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trace
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     Trace Calculus
     Trace演算
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     The Trace of Power
     权力的踪迹
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  trace
Using related sequences of Lucas numbers, other 3-manifolds are constructed, their geometric structures determined, and a curious relationship between the homology and the invariant trace-field examined.
      
Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates
      
We show that the trace of an indefinitely oscillating function on a subspace of ?d is not always indefinitely oscillating.
      
In the periodic case, the number of oscillations of the trace depends on the regularity of the function.
      
As applications, we obtain characterizations of the Besov and Triebel-Lizorkin spaces on Lipschitz curves, and the trace theorem on Γ of the Besov spaces onR2.
      
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Nine Marchi series of albino rats in which various points of the retina were destroyed by the method of thermocautery have been carefully studied. The courses and the terminations of the degenerated optic fibers have been determined. The results are summarized by a composite diagram (fig. 9). It shows:(1) that the fibers issuing from the upper quadrant of the retina are lying in the lateral of the optic nerve, crossed in the lower level of the chiasma passed along the medial part of the crossed optic tract and...

Nine Marchi series of albino rats in which various points of the retina were destroyed by the method of thermocautery have been carefully studied. The courses and the terminations of the degenerated optic fibers have been determined. The results are summarized by a composite diagram (fig. 9). It shows:(1) that the fibers issuing from the upper quadrant of the retina are lying in the lateral of the optic nerve, crossed in the lower level of the chiasma passed along the medial part of the crossed optic tract and terminated partly in the ventral of the posterior half of the lateral geniculate body and partly in the caudolateral part of the superior colliculus;(2) that those from the lower retina are lying in the lower part of the nerve, crossed in the higher level of the chiasma, passed along the lateral border of the crossed tract, and terminated partly in the dorsal part of the anterior half of the lateral geniculate body and partly in the medio-oral part of the superior colliculus;(3) that those from the temporal retina are lying in the lateral part of the nerve, crossed in the lower level of the chiasma, passing through the inner part of the tract and terminated partly in the medial part of the lateral geniculate body and partly in the lateral part of the superior colliculus;(4) that those from the nasal retina are lying in the medial of the nerve, crossed in the higher level of the chiasma, passing through the outer border of the tract and terminated partly in the lateral part HSIANG-TUNG CHANGof the anterior half of the geniculate body and partly in the medial part of the superior colliculus;(5) that those from the peripheral margin of the temporal retina are lying in the lateral half of the nerve, uncrossed in the chiasma, passing through the upper half of the tract, terminated in the central part of the geniculate body and never reached the superior colliculus; and(6) that the anterior and posterior accessory optic tracts composed probably of the collaterals of the crossed optic neurons are traced to the corpus Luysii and the nucleus opticus tegmenti respectively.(7) that the optic fibers also terminate in the pretectal nucleus of the thaIamus.

本實驗曾將九隻白鼠之視網膜的各處用電燒法加以毁壞,然後用马基氏染色法(Marchi's method)製成連續切片,详加研究,以斷定其枯萎的神经纖维所经之路徑及终止之點。 實驗结果如下: (一) 自網膜上部發出之神经纖維,位於視神经之外侧,由視神经叉之近尾段跨越於對面,又经對邊視神经通路之内側部,而一部终止於背外側膝體之后腹部,一部终止於上叠體之外侧部。 (二) 自網膜下部發出之纖維,位於視神经之下侧,由視神经叉之近首段跨越於對邊,再沿對邊視神经通路之外侧進行,而一部终止於背外側膝體之前背部,一部终止於上叠體之前内側部。 (三) 自網膜外侧部發出之纖维,位於視神经之外侧部,由視神经叉之近尾段跨越於對面,再沿對邊視神经通路之内側部進行,而一部终止於背外側膝體之后内側部,一部终止於上叠體之外側部。 (四) 自網膜内側部發出之纖维,位於视神经之内側,由视神经叉之近首叚跨越於對面,再经對邊視神经通路之外邊,而一部终止於背外側膝體之前外側部,一部终止於上叠體之内側部。 (五) 自網膜之外側邊緣部發出之纖维,位於视神经之外側,不到對邊,经本邊視神经通路之下半部而终止於背外侧膝體之中央。無及於上叠體者。 (六) 前副視神经...

