH)}(\bsI - \alpha \bsK), \alpha \in \bbC, naturally reduces to appropriate Fredholm determinants in the Hilbert spaces \cH (and \cH_1 \oplus \cH_2). Explicit applications of this reduction theory are made to Schr\"odinger operators with suitable bounded operator-valued potentials. In addition, we provide an alternative approach to a fundamental trace formula first established by Pushnitski which leads to a Fredholm index computation of a certain model operator.Comment: 50 pages; some typos remove

Herschel/HIFI observations of spectrally resolved methylidyne signatures toward the high-mass star-forming core NGC6334I

In contrast to extensively studied dense star-forming cores, little is known about diffuse gas surrounding star-forming regions. We study molecular gas in the high-mass star-forming region NGC6334I, which contains diffuse, quiescent components that are inconspicuous in widely used molecular tracers such as CO. We present Herschel/HIFI observations of CH toward NGC6334I observed as part of the CHESS key program. HIFI resolves the hyperfine components of its J=3/2-1/2 transition, observed in both emission and absorption. The CH emission appears close to the systemic velocity of NGC6334I, while its measured linewidth of 3 km/s is smaller than previously observed in dense gas tracers such as NH3 and SiO. The CH abundance in the hot core is 7 10^-11, two to three orders of magnitude lower than in diffuse clouds. While other studies find distinct outflows in, e.g., CO and H2O toward NGC6334I, we do not detect outflow signatures in CH. To explain the absorption signatures, at least two absorbing components are needed at -3.0 and +6.5 km/s with N(CH)=7 10^13 and 3 10^13 cm^-2. Two additional absorbing clouds are found at +8.0 and 0.0 km/s, both with N(CH)=2 10^13 cm^-2. Turbulent linewidths for the four absorption components vary between 1.5 and 5.0 km/s in FWHM. We constrain physical properties of our CH clouds by matching our CH absorbers with other absorption signatures. In the hot core, molecules such as H2O and CO trace gas that is heated and dynamically influenced by outflow activity, whereas CH traces more quiescent material. The four CH absorbers have column densities and turbulent properties consistent with diffuse clouds: two are located near NGC6334, and two are unrelated foreground clouds. Local density and dynamical effects influence the chemical composition of physical components of NGC6334, causing some components to be seen in CH but not in other tracers, and vice versa.Comment: Accepted by A&A Letters; 5 pages, 1 figure; v2: minor textual and typographical change

Herschel/HIFI detections of hydrides towards AFGL 2591: Envelope emission versus tenuous cloud absorption

The Heterodyne Instrument for the Far Infrared (HIFI) onboard the Herschel Space Observatory allows the first observations of light diatomic molecules at high spectral resolution and in multiple transitions. Here, we report deep integrations using HIFI in different lines of hydrides towards the high-mass star forming region AFGL 2591. Detected are CH, CH^+, NH, OH^+, H_2O^+, while NH^+ and SH^+ have not been detected. All molecules except for CH and CH^+ are seen in absorption with low excitation temperatures and at velocities different from the systemic velocity of the protostellar envelope. Surprisingly, the CH(J_(F,P) = 3/2_(2,−) − 1/2_(1,+)) and CH^+(J = 1−0, J = 2−1) lines are detected in emission at the systemic velocity. We can assign the absorption features to a foreground cloud and an outflow lobe, while the CH and CH^+ emission stems from the envelope. The observed abundance and excitation of CH and CH^+ can be explained in the scenario of FUV irradiated outflow walls, where a cavity etched out by the outflow allows protostellar FUV photons to irradiate and heat the envelope at larger distances driving the chemical reactions that produce these molecules