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     EXISTENCE OF WEAK SOLUTIONS OF 2-D EULER EQUATIONS WITH INITIAL VORTICITY ω_0∈E(log ̄+L) ̄α (α>0)
     EXISTENCE OF WEAK SOLUTIONS OF 2-D EULER EQUATIONS WITH INITIAL VORTICITY ω_0∈E(log~+L)~α(α>0)
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     In this paper, we proved the Lp-boundedness of the Marcinkiewicz integral μΩ(f) on product domains Rn × Rm,where Ω∈L(log+L)2β(Sn-1 × Sm-1)( β > 1).
     本文证明了乘积空间Rn×Rm上Marcinkiewicz积分μΩ(f)的Lp有界性,其中Ω∈L(log+L)2β(Sn-1×Sm-1),β>1.
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     Occult cervical metastatic rate in 20 T1+T2 and 28 T3+T4 was 28.2%and 35.6%respectively. There was no significant difference between them analyzed by Kaplan-Meier(Log Rank=0.02, P=0.9000).
     20例T1+T2及28例T3+T4病例的隐性颈淋巴结转移率分别为28.2%和35.6%,无显著性差异(Log Rank=0.02,P=0.9000)。
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     The main result in this note is: let f be meromorphic and satisfy A (r, f) =O(log1 +εr ) with a psitive number ε(<1), and then we have A (r, Qf)=O(log1+εr) for any rational function Q.
     本文证明了下述结论:设f为开平面上的亚纯函数且A(r,f)=O(log1+εr)(ε为小于1的正数),则对任何有理函数Q,有A(r,Qf)=O(log1+εr).
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     There were no significant differences among the three groups (log Rank test, P=0.15).
     经时序检验(log Rank test)三组生存期无显著性差异(P=0.15)。
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     Still in topic 2,eq.
     (log2Q)倍。
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     The Power of Log Rank Test
     Log rank检验的功效
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26(4):1066-1099, [1997]), our fast SO(3) algorithm can be improved to give an algorithm of complexity O(B3log?2B), but at a cost in numerical reliability.
      
32% or less, have been evaluated in a full panel of 60 human cancer cell lines over a 5-log dose range at the National Cancer Institute.
      
The QSAR model indicates that the thermodynamic descriptors (heat of formation, log P, and molar refractivity) and steric descriptor (solvent assessable surface area) play an important role for the anti-HIV activity.
      
for an investor who has available a bank account and a stock whose price is a log normal diffusion.
      
With ΩεL (log+L)(Sn-1) and suitable h ∈ Lγ(RI)(1>amp;lt;γ?2), the weak type (1, 1) of the square function and the maximal operator were , are studied in this paper.
      
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The viscosities of the binary solutions of n-butyl alcohol and N-ethylanilinehave been measured at 15.00℃ in an Ubbelohde viscometer.The fluidities of n-butyl alcohol and N-ethylaniline were found to be 29.61 and 39.05 rhes respec-tively,while the solution at ca.30 mole percent butyl alcohol shows a maximumfluidity of 41.10 rhes.This increase of fluidity probably results from the break-ing of association interactions between the hydroxyl bonds of butyl alcoholmolecules in the solution.Deviations from the linear...

The viscosities of the binary solutions of n-butyl alcohol and N-ethylanilinehave been measured at 15.00℃ in an Ubbelohde viscometer.The fluidities of n-butyl alcohol and N-ethylaniline were found to be 29.61 and 39.05 rhes respec-tively,while the solution at ca.30 mole percent butyl alcohol shows a maximumfluidity of 41.10 rhes.This increase of fluidity probably results from the break-ing of association interactions between the hydroxyl bonds of butyl alcoholmolecules in the solution.Deviations from the linear additivity of fluidities arepositive for all concentrations.The experimental data can be represented fairlywell by an equation similar to that proposed by Eyring,i.e.φ=((?)/Nh)exp(-(x_1△F_1+x_2△F_2+Bx_1x_2/RT))with the parameter B=-374 cal/mole,and equally well by the equation of vander Wyk:logφ=x_1~2 logφ_1+x_2~2logφ_2+B'x_1x_2with the parameter B'=3.363.

