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Therefore, our results give in particular a unified construction for many moduli spaces considered in the literature.


Only certain smooth classes of the low pass filters that are determined by these scaling functions, however, appear to be characterized in the literature (see Chapter 7 of [3] for an account of these matters).


The following open question was implicit in the literature: Are there singular


The approach is illustrated on proteome maps reported in the literature.


Based on the literature [1], this paper changes the essential conditionα ∫g(t)/tr(s)ds ≤ 1 into∫g(t)/tr(s)ds ≤θ.

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 Von Knorre first suggested the use of benzidine and otolidine for the determination of tungsten. With the latter reagent, he succeeded also in separat ing tungstate from phosphate. Later on, odianisidine and vanillylidene benzidine have been proposed as precipitants for tungstate. The optimum pH ranges for the quantitative precipitation of tungstate by means of these precipitants and tetraminodiphenyl, which have not yet been found in the literature, are: benzidine pH: 2.05.5 otolidine 2.94.7 ... Von Knorre first suggested the use of benzidine and otolidine for the determination of tungsten. With the latter reagent, he succeeded also in separat ing tungstate from phosphate. Later on, odianisidine and vanillylidene benzidine have been proposed as precipitants for tungstate. The optimum pH ranges for the quantitative precipitation of tungstate by means of these precipitants and tetraminodiphenyl, which have not yet been found in the literature, are: benzidine pH: 2.05.5 otolidine 2.94.7 odianisidine 2.04.1 vanillylidene benzidine 1.73.9 tetraminodiphenyl 1.74.8 The effect of introducing various groups into the benzidine molecule upon the tungsten precipitating property is not profound. The relation between quantitative precipitation of tungstate with benzidine and the product of concentrations of both constituents before precipitation Was studied. It is found that quantitative precipitation of tungstate ions Can be realized only when the product of concentrations of reactants before precipitation is equal to or greater than 0.8 × 10~(5), and the moles of benzidine added must be at least equal to that of tungstate. The gravimetlic determination of tungsten by means of otolidine may be applied to samples containing as low as 10 mg of rungsten trioxide in 200 ml solution, if an absolute error of 0. 5 mg can be tolelxted. For larger quantities of tungsten present in sample, the absolute errors amount to only 0.10.2 mg. Tetraminodiphenyl may be used as a tungsten precipitant, but no advantage over benzidine Wan found in our present studies.  1.用二胺聯苯及其數種衍生物沉澱鎢酸根時,其適宜的pH範圍如下:[4,4′]二胺聯苯 pH:2.05.5[3,3′]二甲基[4,4′]二胺聯苯 2.94.7[3,3′]二甲氧基[4,4′]二胺聯苯 2.04.1[4]對胺聯苯氮甲烯[2]甲苯酚 1.73.9[3,4,3′,4′]四胺聯苯 1.74.8 2.用[4,4′]二胺聯苯作沉澱劑時,二胺聯苯和鎢酸根在沉澱前的濃度之乘積與後者沉澱完全與否的關係,曾加研究。 3.用[3,3′]二甲基[4,4′]二胺聯苯作沉澱劑時,能测定低至10毫克的三氧化鎢。  (1) Cytochrome c containing 0.43% iron has been obtained from beef, pig or horse heart muscles by direct adsorption of the neutralized trichloroacetic acid extracts of heart muscle on the cation exchanger"synthetic zeolite" followed by elution with 3.84 M ammonium sulfate and precipitation with 20% trichloroacetic acid. This provides a simple method for largescale preparation of pure cytochrome c. (2) The ratio of optical densities at 550 mμ(reduced) and 278 mμ of 0.43% iron cytochrome c varies, with its degree... (1) Cytochrome c containing 0.43% iron has been obtained from beef, pig or horse heart muscles by direct adsorption of the neutralized trichloroacetic acid extracts of heart muscle on the cation exchanger"synthetic zeolite" followed by elution with 3.84 M ammonium sulfate and precipitation with 20% trichloroacetic acid. This provides a simple method for largescale preparation of pure cytochrome c. (2) The ratio of optical densities at 550 mμ(reduced) and 278 mμ of 0.43% iron cytochrome c varies, with its degree of reduction, from 1.13 to 1.26. The average ratio of our preparations is 1.23. (3) The absorption spectra(230600 mμ) of oxidized and reduced cytochrome c have been measured. The molecular extinction coefficient at 550 mμ of oxidized, 0.43% iron, cytochrome c is 0.80×10~4. This value differs considerably from that reported in the literature. (4) Some enzymic properties of cytochrome c containing 0.43% iron are compared with those of a preparation containing 0.34% iron and are found to be identical. Both can be converted into''endogenous" cytochrome c. (5) Whether pure cytochrome c contains more than 0.43% iron has been discussed. It seems that no convincing evidence has been presented to show that cytochrome c preparations with iron content higher than 0.43% as obtained by some workers do not contain a small amount of ironrich impurity.  (一)用陽離子交换劑(synthetic zeolite)直接吸附高等動物心肌抽提液一次,並用3.84M硫酸銨作洗脫劑,即可製得含鐵量0.43%的細胞色素c。因此提供了一個大量製備純細胞色素c的簡單方法。 (二)含鐵量0.43%的細胞色素c,它的550mμ和278mμ光密度的比值,視產品的還原程度而定,其範圍從1.13到1.26,我們所製得的產品,其比值在1.23左右。 (三)我們测量了氧化及還原的細胞色素c(含鐵0.43%)從230mμ到600mμ的吸收光譜,並發現和前人所報告的略有不同。氧化細胞色素c在550mμ的消光係數為0.80×10~4,此值與文獻上的數值相差很多。 (四)我們比較了含鐵量0.43%的細胞色素c和含鐵量0.34%的細胞色素c的一些酶性質,證明他們是相同的;並且兩者都可以變成“內源”細胞色素c。 (五)我們認為現有的實驗證據不足以說明純細胞色素c的含鐵量大於0.43%。  Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13term 2electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good oneelectron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction... Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13term 2electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good oneelectron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction in elliptical coordinates involving 5 parameters and obtained 3.603 eV for the binding energy of H_2, which is to be compared with the ex perimental value of 4.72 eV. In the present investigation we have proposed a new type of trial eigenfunction for the molecular orbital: (1) with p = centers a, b, g, c, d,…… i = electron 1 or 2 (2) where the p's are centers along the bond axis ab (Fig. 1). In this simple problem both the Fock and Hartree methods yield the same result. The molecular orbital ψ must satisfy the following integral equation: (3) where ε is the energy of the molecular orbital, F is the Fock operator which is equal to H+G(1), while H is the oneelectron Hamiltonian operator: H = 1/2▽~21/r_a1/r_b (4) and G(1) is the interaction potential (5) Substituting (1) into (3), we obtain the linear combination coefficients c_p, which must satisfy the following secular equation: (6) where is the solution of the secular determinant and The F_(pq)'s are not at first known, but depend upon the c_p's. A method of successive approximation must therefore be adopted. A set of c_p values may be assumed, the F_(pq)'s calculated, the secular determinant (7) solved, and a new set of c_p values found. This process is repeated until a "selfconsistent" set of c_p values is obtained. The above procedure was first proposed by Roothaan (1951), not for H_2 but for more complex molecules. It was called by him the "LCAO SCF (linear combination of atomic orbitals selfconsistent field) method". The new feature of the present investigation is that we not only use LCAO but also LCNAO (linear combination of nonatomic orbitals, such as x_g, x_c, x_d, …). The order of secular determinant (7) may be reduced to half if we replace the eigen functions x_a, x_b .... by their symmetrical and antisymmetrical linear combinations x_a + x_b and x_ax_b. Numerical calculations have been carried out both for the three and the twocentered molecular orbitals. The threecentered molecular orbital is (10) (11) where S_(ab) and S(ag) are the overlapping integrals between x_a and x_b, and between x_a and x_g respectively. The parameters a and g have 'been obtained to give minimum energy by the method described above. They are a=l.190, g=0.22, and the binding energy is 3.598 eV, which is almost as good as that obtained by Coulson (3.603 eV) using a trial function of 5 parameters. The twocentered molecular orbital is (12) (13) which gives a maximum binding energy of 3.630 eV for a=1.190 and R~(ac)=R(bd)=0.105 (Fig. 1). This result is 'better than Coulson's. If we allow different values for the exponent α in x_a and x_g in equation (11), or if we use a fourcentered molecular orbital, such as ψ=a(x_a + x_b) + b(x_c + x_d) with four parameters, namely α_a=α_b, α_c=α_d, R_(ac)=R_(bd) and the ratio b/a, it is possible to obtain a still better result. Extension of the present method to the treatment of more complex molecules is now under investigation.  (1)討論了用自洽勢場多中心分子軌道法來處理H_2分子的一般方法。 (2)用僅含兩個參變數三中心分子軌道進行了具體計算,求得H_2分子的結合能為3.598eV,接近於Coulson用五個參變數的雙中心分子軌道所得的結果(3.603eV)。 (3)用不在原子核上的兩中心的分子軌道求得H_2分子的結合能為3.630 eV,此上述結果為好。並指出如用不同的α值和四個或四個以上中心的分子軌道,很有可能得到更好的結果。以上處理方法有可能推廣到比H_2更為複雜的分子。   << 更多相关文摘 
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