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1.
2.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献
3.
Murray Hodgson 《Applied Acoustics》2004,65(1):69-89
The acoustical characteristics of 14 university classrooms at the University of British Columbia were measured before and after renovation—seven of these are discussed in detail here. From these measurements, and theoretical considerations, values of quantities used to assess each classroom configuration were predicted, and used to evaluate renovation quality. Information on each renovation was determined with the help of the university campus-planning office and/or the project acoustical consultant. These were related to the evaluation results in order to determine the relationship between design and acoustical quality. The criteria focused on the quality of verbal communication in the classrooms. Room-average Speech Intelligibility (SI) and its physical correlate, Speech Transmission Index (STI), were used to quantify verbal-communication quality. A simplified STI-calculation procedure was applied. The results indicate that some renovations were beneficial, others were not. Verbal-communication quality varied from ‘poor’ to ‘good’. The effect of a renovation depends on a complex interplay between changes in the reverberation and changes in the signal-to-noise level difference, as affected by sound absorption and the source outputs. Renovations which reduce noise are beneficial unless signal-to-noise level differences remain optimal. Renovations often put too much emphasis on adding sound absorption to control reverberation, at the expense of lower speech levels, particularly at the backs of classrooms. The absorption and noise contributed by room occupants has apparently often been neglected. 相似文献
4.
We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase. 相似文献
5.
We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media. 相似文献
6.
Vinod Kumar Pragya Das R.P. Singh S. Muralithar R.K. Bhowmik 《The European Physical Journal A - Hadrons and Nuclei》2003,17(2):153-157
The fusion evaporation reaction 122Sn(14N, 4n)132La was used to populate the high-spin states of 132La at the beam energy of 60 MeV. A new band consisting of mostly E2 transitions has been discovered. This band has the interesting links to the ground state 2- and the isomeric state 6-. A new transition of energy 351 keV connecting the low-spin states of the positive-parity band based on the πh
11/2 ⊗ νh
11/2 particle configuration, has been found. This has played a very important role in resolving the existing ambiguities and inconsistencies
in the spin assignment of the band head.
Received: 12 August 2002 / Accepted: 18 March 2003 / Published online: 7 May 2003 相似文献
7.
恩格尔系数衡量城镇居民生活水平适用性 总被引:2,自引:0,他引:2
根据我固1980年和2000年恩格尔系数所反映的各省(市)居民生活水平资料,发现两个不同时期其真实性有很大差异,分析了造成这种差别的原因:(1)职工非现金福利收入的增加;(2)少数职工的非法收入的大量增加;(3)居民饮食结构的改变;(4)物价上涨的影响;(5)恩格尔系数本身存在技术问题;(6)抽样调查本身存在问题,提出用一种“新系数”来衡量城镇居民生活水平,其优点是:(1)不受各地区实际支出,即人为控制调节的影响;(2)不需用其他指标作解释,直观性强;(3)因可以扣除物价因素,它不受物价波动的影响;(4)调查户填报和计算简易方便。可扩大样本调查量,提高反映住户总量可靠性。 相似文献
8.
M. Faucher D. Garcia E. Antic-Fidancev M. Lemaitre-Blaise 《Journal of Physics and Chemistry of Solids》1989,50(12)
Some structural and spectroscopic features of rare earth orthoaluminates are examined.The trigonal→ orthorhombic transition is studied in a series of NdxSm1−xAlO3 compounds. The evolution of the crystal structure is followed by X-ray analysis and optical absorption. The free ion and crystal field parameters of Nd3+ (4f3 configuration) are determined in LuAlO3:Nd3+.The anomaly of the calculated splitting of the
levels is slight, but well characterized in NdAlO3. The spin correlated crystal field and orbitally correlated crystal field models are tested as well as an empirical correction which was proposed earlier. 相似文献
9.
10.