Upper classes for the increments of the fractional Wiener process

Summary LetX(t) be a fractional Wiener process, i.e., a centered Gaussian process on [0, ) with stationary increments and varianceEX ² (t)=t ², anda(t) a positive nondecreasing function witha(t)t. We investigate the a.s. asymptotic behaviour of the incrementsI(t, a (t))=max{X{u+a(t))–X(u): 0ut–a(t)} (and some others that are similarly defined) ast.     

Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.     

Tetrakis(diethyl‐phosphonat)‐, Tetrakis(ethyl‐phenylphosphinat)‐ und Tetrakis(diphenylphosphin‐oxid)‐substituierte Phthalocyanine

Tetrakis(diethyl phosphonate), Tetrakis(ethyl phenylphosphinate)‐, and Tetrakis(diphenylphosphine oxide)‐Substituted Phthalocyanines The title compounds 7, 9 , and 11 are obtained by tetramerization of diethyl (3,4‐dicyanophenyl)phosphonate ( 5 ), ethyl (3,4‐dicyanophenyl)phenylphosphinate ( 8 ), and 4‐(diphenylphosphinyl)benzene‐1,2‐dicarbonitrile ( 10 ). The ³¹P‐NMR spectra of the phthalocyanines 7, 9 , and 11 and of their metal complexes present five to eight signals confirming the formation of four constitutional isomers with the expected C_4h, D_2h, C_2v, and C_s symmetry. In the FAB‐MS of the Zn, Cu, and Ni complexes of 7 and 9 , the peaks of dimeric phthalocyanines are observed. By gel‐permeation chromatography, the monomeric complex [Ni( 7 )] and a dimer [Ni( 7 )]₂ can be separated. These dimers differ from the known phthalocyanine dimers, i.e., possibly the P(O)(OEt)₂ and P(O)(Ph)(OEt) substituents in 7 and 9 are involved in complexation. The free phosphonic acid complex [Zn( 12 )] and [Cu( 12 )] are H₂O‐soluble. In the FAB‐MS of [Zn( 12 )], only the peaks of the dimer are present; the ESI‐MS confirms the existence of the dimer and the metal‐free dimer. In the UV/VIS spectrum of [Zn( 12 )], the hypsochromic shift characteristic for the known type of dimers from 660–700 nm to 620–640 nm is observed. As in the FAB‐MS of [Zn( 12 )], the free phosphinic acid complex [Zn( 13 )] shows only the monomer, an ESI‐MS cannot be obtained for solubility problems. The UV/VIS spectrum of [Zn( 13 )] demonstrates the existence of the monomer as well as of the dimer.     

Influence of surface structure on surface analytical statements

The influence of surface structure of technical materials on results and statements of surface analytical methods has been investigated. Especially surface roughness as a typical property of rolled products has been observed. For this purpose samples of steel (technical surface, roughness up to 5 m) and silicon wafers (polished surface) have been analyzed by SNMS and GDOS in order to get information about changes of the surface roughness as function of the sputtering time and their influence on the statements about the depth profiles obtained.     

Some aspects of tailoring flame retardancy in HET-acid-based flame retardants

HET acid was condensed with either ethylene glycol or 1,4-butanediol to yield the respective oligoesters. These oligoesters were characterized by molecular weight, measured by vapor-pressure osmometry. The degradation mechanism of oligoesters of HET acid with either ethylene glycol or 1,4-butanediol was elucidated. The thermal properties of these polyesters were studied using differential thermal analysis and thermal volatilization analysis. The mechanism of degradation was proposed on the basis of pyrolysis–gas chromatography studies, the degradation products being subsequently identified by mass spectrometry. It turned out that in the course of decomposition, hexachlorocyclopentadiene was formed, which is believed to be the active substance for flame retardance in these systems. The aspect of tailoring flame retardancy by changing the chemical environment, i.e., by using different diols, is discussed.     

Thermoconversion of Caryophyllene- to Farnesene-Type Sesquiterpenes. Short access to the enantiomers of (6RS,7RS)- and (6RS,7SR)-6,7-epoxy-6,7-dihydro-β-farnesenes

Flash-vacuum thermolysis of the four diastereoisomeric 5,6-epoxy-5,6-dihydro-caryophyllenes 1–4 at 500–550°/0.1–0.7 Torr leads to the hitherto unreported enantiomers of (6RS,7RS)- and (6RS,7SR)-6,7-epoxy-6,7-dihydro-β-farnesenes ((±)- 5 and (±)- 6 , resp.). In particular, (+)- 5 is formed in 45% yield (ca. 90% ee) and is, thus, an attractive chiral building block for natural-product synthesis.     

