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 In this paper a new divided difference algorithm has been given. It has better properties than salzer's ortho—triple algorithm (of [1]). Let (*) {(x_(3v), y_(3v)), (x_(3v+1), y_(3v)), (x_(3v), y_(3v+1)), (x_(3v+2), y_(3v)), (x_(3v), y_(3v+2))} (v=0, 1, …, r) be r+1 five—point groups in the plane, where x_(3v+1) (y_(3v+1)) differ from x_0, x_3, …, x_(3v) (y_0, y_1, …, y_(3v)), and x_(3v+2) (y_(3v+2)) differ from x_0, x_3, …, x_(3v), x_(3v+1) (Y_0, y_3, …, y_(3v), y_(3v+1)). Assume that the values... In this paper a new divided difference algorithm has been given. It has better properties than salzer's ortho—triple algorithm (of [1]). Let (*) {(x_(3v), y_(3v)), (x_(3v+1), y_(3v)), (x_(3v), y_(3v+1)), (x_(3v+2), y_(3v)), (x_(3v), y_(3v+2))} (v=0, 1, …, r) be r+1 five—point groups in the plane, where x_(3v+1) (y_(3v+1)) differ from x_0, x_3, …, x_(3v) (y_0, y_1, …, y_(3v)), and x_(3v+2) (y_(3v+2)) differ from x_0, x_3, …, x_(3v), x_(3v+1) (Y_0, y_3, …, y_(3v), y_(3v+1)). Assume that the values of f(x, y) at all the points of (*) have been given In this paper we have constructed the following class of interpolation polynomials: P(x, y)=(x_0y_0)+(x_1x_0y_0) (xx_0)+(x_2x_1x_0y_0) (xx_0) (xx_1)+(x_0y_1y_0) (yy_0)+(x_0y_2y_1y_0) (yy_0) (yy_1)+…+(xx_0)(yy_0)…(xx_(3r3))(yy_(3r3))··{(x_(3r)…y_(3r)…)+(x_(3r+1)…y_(3r)…)(xx_(3r))+(x_(3r+2)…y_(3r)…)(xx_(3r)) (xx_(3r+1))+(x_(3r)…y_(3r+1)…) (yy_(3r))+(x_(3r)…y_(3r+2)…) (yy_(3r)) (yy_(3r+1))} where the generalized divided difference coefficients are determined by (1)—(5). In our paper have been proved the following theorems: Theorem3. For every point of (*) we have P(x_i, y_j)=f (x_i, y_j) Theorem5. If f (x, y) has continuous partial derivatives of second order, then the confluent form P~(k)(x, y) of the interpolation polynomial P(x, y) at each point (x_(3k), y_(3k)) satisfies the following osculatory interpolation conditions P_(x_(3k,3k)~n)~(k) =f_(x_(3k,3k)~n), P_(y_(3k,3k)~n)~(k)=f_(y_(3k,3k)~n) (n=1,2; k=0,1,…,r) Finally we have give three concrete formulas to indicate an application of this algorithm.  H.E.Salzer曾給出了平面区域上直角三点組上的二元插值公式。它的最主要的优点是:1)插值結点組可以相当任意的选擇,2)差商系数可以用遞推公式来計算。但它的一个缺点是造出的插值多項式次数要比在同样个数的适定結点組上造出的插值多項式次数(二元混合次数)来的高(見[2])。亦就是說缺項较多。本文提出了一种所謂“十字型五点組”上的二元插值公式,它不仅保留了H.E.Salzer直角三点組插值法的上述优点,而且它的汇合形式还具有二阶偏微商的切触条件。  On the relations between calculi, Moh Shawkwei modified concepts of homomorphism and isomorphism between associate calculi defind by Mapkab to the following four relations between general calculi mutual embedding, mutually strong embeding, similarity and strong similarity, in 1963. Evidently, by the following figure, it may be shown which is stronger or weaker (from left to right): Strong similarity Similarity mutually strong embedding mutual embedding But whether the inverses hold or not is unsolvable. In... On the relations between calculi, Moh Shawkwei modified concepts of homomorphism and isomorphism between associate calculi defind by Mapkab to the following four relations between general calculi mutual embedding, mutually strong embeding, similarity and strong similarity, in 1963. Evidently, by the following figure, it may be shown which is stronger or weaker (from left to right): Strong similarity Similarity mutually strong embedding mutual embedding But whether the inverses hold or not is unsolvable. In this paper, we prove that the inverses are not hold by means of two contraexamyles: the one is the two colculi which have the ralation of mutually strong embedding but no relation of similarity, as following: the corresponding embedding algorithms are: respectively; the another is the two colculi which have the relation ot similarity but no relation of mutually strong embedding, as following: Besides, we introduce two kinds of colculi: pseudounitarystring calculus and unitarystring calculus, the particular case of latter is associate calculus, and prove that mutual embedding and similarity, for two calculi introduced and finite calculus, are the same thing.  本文解决一般演算之间的四个关系:强相似、相似、互相强嵌入、互相嵌入的相互联系。证明了一对演算之间可以只具有相似关系,而不具有互相强嵌入关系,或者相反,从而四个关系的互相联系完全明白。同时证明,对某些种类的演算而言,互相嵌入和相似是同一回事。  