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It can be used to study the weighted average of the form $(T^\alpha (\hbox {ln }T)^\beta)^{1}\int _0^T h(t) \, dt.$


Finally, every frame can be written as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.


represents an average over rotations, of the SteinTomas restriction phenomenon.


Convolution, Average Sampling, and a Calderon Resolution of the Identity for ShiftInvariant Spaces


In previous work, under some assumptions, we specified a replacement rule which minimizes the longrun (expected) average cost per unit time and possesses control limit property.

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 The betaray 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 electronvolts.  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(Gausscm.)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 photoneutron 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 βactivity. By measuring the activity of silver and the apparent absorption coefficient of the... By surrounding a photoneutron 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 βactivity. 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 halfvalue 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 80800 volts if τ be given the value 0.11.0 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。  In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function... In the statistical theory of superlattices in binary alloys, the dependence of the interaction energy upon atomic arrangements is taken into account by regarding the interaction energy in Bethe's theory as an average quantity depending on the degree of order and the composition of the alloy. Two simple assumptions concerning the functional relationship of the interaction energy with order and composition are made. The first is a linear function of order and composition. The second is a linear function of the average numbers of pairs of atoms. The result of applying these assumptions to superlattices of the type AB is that the critical temperature as a function of the composition is a maximum for equal sumber of A and B atoms only when a certain relation between the coefficients in the assumed function is satisfied. In the cass of superlattices of type AB3 the theory of Bragg and Williams is used for simplicity. It is shown that when the composition varies, the maximum of the critical temperature may occur at any desired composition by a suitables adjustment of the coefficients in the assumed functions. There is thus a hope of removing the discrepancy between theory and experiment on this line. The anomalous specific heat at the critical temperature is also calculated for different compositions. In the case of the AB type of superlattices, Bethe's formula for the energy is no longer valid, and in order to calculate the specific heat, an approximate formula for the energy is obtained by analogy with the theory of Bragg and Williams. Finally, the problem of separation into more than one phase is briefly discussed.  在二元合金超格之统计力学理论中,原子间互作用能量,因原子之排列不同而异,其所生之影响,吾人擬於此篇中讨论之。吾人认为有Bethe氏理论中之相互作用能量,实为一平均值,其值因合金之秩序程度及其成分而异。吾人作二简单假设:一设相互作用能量为秩序及成分之线性函数,另一设其与原子对偶之数成线性函数。将此等假设应用於AB类之合金,则必须在所设函数中之系数间,有适当关系,合金之临界温度,始在成分为1:1时,有极大值。在AB_3类之合金,吾人乃应用Bragg及Williams二氏之理论以求简便。於此可证明若所设函数中之系数,可任意调整则所计算出之临界温度之极大值可在任何成分发生。故关於此点理论与实验不合之处,可望解决。又合金之反常比热,亦经算出。在AB类之合金,Bethe氏原来之能量公式不復可用,故另用与Bragg及Williams理论比较而得之公式计算。又关於合金可分为二相或多相之问题,此篇亦大略论及。   << 更多相关文摘 
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