正丁醇—N-乙基苯胺雨元溶液在15.00℃时的粘度,已被测定。这溶液的流度在正丁醇的分子浓度是30%时,呈现一最大值。溶液的流度增高,可能是由于正丁醇分子聚合的离解所致。实验数据可以相当满意地用类似 Eyirng 所提出的雨元溶液粘度公式或 van der Wyk 的公式来表示。

Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in 2781-44...

Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in 2781-44 as national standard to specify the fine aggregate for concrete in USSR. It was introduced to China in 1952 and soon becomes popular in all technical literatures concerning concrete aggregates and materials of construction.After careful and thorough investigation from ordinary and special gradings of sand, the equation of d_(cp) appears to be not so sound in principle and the value of d_(cp) computed from this equation is not applicable to engineering practice. The assumption that the initial average diameter (ν) of sand grains between consecutive seives is the arithmetical mean of the openings is not in best logic. The value of an average diameter computed from the total number of grains irrespective of their sizes will depend solely on the fines, because the fines are much more in number than the coarses. Grains in the two coarser grades (larger than 1.2 mm or retained on No. 16 seive) comprising about 2/5 of the whole lot are not duly represented and become null and void in d_(cp) equation. This is why the initiator neglected the last two terms of the equation in his own computation. Furthermore, the value of d_(cp) varies irregularly and even inversely while the sands are progressing from fine to coarse (see Fig. 4).As F. M. is still the only practical and yet the simplest index in controlling fineness of sand, this paper attempts to interpret it with a sound physical concept. By analyzing the F. M. equation (2a) in the form of Table 9, it is discovered that the coefficients (1, 2…6) of the separate fractions (the percentages retained between consecutive seives, a1, a2…a6) are not "size factors" as called by Prof. H. T. Gilkey (see p. 93, reference 4), but are "coarseness coefficients" which indicate the number of seives that each separate fraction can retain on them. The more seives the fraction can retain, the coarser is the fraction. So, it is logical to call it a "coarseness coefficient". The product of separate fraction by its corresponding coarseness coefficient will be the "separate coarseness modulus". The sum of all the separate coarseness moduli is the total "coarseness modulus" (M_c).Similarly, if we compute the total modulus from the coefficients based on number of seives that any fraction can pass instead of retain, we shall arrive at the true "fineness modulus" (M_f).By assuming the initial mean diameter (ν') of sand grains between consecutive seives to be the geometrical mean of the openings instead of the arithmetical mean, a "modular diameter" (d_m), measured in mm (or in micron) is derived as a function of M_c (or F. M.) and can be expressed by a rational formula in a very generalized form (see equation 12). This equation is very instructive and can be stated as a definition of mqdular diameter as following:"The modular diameter (d_m) is the product of the geometrical mean ((d_0×d_(-1))~(1/2) next below the finest seive of the series and the seive ratio (R_s) in power of modulus (M_c)." If we convert the exponential equation into a logarithmic equation with inch as unit, we get equation (11) which coincides with the equation for F. M. suggested by Prof. Abrams in 1918.Modular diameter can be solved graphically in the following way: (1) Draw an "equivalent modular curve" of two grades based on M_c (or F. M.) (see Fig. 6). (2) Along the ordinate between the two grades, find its intersecting point with the modular curve. (3) Read the log scale on the ordinate, thus get the value of the required d_m corresponding to M_c (see Fig. 5).As the modular diameter has a linear dimension with a defin

細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是...

細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是兩篩篩孔的幾何平均值,以代替數學平均值(即斯氏平均?

A water-extracted polycaprolactam sample was fractionated from a 2% solution in 85% formic acid at 25℃, water being used as precipitant. Carboxyl end-group titration and viscosity measurements in 40% H_2SO_4 at 25℃ were carried out for the fractions obtained. The experimental data fit either of the following equations: [η] = 5.92 × 10~(-4) M~(0.686) [η] = 2.44 × 10~(-5)M + 0.080 in the molecular weight range of 3000-13000, concentrations being in g/dl. Viscosity data were treated according to the empirical...

