THE NUMERICAL STABILITY OF THE θ-METHOD FOR DELAYDIFFERENTIAL EQUATIONS WITH MANY VARIABLEDELAYS

1.IntroductionInthispaper,wewillinvestigatethenumericalsolutionsofthefollowinginitialvalueproblemsforDDEswithmanyvariabledelayswherea,bl,b2,...,bmandcoEC,0相似文献   

Energy spectrum of cosmic-ray neutrinos in the atmosphere

Summary The energy spectrum of cosmic-ray neutrinos in the atmosphere has been calculated for the neutrino energy from 0.2 GeV to 10⁸ GeV by taking into account the results of p-p collision, p-nucleus collision, nucleus-nucleus collision, the energy spectrum of primary cosmic rays, momentum spectrum and charge ratio of cosmic-ray muons measured by MUTRON, and the production of prompt neutrinos in the decay of charmed particles. Our result on neutrino intensity is in good agreement with the result of Osborneet al. for the horizontal direction if their muon spectrum has been corrected, and also with the result of Volkova for the vertical direction except for the lower energies. For the horizontal direction the intensity of prompt muon-neutrinos exceeds that of muonneutrinos from the conventional processes at the neutrino energy of 10⁶ GeV and also the intensity of prompt electron-neutrinos exceeds that of electron-neutrinos from the conventional processes at the energy of 10⁵ GeV. The corresponding values for the vertical direction are 10⁵ GeV and 10⁴ GeV, respectively. In the energy region from 0.3 GeV to 3 GeV, the expected value for the ratio of intensity of electron-neutrino to that of muon-neutrino is obtained as 0.42±0.08 and this is excellent agreement with the experimental value 0.36±0.13 of NUSEX group.

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Riassunto è stato calcolato lo spettro d’energia dei neutrini dei raggi cosmici nell’atmosfera per un’energia neutrinica da 0.2 a 10⁸ GeV tenendo conto dei risultati delle collisioni p-p, p-nucleo, nucleo-nucleo, dello spettro d’energia dei raggi cosmici primari, dello spettro dell’impulso e del rapporto di carica dei muoni dei raggi cosmici misurato da MUTRON e dalla produzione di neutrini pronti nel decadimento di particelle con charm. Il nostro risultato sull’intensità dei neutrini è in buon accordo con il risultato di Osborneet al. per la direzione orizzontale se il loro spettro muonico viene corretto, ed anche con il risultato di Volkova per la direzione verticale tranne che per le energie piú basse. Per la direzione orizzontale l’intensità dei neutrini muonici pronti è maggiore di quella dei neutrini muonici che derivano dai processi convenzionali ad energia neutrinica di 10⁶ GeV ed anche l’intensità dei neutrini elettronici pronti è maggiore di quella dei neutrini elettronici che derivano dai processi convenzionali all’energia di 10⁵ GeV. I valori corrispondenti per la direzione verticale sono rispettivamente 10⁵ e 10⁴ GeV. Nella regione d’energia tra 0.3 e 3 GeV, il valore atteso ottenuto per il rapporto tra l’intensità dei neutrini elettronici e quella dei neutrini muonici è 0.42±0.08 e questo è in accordo eccellente con il valore sperimentale 0.36±0.13 del gruppo NUSEX.

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Ёнергетический спектр нейтрино космических лучей в атмосфере

Резюме Вычисляется Энергетический спектр нейтрино космических лучей в атмосфере для Энергий нейтрино от 0.2 ГЭВ до 10⁸ ГЭВ, учитывая р-р соударения, р-ядерные соударения, ядерно-ядерные соударения, Энергетический спектр первичных космических лучей, импульсный спектр и зарядовое отнощение мюонов космических лучей, измеренных с помошью МUTRON, и образование нейтрино в распадах очарованных частиц. Нащ результат для интенсивности нейтрино хорощо согласуется с результатом Осборна и др. для горизонтального направления, если их мюонный спектр является правильным, а также с результатом Волковой для вертикального направления, за исключением низких Энергий. Для горизонтального направления интенсивность мгновенных мюонных нейтрино превыщает интенсивность мюон-ных нейтрино из обычных процессов при Энергиях нейтрино 10⁶ ГЭВ. Йнтенсивность мгновенных Электронных нейтрино превыщает интенсивность Электронных нейтрино из обычных процессов при Энергии 10⁵ ГЭВ. Соответствуюшие величины для вертикального направления соответственно равны 10⁵ ГЭВ и ДО⁴ ГЭВ. В области Энергий от 0.3 ГЭВ до 3 ГЭВ ожидаемая величина отнощения интенсивностей Электронных нейтрино к интенсивности мюонных нейтрино составляет 0.42±0.08. Ёта величина прекрасно согласуется с Экспериментальным результатом 0.36±0.13, полученным группой