本實驗曾將九隻白鼠之視網膜的各處用電燒法加以毁壞,然後用马基氏染色法(Marchi's method)製成連續切片,详加研究,以斷定其枯萎的神经纖维所经之路徑及终止之點。 實驗结果如下: (一) 自網膜上部發出之神经纖維,位於視神经之外侧,由視神经叉之近尾段跨越於對面,又经對邊視神经通路之内側部,而一部终止於背外側膝體之后腹部,一部终止於上叠體之外侧部。 (二) 自網膜下部發出之纖維,位於視神经之下侧,由視神经叉之近首段跨越於對邊,再沿對邊視神经通路之外侧進行,而一部终止於背外側膝體之前背部,一部终止於上叠體之前内側部。 (三) 自網膜外侧部發出之纖维,位於視神经之外侧部,由視神经叉之近尾段跨越於對面,再沿對邊視神经通路之内側部進行,而一部终止於背外側膝體之后内側部,一部终止於上叠體之外側部。 (四) 自網膜内側部發出之纖维,位於视神经之内側,由视神经叉之近首叚跨越於對面,再经對邊視神经通路之外邊,而一部终止於背外側膝體之前外側部,一部终止於上叠體之内側部。 (五) 自網膜之外側邊緣部發出之纖维,位於视神经之外側,不到對邊,经本邊視神经通路之下半部而终止於背外侧膝體之中央。無及於上叠體者。 (六) 前副視神经通路,终止於路易斯氏體(Corpus Luysii),而后副视神经通路則终止於视底巢(

An electrophotometric method has been worked out for the determination of magnesium in cast iron using titan yellow as indicator.Briefly,the method consists of dissolving the sample in dilute sulphuric acid,separating iron and other metals such as copper and nickel by electrolysis with mercury cathode and precipitating manganese from ammoniacal solution with ammonium persulfate.Ammonimn salt,silica and traces of aluminaare thenremoved. Finally,the prepared titan yellow reagent is added to the solutionand...

An electrophotometric method has been worked out for the determination of magnesium in cast iron using titan yellow as indicator.Briefly,the method consists of dissolving the sample in dilute sulphuric acid,separating iron and other metals such as copper and nickel by electrolysis with mercury cathode and precipitating manganese from ammoniacal solution with ammonium persulfate.Ammonimn salt,silica and traces of aluminaare thenremoved. Finally,the prepared titan yellow reagent is added to the solutionand the magnesium content determined from the electrophotometric reading.The time required for each determination is approximately 5 hours. The effect of interfering elements which are likely present in cast iron such as manganese, silicon,phosphorus, aluminum, copper, nickel and vanadium as well as ammonium ion and alkali and alkaline earth metals has been studied and discussed.It has been shown that manganese, silicon, aluminum,copper,nickel,iron and ammonium ions can be removed down to such low values as to cause no significant interference.Phosphorus under 0.4% has no appreciable effect.Vanadium is not separated in the present method,but fortunately it is usually present in insignificant amounts in ordinary cast iron.The effect of calcium is compensated by the introduction of saturated calcium sulphate solution before the titan yellow addition. Potassium and sodium have no appreciable effect when present in small amounts. The results obtained by the present method for the determination of magnesium in 11 known samples are good,the average difference being 0.002% in a range of 0.000% to 0.140% Mg.The data obtained by the present method are also in good agreement with those obtained by gravimetric methods On seven nodular iron samples made by the Metallurgical Division of our Institute.A detailed procedure for the determination of magnesium in cast iron has been suggested and included in this paper.In view of its rapidity and fair accuracy,the new photometric method might prove useful for the purpose of control in a nodular iron foundry.

本文报告将地丹黄比色法应用於测定铸铁中之镁的试验结果.如将铁、锰、铝、矽等干扰物质预先除去,则镁的测定并无困难.依照本文所擬的方法分析,所需时间约为五小时,较重量法迅速得多.

1. The oil from fruits of Chinese drug,"Ya-tan-tze", 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 bromo-derivative method. The percentage contents of the various fatty acids...

1. The oil from fruits of Chinese drug,"Ya-tan-tze", 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 bromo-derivative 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. 61-63℃, 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. 104-106℃, 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。

 
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