A water-extracted polycaprolactam sample was fractionated from a 2% solution in 85% formic acid at 25℃, water being used as precipitant. Carboxyl end-group titration and viscosity measurements in 40% H_2SO_4 at 25℃ were carried out for the fractions obtained. The experimental data fit either of the following equations: [η] = 5.92 × 10~(-4) M~(0.686) [η] = 2.44 × 10~(-5)M + 0.080 in the molecular weight range of 3000-13000, concentrations being in g/dl. Viscosity data were treated according to the empirical equatibns lnη_r / c = [η] - β[η]~2c (1) η_(sp) / c = [η] + k'[η]~2c (2) log(η_(sp) / c) = log[η] + k[η]c (3) The intrinsic viscosities obtained from (1) and (3) are identical, while those obtained from (2) are smaller by 1-2%. The values of β and k' vary with molecular weight. They increase appreciably with decreasing molecular weight. This anormalous behavior indicates that the value of k' is in no way connected with the solvent-power of the solvent for the polymer, when strong solvation is of prime importance for the dissolution of polymer. In 40% H_2SO_4 solution, polycaprolactam shows no appreciable degradation and no polyeletrolyte 'behavior. We have also acertained that the solution is Newtonian by deter- mining the efflux times in a capillary viscometer under various external hydrostatic heads. So we concluded that 40% H_2SO_4 is a suitable solvent for the viscometric determination of molecular weight of polycaprolactam. From the intrinsic viscosity-molecular weight relation obtained, the Stokes radii of the macromolecules in solution have been calculated according to the theory of Debye and Bueche. The resuk shows that polycaprolactam molecules in 40% H_2SO_4 solution are quite coiled and can be regarded as random coils.

(1)聚己內醯胺試樣在85%甲酸溶液中加水分級沉澱,得到分子量不同的級份,經羧基滴定,並於40%硫酸溶液中,在25°時测定粘度,得到下面的特性粘數分子量關係式: [η]=5.92×10~(-4) M~(0.686)或 [η]=2.44×10~(-5) M+0.080濃度單位是克/分升,分子量範圍是3000-13000。 (2)聚己內醯胺的40%硫酸溶液的粘度數據,試用了三種外推公式: lnη_r/c=[η]-β[η]~(2)c (1) η_(sp)/c=[η]+k′[η]~(2)c (2) logη_(sp)/c=log[η]+k[η]c (3) 用式(1)和式(3)得到的[η]值相同,式(2)得到的略小1-2%。β和k′值隨分子量的减小而顯著地增大,這和一般的高聚物——溶劑體系的行為相反。當高分子與溶劑分子間的氫鍵作用是高聚物溶解的主要因素時,用k′值來做溶劑能力的估計,是完全沒有意義的。 (3) 聚己內醯胺在40%硫酸裏,溶液粘度的切變速度依賴性是可以忽略的。我們認為40%硫酸是測定聚己內醯胺的粘均分子量的最合適溶劑。 (4) 從粘度數據依照Debye和Bueche的特性粘數理論,算出聚己內醯胺分子在40...

(1)聚己內醯胺試樣在85%甲酸溶液中加水分級沉澱,得到分子量不同的級份,經羧基滴定,並於40%硫酸溶液中,在25°時测定粘度,得到下面的特性粘數分子量關係式: [η]=5.92×10~(-4) M~(0.686)或 [η]=2.44×10~(-5) M+0.080濃度單位是克/分升,分子量範圍是3000-13000。 (2)聚己內醯胺的40%硫酸溶液的粘度數據,試用了三種外推公式: lnη_r/c=[η]-β[η]~(2)c (1) η_(sp)/c=[η]+k′[η]~(2)c (2) logη_(sp)/c=log[η]+k[η]c (3) 用式(1)和式(3)得到的[η]值相同,式(2)得到的略小1-2%。β和k′值隨分子量的减小而顯著地增大,這和一般的高聚物——溶劑體系的行為相反。當高分子與溶劑分子間的氫鍵作用是高聚物溶解的主要因素時,用k′值來做溶劑能力的估計,是完全沒有意義的。 (3) 聚己內醯胺在40%硫酸裏,溶液粘度的切變速度依賴性是可以忽略的。我們認為40%硫酸是測定聚己內醯胺的粘均分子量的最合適溶劑。 (4) 從粘度數據依照Debye和Bueche的特性粘數理論,算出聚己內醯胺分子在40%硫酸裏的等效Stokes半徑,說明聚己內醯胺分子在40%硫酸溶液裏的形態,可以看作是無規則的線團。

 
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