Mössbauer studies of thiospinels. V. The systems Cu1−xFexMe2S4 (Me = Cr, Rh) and Cu1−xFexCr2(S0.7Se0.3)4

With the exception of FeRh₂S₄, powder samples of all systems studied have been obtained as spinel phase without essential impurities. The lattice constants follow Vegard's law. From the Seebeck coefficients and the Mössbauer spectra the valence distribution Cu¹⁺_1−xFe²⁺_2x−1Fe³⁺_1−x[Me³⁺₂]X²⁻₄ is derived for 0.5 x 1, while there is only Fe³⁺ present for 0 < x 0.5. Samples with the overall composition FeRh₂S₄ contain mostly Rh₂S₃ and iron sulfide phases, but less than 20% of a spinel phase.     

Bestimmung des Metabolismus und der Produktionsrate von Testosteron, Dehydroepiandrosteron und Dehydroepiandrosteronsulfat

Zusammenfassung Nach i.v. Injektion von 4–6 Ci¹⁴C-Testosteron und 7–8 Ci³H-Androstendion oder entsprechenden Mengen¹⁴C-Dehydroepiandrosteron und³H-Dehydroepiandrosteronsulfat wurden die Glucuronide von Testosteron, Androsteron, Ätiocholanolon und Dehydroepiandrosteron sowie Dehydroepiandrosteronsulfat säulen- (Al₂O₃), papier- (Bush A₂) und dünnschicht-chromatographisch (Chloroform/Äthylacetat 41) aus Urin abgetrennt und gas-chromatographisch (1% XE-60, Flammenionisationsdetektor) bestimmt. Nach splitting des Trägergases und Kondensation der gasförmigen Steroide in einem wattegefüllten Glasröhrchen eines Gasfraktionskollektors wurde die¹⁴C- und³H-Aktivität der einzelnen Androgenmetaboliten mit einem Müssigkeitsszintillationszähler gemessen und aus der spezifischen Aktivität (Impulse/Mikrogramm) die Produktions- und Interkonversionsraten von Testosteron, DHEA und DHEA-Sulfat berechnet.

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Determination of the metabolism and production rates androstendione of testosterone, dehydroepiandrosterone, and dehydroepiandrosterone sulphate

After the i.v. application of 4–6 Ci¹⁴C-testosterone and 7–8 Ci³H-androstendione or equivalent dosages of tritium dehydroepiandrosterone sulphate and dehydroepiandrosterone the gluouronides of testosterone, etiocholanolone, androsterone and dehydroepiandrosterone and dehydroepiandrosterone sulphate were separated from urine by column (Al₂O₃), paper (system Bush A₂) and thin-layer (chloroform:ethylacetate=41) chromatography. After a final gas-liquid chromatography on 1% XE-60 the androgen metabolites were estimated quantitatively by flame-ionisation detector. The radioactivity (³H and¹⁴C impulses) of the compounds was measured after splitting the carrier gas and condensation of the steroids in a gas-fraction collector. From the specific activity (Imp/g) the production and interconversion rates of testosterone, dehydroepiandrosterone and dehydroepiandrosterone sulphate were calculated.

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Die Arbeit wurde mit Mitteln des Bundesministeriums für Wissenschaftliche Forschung gefördert.     

Determination of butyltins in environmental samples using sodium tetraethylborate derivatisation: characterisation and minimisation of interferences

Interferences affecting the determination of butyltin species by sodium tetraethylborate (STEB) derivatisation followed by purge-trap preconcentration were systematically studied using synthetic solutions, natural water samples and sediment extracts. Substances that did not cause interferences included most common cations (apart from those metal ions listed below), anions, metalloids and polar organic compounds. Natural organic matter (NOM) specifically interfered with tributyltin (TBT) due to a mechanism involving partitioning of the butyltin to the hydrophobic portions of the NOM. The metal ions Ag(I) (≥2 μM), Cd(II) (≥2 μM), Cu(II) (≥0.5 μM) interfered predominantly with the determination of monobutyltin (MBT) due to catalytic degradation of the STEB reagent. Pb(II) (≥14 μM) interfered with butyltin determination by an unknown mechanism. Other interferences to the purge-trap method were shown to occur in the presence of chelating agents (e.g. EDTA) or hydrophobic liquids such as diesel fuel. A mixture comprising methanol (MeOH), EDTA and Mn(II) was used to partially mask the effect of interfering NOM and metals. Spike recoveries (mean±S.D. of n=7 different samples) of MBT, dibutyltin (DBT) and TBT in contaminated natural water samples were improved from 70±36,90±11 and 91±24 to 102±10,98±3 and 98±4%, respectively. Spike recoveries (mean±S.D. of n=5 different samples) of MBT, DBT and TBT in aliquots of sediment extracts were improved from 86±17,79±18 and 59±32 to 97±6.2,103±3.6 and 103±5.0%, respectively. The ability to analyse larger aliquots of sediment extracts in the presence of the masking mixture improved the detection limit four-fold if MBT and DBT determination was required and 10-fold if only TBT determination was required.