     

Family of symplectic implicit Runge-Kutta formulae

A family of formulae for the sympletic IRK method is investigated. Specifically, focus is given to general solutions for formula parameters of IRK under the symplectic and the order conditions. Examples of such formulae are constructed for up to three stages.     

The catalytic hydrogenolysis of benzylamine derivatives

The hydrogenolysis of optically active ethyl 2-amino-2-phenylpropionate (I), its N-methyl (II), and N,N-dimethyl (III) derivatives was studied using Raney Ni and Pd as the catalysts. The Raney Ni catalysed hydrogenolysis of II and III, as well as the reaction catalysed by Pd, occurred predominantly with inversion of configuration; this is not in accord with the hydrogenolysis of corresponding benzyl alcohols. This difference can be ascribed to the difference of the affinity for Ni between N and O atoms. The “SN_Ni” process may be inhibited in the Raney Ni catalysed hydrogenolysis of II and III since the amino group acts as a self-catalyst poison, and the “S_N2” process appears to be preferable to the “S_Ni” one. The predominance of the configurationally inversion was also observed in the Pd catalysed hydrogenolysis of I. These results over Pd are reasonable in reflecting that the N atom has not so high affinity for Pd. The hydrogenolysis of a quarternary ammonium bromide of I was also reported.     

Simulation of stochastic differential equations

A lot of discrete approximation schemes for stochastic differential equations with regard to mean-square sense were proposed. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We will propose another type of error analysis. Also we will show results of simulation studies carried out for these schemes under our notion.     

Soft-landing isolation of vanadium-benzene sandwich clusters on a room-temperature substrate using n-alkanethiolate self-assembled monolayer matrixes

Gas-phase synthesized vanadium-benzene 1:2 (VBz(2)) sandwich clusters were size-selectively deposited onto bare gold and long-chain n-alkanethiolate [-S-(CH(2))(n-1)-CH(3); n = 16, 18, and 22] self-assembled monolayer (SAM)-coated gold substrates under ultrahigh vacuum (UHV) conditions. Investigation of the resulting deposited clusters was performed by infrared reflection absorption spectroscopy (IRAS) and thermal desorption spectroscopy (TDS). The IR frequencies of the soft-landed VBz(2) clusters show excellent agreement with the fundamentals reported in IR data of VBz(2) in an argon matrix. The analysis of IRAS spectra reveals that while there was no orientational preference of the VBz(2) clusters on a bare gold substrate, the VBz(2) clusters deposited onto the SAM substrates were highly oriented with the molecular axis 70-80 degrees tilted off the surface normal. In addition, analysis of TDS spectra revealed unusually large adsorption heats of the physisorbed VBz(2) clusters. The present results are explained by cluster penetration into the long-chain alkanethiolate SAM and for the first time demonstrate the matrix isolation of gas-phase organometallic clusters around room temperature.     

Less than 10 defects/cm·μm in molecular beam epitaxy grown GaAs by arsenic cracking

Drastic reduction of irregular defect density in molecular beam epitaxy (MBE) grown GaAs is obtained by using a novel arsenic Knudsen effusion cell with a cracking furnace. A surface defect density of less than 10 cm⁻² is routinely achieved for continuously grown three 3-inch diameter, 1.7 μm thick, metal-semiconductor-field effect transistor (MESFET) structures when the cracking is carried out at about 700°C, which is the critical temperature for the conduction type change, and with the group III Knudsen cell only heated near the orifice of the crucible (top heat cell). These optimized cracking conditions also lead to successful mass production of some microwave devices with not only ultra-low defect density but suitable electrical performances.