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941.
Another Note on the Greatest Prime Factors of Fermat Numbers 总被引:1,自引:0,他引:1
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the mth Fermat number, then P(Fm) 2m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m a18.AMS Subject Classification (1991) 11A51 11J86 相似文献
942.
Amorphous, nanocrystalline, and bulk AlO(OH) · xH2O crystals have six fundamental modes (FM) of vibration in a nonlinear AlO(OH) molecular structure. Most of them appear in groups of four IR and Raman bands. Their positions and relative intensities differ significantly in three specimens. The nanocrystals (monoclinic structure with z=8 molecules per unit cell) have four OH stretching bands at values enhanced by up to 360 cm−1 at 3120, 3450, 3560 cm−1 in comparison to those in bulk crystals or amorphous specimens. The first two bands are broad, bandwidth Δν1/2200 to 350 cm−1, while the other two are sharp, Δν1/290 cm−1. The sharp bands shift to 3525 and 3595 cm−1 after heating the sample at 100°C. They no longer appear after heating at 300 or 500°C for 2 h (the specimen decomposes to Al2O3), leaving behind only two bands at 3100 and 3400 cm−1. A Δν1/2 value of 500 cm−1 appears in the 3400 cm−1 in a delocalized distribution of H atoms. Two bands also occur at 3098 and 3300 cm−1 in bulk crystals (orthorhombic structure with z=4) or at 2990 and 3515 cm−1 in an amorphous sample. More than one bands appear in a FM vibration in occurrence of sample in more than one conformers. The amorphous sample has approximately the same conformer structure as the bulk crystals. An amorphous surface structure exists in nanocrystals with a group of three bands at 1420, 1510 and 1635 cm−1 in an interconnected network structure. It encapsulates the nanocrystals in an amorphous shell. Its volume fraction, 33% estimated from the integrated intensity in three bands, determines 2.2 nm thickness in the shell in spherical shape of nanocrystals in 35 nm diameter. 相似文献
943.
We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K for cases of <1, >1 and =1. 相似文献
944.
A. I. Belousova Yu. E. Lozovikb 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(2):251-264
A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can
be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum
dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found.
Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In
mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells
takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic”
clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest
nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric
groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in
clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure
factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of
the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms
of clusters is considered. 相似文献
945.
946.
R. Unanyan S. Guérin B. W. Shore K. Bergmann 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(3):443-449
In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the
rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when
each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction
strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete
and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated
Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage
by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation
of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields. 相似文献
947.
回顾介绍了葛庭燧院士的生平和他在科学研究、人才培养方面所作出的贡献,展示了他的高尚情操,分析了他取得卓著成就的原因. 相似文献
948.
949.
H.-K. Zhao Q. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(4):419-427
We have investigated the spectral density of shot noise for the
system of a quantum dot (QD) coupled to two single-wall carbon
nanotube terminals irradiated with a microwave field on the QD. The
terminal features are involved in the shot noise through modifying
the self-energy of QD. The contributions of carbon nanotube
terminals to the shot noise exhibit obvious behaviors. The novel
side peaks are associated with the photon absorption and emission
procedure accompanying the suppression of shot noise. The shot noise
in balanced absorption belongs to sub-Poissonian, and it is
symmetric with respect to the gate voltage. The differential shot
noise displays intimate relation with the nature of carbon nanotubes
and the applied microwave field. It exhibits asymmetric behavior
for the unbalanced absorption case versus gate voltage. The Fano
factor of the system exhibits the deviation of shot noise from the
Schottky formula, and the structures of terminals obviously
contribute to it. The super-Poissonian and sub-Poissonian shot noise
can be achieved in the unbalanced absorption in different regime of
source-drain bias. 相似文献
950.
S. Duhot R. Mélin 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(3):289-296
A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases
on the Fermi wavelength while one particle states are localized on the CDW coherence length ξCDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences
of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds
for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon:
(i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian
approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin
density wave (SDW) is limited by the coherence length ξSDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW
separated by a distance ξSDW. 相似文献