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estimates
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Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates
      
Singular Value Estimates for Certain Convolution-Product Operators
      
We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.
      
Singular Value Estimates for Certain Convolution-Product Operators
      
Estimates from below for the norms of linear means of multiple Fourier series are obtained.
      
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The beta-ray spectrum of RaE was investigated by the cloud chamber experiments. About 600 tracks with H σ above 2000 were obtained. The spectrum was found to have an end point at 7500 Hσ. The average energy per disintegration was estimated to be 4.01×105 electron-volts.

戊种镭原质(Ra E)所放出之β线穿过威尔圣成云箱之径迹(tracks),用照相机照下。因成云箱在磁场中,而磁力之方向又与β线所取之途径垂直,故由照片上所量出径迹之半径,ρ,可定β线之能力,盖磁场之强度,H,亦已知也。通常以Hρ代表能力大小之相当值。用戊种镭原质所摄之照片上量出10Oβ线径迹,其Hρ值皆在2000高斯-厘米(Gauss-cm.)以上。以各种Hρ值及在该值范围内所有径迹之数目作一曲线。将该曲线延长至与Hρ轴相交,其交点7500高斯——厘米,即为β线具有最大能力者之Hρ值。由β线能力大小之分配,用绘图方法得计算该线之平均能力,其值为4.01×10~5电子——伏特(electron—volts)。

By surrounding a photo-neutron source of Ra+Ee with a thin spherical sbell of paraffin, a continuous spectrum of scattered neutrons, extending from zero energy to the energies of the primary neutrons is obtained. When a silver detector is exposed to such a spectrum, a part of the neutrons having just the energies at resonance with the silver nuclei is strongly absorbed by the detector and thereby produces the induced β-activity. By measuring the activity of silver and the apparent absorption coefficient of the...

By surrounding a photo-neutron source of Ra+Ee with a thin spherical sbell of paraffin, a continuous spectrum of scattered neutrons, extending from zero energy to the energies of the primary neutrons is obtained. When a silver detector is exposed to such a spectrum, a part of the neutrons having just the energies at resonance with the silver nuclei is strongly absorbed by the detector and thereby produces the induced β-activity. By measuring the activity of silver and the apparent absorption coefficient of the resonance neutrons in a thin silver absorber, the total width of the resonance levels effective to neutron capture and located in the above spectrum is estimated. Let τ He the average value of one half of the half-value width of the resonance levels, expressed in volts, and n be the number of resonance levels here concerned. We find nτ=260 volts for the silver nuclei of half period 22" if the energies of the primary neutrons are taken to be 2x 105 volts. Knowing nτ, we can evaluate the average spacing between adjacent resonance levels effective to neutron capture by giving a plausible value to τ. We find a spacing of the order 80-800 volts if τ be given the value 0.1-1.0 volt. This result is in good accord with the recent theoretical calculation of Bethe and also with observations of resonance groups in the low energy region.

把‘镭—铍’所产生的‘光中子’,穿过一层半厘米厚的白蜡,我们便得到一‘连续的中子谱’。他们中间有些中子,能和银的原子核起‘共振作用’,因此可以被银片吸收,而产生‘人工放射银’先测量人工放射的强度和‘共振中子’在银片中的吸收率,再应用原子核内共振能层的宽度,我们便可以求出银的原子核内‘共振能层’的密度大约共振能在零和二十万伏特中间,平均每隔一二百伏特便有一可以吸收质子的共振能层,和理论很相符合。

The average nuclear level spacings of In, Ir and Au are estimated from the beta-ray activities induced by the primary photo-neutrons emitted from a Ra+Be source. A Geiger-Muller counter made of aluminum is used for measuring the induced activities. The saturated induced activities for the three elements are found to be 0.665±0.23 0.982±.03l, 0.453±0.21 (no./sec.) respectively. The estimation for the average nuclear level spacings is made in accordance with Breit-Wigner's one level formula, the resnlts...

The average nuclear level spacings of In, Ir and Au are estimated from the beta-ray activities induced by the primary photo-neutrons emitted from a Ra+Be source. A Geiger-Muller counter made of aluminum is used for measuring the induced activities. The saturated induced activities for the three elements are found to be 0.665±0.23 0.982±.03l, 0.453±0.21 (no./sec.) respectively. The estimation for the average nuclear level spacings is made in accordance with Breit-Wigner's one level formula, the resnlts being 5.6, 15 and 6 volts for In, Ir, Au respectively. The spacing of Ir is probably somewhat over estimated since the values of the energy and absorption coefficient of the resonance neutron group, used in the estimation, are not very accurate.

作者用镭加钡之光感中子以射击铟铱金三元素,而以一铝质盖密计(GeigerMuller counter)测其感应放射能。得各元素感应放射能之饱值,铟为0.665士.023.铱为0.982±.031,金为0.453±.024.依白威二氏(Breit-Wigner)之单能准式,吾人可自感应放射能之值道出原子核能准之平均间隔。所得结果,铟铱金各为5.6,15,6伏特。因计算时所用共振中子之能及吸收系数不太准确,估计所得铱之间隔大概过高。

 
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