This article Shows a simple method with which we can obtain the sum formula of S_(x+1)(n) from the sum formula of S_K(n)=1~K+2~k+…+n~k where K=1,2,…. Using this method, we can obtain the next Bernowlli's number B_(k+1) in passing.

The sum of heterotrophic bacteria was( 2.37±1.83)×10~7 cfu/L and Vibrio were (11.77±13.86)×10~5 cfu/L in cultural water, but in sediment surface the heterotrophic bacteria were (7.90±29.08)×10~8 cfu/L, the Vibrio (1.18±3.27)×10~7 cfu/L.

The energy response function of the array has been given,i, e. lg(E_0)=lg(0.4×∑N_i)±0.226,where E_0(TeV) is the primary energy of the incident particle,∑N_i is the sum of detected particle number on FT detectors.

We suggest that the relative abundances be normalized so that the sum of the abundances for all spots considered is the same for all maps.

LetJ={1,2,...}d and let {Xj, j∈J} be an α-mixing sequence which is not necessarily stationary and letS(nA) be the sum of allXj for whichj/n∈A.

Let G be a graph and denote by Q(G)=D(G)+A(G), L(G)=D(G)-A(G) the sum and the difference between the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively.

In particular, if d?3 and the sum of degrees of any s (s=2 or 3) nonadjacent vertices is at least n+(s-1)k+1-d, then dk(G)?d.

The results indicate that the original number of OSL traps that have captured electroncs is linearly related with the sum of TL decay during the OSL process.

This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the...

This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the sum of modified stiffness of all the bar-ends at a joint as the auxiliary frame constant. The basic frame constants at the left of right ends of all the bars are computed by the consecutive applications of a single formula in a chain manner. The auxiliary frame constant at any joint where it is needed is computed from the basic frame constants at the two ends of any bar connected to the joint, so that its value may be easily checked by computing it from two or more bars connected to the same joint.Although the principle of this method was developed by Dr. Klouěek and Prof. Meng, the formulas presented in this paper for computing the basic and auxiliary frame constants, besides being believed to be original and by no means the mere amplification of those presented by the two predecessors, are of much improved form and more convenient to apply.By the author's formula, the basic frame constants in closed frames of comparatively simple form may be computed in a straight-forward manner without much difficulties, and this is not the case with any other similar methods except Dr. Klouěek's.The case of sidesway is treated as usual by balancing the shears at the tops of all the columns, but special formulas are deduced for comput- ing those column shears directly from joint rotations and sidesway angle without pre-computing the moments at the two ends of all the columns.In the method of propagating unbalanced moments proposed by Mr. Koo I-Ying and improved by the author, the unbalanced moments at all the bar-ends of each joint are first propagated to the bar-ends of all the other joints to obtain the total unbalanced moments at all the bar-ends, and then are distributed at each joint only once to arrive at the balanced moments at all the bar-ends of that joint. Thus the principle of propagating joint rotations with indirect computation of the bar-end moments is ingeneously applied to propagate unbalanced moments with direct computation of the bar-end moments, and, at the same time, without the inconvenient use of two different moment distribution factors as necessary in all the onecycle methods of moment distribution. The basic frame constant employed in this method is the same as that in the method of propagating joint rotations, so that its nearest approximate value at any bar end may be computed at once by the formula deduced by the author. Evidently, this method combines all the main advantages of the methods proposed by Profs.T. Y. Lin and Meng Chao-Li and Dr. Klouěek, and is undoubtedly the most superior one-cycle method of moment distribution yet proposed as far as the author knows.Typical numerical examples are worked out in details to illustrate the applications of the two methods.

(1) Sodium salt of reduced codehydrogenase I has been obtained in good yield as a dry powder from codehydrogenase I by reduction with alcohol and alcohol dehydrogenase. This preparation was stable for at least 5 months when kept dry at -15℃. (2) The properties of the particle-bound codehydrogenase I cytochrome reductase system in heart muscle preparation were found to differ considerably from those of the soluble enzyme as obtained by Mahler et al. Among other things, the affinity for cytochrome c of the particle-bound...

(1) Sodium salt of reduced codehydrogenase I has been obtained in good yield as a dry powder from codehydrogenase I by reduction with alcohol and alcohol dehydrogenase. This preparation was stable for at least 5 months when kept dry at -15℃. (2) The properties of the particle-bound codehydrogenase I cytochrome reductase system in heart muscle preparation were found to differ considerably from those of the soluble enzyme as obtained by Mahler et al. Among other things, the affinity for cytochrome c of the particle-bound enzyme is much greater than the soluble enzyme. The Michaelis constant for cytochrome c of the former is only one twelfth of that of the latter.(Fig. 2A). (3) With either oxygen or excess cytochrome c as electron acceptor, it was found that the overall activity, in terms of rate of oxygen consumption or cytochrome c reduction, when both succinate and reduced codehydrogenase I were oxidized simultanously, did not represent the sum of the rates of oxidation when these two substrates were separately oxidized but equalled only the faster of the two separate oxidation rates(Fig. 5, Tables 1, 2). If 2,6-dichlorophenol indophenol was used as the electron acceptor, the overall rate of simultaneous oxidation of these two substrates was found to equal exactly the sum of the rates of separate oxidation(Table 3). (4) When either oxygen or excess cytochrome c was used as the electron acceptor, reduced codehydrogenase I and succinate each inhibited the rate of oxidation of the other(Figs 4, 6 & 7). Evidence has been presented to show that the inhibition of succinate oxidation by reduced codehydrogenase I is not due to the accumulation of oxaloacetate. (5) When malonate was also added to the reaction mixture, succinate no longer produced any inhibition of the oxidation of reduced codehydrogenase I(Fig. 8). (6) It is therefore concluded that in heart muscle preparation both succinate and reduced codehydrogenase I are oxidized by cytochrome c through a common, velocity limiting factor. This is in accordance with the view previously reached by some workers from studies on the action of certain inhibitors. However, it should be noted that in our experiments no agents which might produce any conceivable change in the colloidal structure of the enzyme system has been employed. (7) It should be emphasized that our results clearly show that great caution must be exercised in drawing conslusion on the role an enzyme might play in a complex enzyme system from studies of the properties of a solubilized enzyme. (8) It is believed that the competition of two enzyme systems for a common linking factor as demonstrated in this report has provided a new method for studies on the mutual relations of two or more enzyme systems.

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