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Motivated by the physical concept of special geometry, two mathematical constructions are studied which relate real hypersurfaces to tube domains and complex Lagrangian cones, respectively.


A physical implication is that the corresponding wave function ψ(t, x) = eitHf(x) admits appropriate time decay in the Besov space scale.


The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of fullsky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.


It has potential to reduce physical skin penetration by injection and provide potentially effective vaccines.


Reported QSRR models are critically reviewed, bearing in mind their statistical predictability physical meaning.

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 1. The oil from fruits of Chinese drug,"Yatantze", Brucea javanica(Linn.) Merr., has been studied, and its physical and chemical constants determined. The composition of fatty acids and unsaponifiable matter were also individually identified. 2. The composition of fatty acids was fractionated by a specially modified method of fractional precipitation with silver nitrate solution, while the unsaturated fatty acids were fractionated with bromoderivative method. The percentage contents of the various fatty... 1. The oil from fruits of Chinese drug,"Yatantze", Brucea javanica(Linn.) Merr., has been studied, and its physical and chemical constants determined. The composition of fatty acids and unsaponifiable matter were also individually identified. 2. The composition of fatty acids was fractionated by a specially modified method of fractional precipitation with silver nitrate solution, while the unsaturated fatty acids were fractionated with bromoderivative method. The percentage contents of the various fatty acids present are as follows: (1) Saturated fatty acids: Arachidic acid......66.94% Unknown acid......30.09% Caproic acid......2.96% (2) Unsaturated fatty acids: Oleic acid......99.25% Linolenic acid......0.75% Clupanodonic acid......trace 3. From the unsaponifiable matter fraction, a higher homologue of hydrocarbon was isolated. It is a kind of colourless flake crystal, m.p. 6163℃, its formula being proposed as C_(35)H_(72) by molecular weight(Rast method) determination. This hydrocarbon is thus preliminarily proved as an isomer of pentatriacontane, a new constituent in this genus of the plant, although the isolation of another hydrocarbon, hentriacontane, C_(31)He_(64), from the fruits of Brucea sumatrana Roxb. had been previously reported. Besides the hydrocarbon, a trace of phytosterol was also found in the unsaponifiable matter, its acetylated product, a kind of colourless thin flake crystal, m.p. 104106℃, admixed with a trace of paraffin wax.  此部分工作是作者於1942年在昆明前中央藥物研究所完成,近閱1950年中華醫學雜誌有于光元及李寶實两氏,又1955年中華耳鼻喉科雜誌有王世勳、陳守毅兩氏相继發表的关於鴉胆子固定油具有醫疗乳头瘤或及外耳道和喉乳頭狀瘤之臨床效能报告,为配合此方面研究與决定有效成分問题的發展,作者謹將此文發表。根據本研究,這植物果實固定油成分中含种類繁複的脂酸類和特異的高碳烃及(石享)類等化合物。這似與近年Grabtree及Patter等氏報導關於有機不飽和酸類抑制瘤腫作用有关,(Cancer Research,2:688,1942;4:688,1944:5:546,1945)頗足为探研鴉膽子油治瘤有效成分的参考。  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... 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 278144 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?  Karrer and Enslin reported that the structure of alstyrine (S_(19)H_(22)N_2), a selenium dehydrogenationdegradation product obtained by Sharp from the alkaloid alstonine, is identical with that of corynanthyrine, α[2(4, 5 diethylpyridyl)]βethylindole (Ⅱ), despite the fact that the melting points of these two substances have a 5°difference. In his investigation, the author of the present paper has synthesized two homologues of (II), α(2pyridyl)β methylindole (Ⅲ) and α(2pyridyl)βethylindole (Ⅳ),... Karrer and Enslin reported that the structure of alstyrine (S_(19)H_(22)N_2), a selenium dehydrogenationdegradation product obtained by Sharp from the alkaloid alstonine, is identical with that of corynanthyrine, α[2(4, 5 diethylpyridyl)]βethylindole (Ⅱ), despite the fact that the melting points of these two substances have a 5°difference. In his investigation, the author of the present paper has synthesized two homologues of (II), α(2pyridyl)β methylindole (Ⅲ) and α(2pyridyl)βethylindole (Ⅳ), finding that the former has almost the same ultraviolet absorption spectrum as that of alsyrine and that, like alstyrine, the metho sulphate of the compounds (Ⅲ) and (Ⅳ) gives the same red colour reaction upon treatment with dilute sodiumhydroxide solution. The Fischer indole synthesis to cyclize the phenylhydrazone of the corresponding alkyl 2pyridylketone in the presence of mineral acid was employed by the author in the preparation of compounds (Ⅲ) and (Ⅳ). Besides, three acarboline derivatives, namely, 2(cyclohexylmethyl)βcarboline (Ⅻ), 2[(4'methylcyclohexyl)methyl]βcarboline (XIII) and 2[(2'methylcyclohexyl)methyl] βcarboline (XIV), have also been synthesized; none of them is identical with alstyrine in physical and chemical properties. The preparation of compounds (Ⅻ), ((XIII)) and ((XIV)) was carried out according to the method originated by Bischler and Napieralski. This involved the condensation of tryptamine with a suitable acid, or acid chloride, first to form an amide, which was then cyclized with phosphorus pentoxide, and finally dehydrogenated .partially with selenium. The melting points of the two α(2pyridyl)βalkylindoles, three βcarbolines, their inter mediates, and a few derivatives of theirs are as follows: ■  1.合成了兩種吲(口朶) 衍生物:α(2吡啶基)β甲基吲(口朶) 及α(2吡啶基)β乙基吲(口朶)。前者的紫外線吸收光譜與阿爾斯泰令(alstyrine,係一種由西阿斯木鹼經硒降解後的產物)的吸收光譜極為類似;且二者有一種相同的顏色反應。因此說明阿爾斯泰令的結構可能與可利南斯令(corynanthyrine),α[2(4,5雙乙吡啶基)]β乙基吲(口朶)相同。 2.合成了三種β咔卟啉的衍生物:2環己烷甲基β咔卟啉,2[(4′甲基環己烷)甲基]β咔卟啉及2[(2′甲基環已烷)甲基]β咔卟啉。這些化合物的化學及物理性質都和阿爾斯泰令不同。因此後者不是β咔卟啉衍生物。   << 更多相关文摘 
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