2,864,661 research outputs found
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 for every u \in
\bS(\cH). is Hermitean when is real. No boundedness requirement is
thus assumed on {\em a priori}.Comment: 9 pages, Accepted for publication in Ann. H. Poincar\'
âUser-friendlyâ primary phosphines and an arsine: synthesis and characterization of new air-stable ligands incorporating the ferrocenyl group
Reaction of FcCHâCHâP(O)(OH)â or FcCHâP(O)(OH)(OEt) [Fc=Fe(ηâ”-Câ
Hâ)(ηâ”-Câ
Hâ
)] with excess CHâNâ followed by reduction with MeâSiClâLiAlHâ gives the air-stable primary phosphines FcCHâCHâPHâ and the previously reported analogue FcCHâPHâ in high yields. Reduction of 1,1âČ-FcâČ[CHâP(O)(OEt)â] [FcâČ=Fe(ηâ”-Câ
Hâ)â] and 1,2-Fcâł[CHâP(O)(OEt)â] [Fcâł=Fe(ηâ”-Câ
Hâ
)(ηâ”-Câ
Hâ)] similarly gives the new primary phosphines 1,1âČ-FcâČ(CHâPHâ)â and 1,2-Fcâł(CHâPHâ)â, respectively. The arsine FcCHâCHâAsHâ, which is also air-stable, has been prepared by reduction of the arsonic acid FcCHâCHâAs(O)(OH)â using Zn/HCl. An X-ray structure has been carried out on the arsine, which is only the second structure determination of a free primary arsine. The molybdenum carbonyl complex [1,2-Fcâł(CHâPHâ)âMo(CO)â] was prepared by reaction of the phosphine with [Mo(CO)â(pip)â] (pip=piperidine), and characterized by a preliminary X-ray structure determination. However, the same reaction of 1,1âČ-FcâČ(CHâPHâ)âwith [Mo(CO)â(pip)â] gave [1,1âČ-FcâČ(CHâPHâ)âMo(CO)â] and the dimer [1,1âČ-FcâČ(CHâPHâ)âMo(CO)â]â, characterized by electrospray mass spectrometry. 1,1âČ-FcâČ[CHâPHâMo(CO)â
]â and 1,2-Fcâł[CHâPHâMo(CO)â
]â were likewise prepared from the phosphines and excess [Mo(CO)â
(THF)]
Ferrocenyl hydroxymethylphosphines (ηâ”-Câ Hâ )Fe[ηâ”â»Câ HâP(CHâOH)â] and 1,1âČ-[Fe{ηâ”-Câ HâP(CHâOH)â}â] and their chalcogenide derivatives
The ferrocenyl hydroxymethylphosphines FcP(CHâOH)â [Fc=(ηâ”-Câ
Hâ
)Fe(ηâ”-Câ
Hâ)] and 1,1âČ-FcâČ[P(CHâOH)â]â [FcâČ=Fe(ηâ”â»Câ
Hâ)â] were prepared by reactions of the corresponding primary phosphines FcPHâ and 1,1âČ-FcâČ(PHâ)â with excess aqueous formaldehyde. The crystal structure of FcP(CHâOH)â was determined and compared with the known ferrocenyl hydroxymethylphosphine FcCHâP(CHâOH)â. The chalcogenide derivatives FcP(E)(CHâOH)â and 1,1âČ-FcâČ[P(E)(CHâOH)â]â (E=O, S, Se) were prepared and fully characterised. Crystal structure determinations on FcP(O)(CHâOH)â and FcP(S)(CHâOH)â were performed, and the hydrogen-bonding patterns are compared with related compounds. The sulfide shows no hydrogen-bonding involving the phosphine sulfide group, in contrast to other reported ferrocenyl hydroxymethylphosphine sulfides. The platinum complex cis-[PtClâ{FcP(CHâOH)â}â] was prepared by reaction of 2 mol equivalents of FcP(CHâOH)â with [PtClâ(1,5-cyclo-octadiene)], and was characterised by 31P-NMR spectroscopy and negative ion electrospray mass spectrometry, which gave a strong [M+Cl]â» ion
Derivation of tropospheric methane from TCCON CHâ and HF total column observations
The Total Carbon Column Observing Network (TCCON) is a global ground-based network of Fourier transform spectrometers that produce precise measurements of column-averaged dry-air mole fractions of atmospheric methane (CHâ). Temporal variability in the total column of CHâ due to stratospheric dynamics obscures fluctuations and trends driven by tropospheric transport and local surface fluxes that are critical for understanding CHâ sources and sinks. We reduce the contribution of stratospheric variability from the total column average by subtracting an estimate of the stratospheric CHâ derived from simultaneous measurements of hydrogen fluoride (HF). HF provides a proxy for stratospheric CHâ because it is strongly correlated to CHâ in the stratosphere, has an accurately known tropospheric abundance (of zero), and is measured at most TCCON stations. The stratospheric partial column of CHâ is calculated as a function of the zonal and annual trends in the relationship between CHâ and HF in the stratosphere, which we determine from ACE-FTS satellite data. We also explicitly take into account the CHâ column averaging kernel to estimate the contribution of stratospheric CHâ to the total column. The resulting tropospheric CHâ columns are consistent with in situ aircraft measurements and augment existing observations in the troposphere
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,â) â 1/2_(1,+)) and CH^+(J = 1â0, J = 2â1) 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
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+, H2O+, 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(JF,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.Comment: Accepted for publication in Astronomy and Astrophysics (HIFI first
results issue
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