The structure of cometary dust tails is studied in the frame of mechanical theory with special regards to threedimensional treatment of the problem. We begin with the reexamination of orbit mechanics of cometary particles to derive a set of formulae convenient to subsequent discussions and calculations.Mak ing use of Hamilton's integral b,we have obtained,for example,the equation of orbit in a vectorial form with generalization respecting to force parameter μ(Part 2).On the basis of Part 2,we consider such... The structure of cometary dust tails is studied in the frame of mechanical theory with special regards to threedimensional treatment of the problem. We begin with the reexamination of orbit mechanics of cometary particles to derive a set of formulae convenient to subsequent discussions and calculations.Mak ing use of Hamilton's integral b,we have obtained,for example,the equation of orbit in a vectorial form with generalization respecting to force parameter μ(Part 2).On the basis of Part 2,we consider such problems as follows:the relation between initial conditions together with μ and the orbit characteristics;the algorithm for computercalculation of the motion of particles some interesting features of ele mentary space distributions vertical motion relative to the comet orbit plane and its implications to the tail structure. Arguments given in §2.5 yield two important results.One is a criterion to check the applicability of the FP(Finson and Probstein)method.The other con cerns with the somewhat peculiar structure to appears in the dust tail of comet after perihelion passage,which might be termed as《Neckline structure(henceforce ab breviated to NLS)》. In Part 3,we present a new interpretation of the anomalous tails refered to the concept of NLS.A discussion of the development of NLS is given,and it is shown that the emergence and development of NLS can provide an adequate expla nation for the behaviour of the anomalous tail of C/ArendRoland,1957 Ⅲ.Fur thermore,statistical consideration on the visibility of anomalous sunward tail is at tempted,the result of which also shows that the NLSinterpretation seems to be compatible with the data since 1801. In Part4,we develop a new method for numerical analysis of tail brightness. The basic idea of this method is to combine exact treatment of the motion of a large number of sample particles and countingtechnique to estimate the surface brightness integral,taking account of the dust emission characteristics of comets which may be expressed by three source functions,namely,the emission rate N_d(t),the modified sizedistribution f(γ;t),and the velocity distribution where Ψ(v;r,t)γ=1μ). Distribution of tail brightness thus obtained gives essentially the exact solution for the assigned source funtions,in the sense that it is not affected by any auxiliary approximations.Moreover,no difficulties arise in the handling of source functions, because the requisite procedure can be reduced to the sampling of values of relevant parameters;thus the present method is applicable equally well for the case of ani sotropic emission. In an application of the method for C/ArendRolandPart4),we suppose that the emission rate varies as the inversesquare of heliocentric distanceN_d(t)∝[rc(t)]~(2)), and that the velocity distribution is characterized as the isotropic one with a unique speed vo(t,γ).The function f(γ;t)is left as one to be determined through the comparison with observation. The function f(r)for C/ArendRoland,derived by neglecting its timedependency, is shown in Fig.16.The corresponding brightness probiles are compared with observed ones in Figs.14 and 15,for Apr.28 and Apr.30,respectively,it is worth noting that both main and anomalous tails have been treated in a unified manner, that is,without any temporal anomalies in emission characteristics. With these results,we conclude:(1)The simple forms presupposed for two functionsN_d(t)and Ψ(v;γ,t))may be well accepted as first approximations;(2) The derived function f(γ)shows its broad peak around γ=0.10～0.12 and possibly a secondary peak around γ～0.015;(3)The present brightness analysis adds support, in a quantitative way,to the NLSinterpretation of the.anomalous tails;(4)More observational data and careful analyses are needed,however,to establish the dust emission characteristics of comets.It is hoped that methods and viewpoints described in the present article may serve as the basis for future investigations.  本文以“三维的”粒子运动讨论了尘埃彗尾的结构,为了便于使用电子计算机和讨论各种μ值的粒子的运动,引入哈密顿积分 b,获得了以三维矢量和适用于各种μ值的开普勒运动的各个公式.考虑粒子的三维运动及其运动范围,使过近日点后的尘埃彗尾出现一“颈线结构”.利用此颈线解释向日尾并分析了其产生的可能性.最后给出了一种定量分析尘埃彗尾亮度分布的方法,本法的基本想法是在考虑有关粒子抛射的函数条件下,计算取样粒子的运动,并利用计数法求出其数密度.本文结果在所取函数条件下是一严格解.应用时,我们假定两函数N.(t_i),ψ(v;r,t)及 v_0的函数形式,以有关粒子性质的函数 f(r)为参量,分析了阿朗罗兰彗星的尘埃彗尾(包括向日尾)的亮度分布(图14,15),并得到函数 f(r)(图16).   << 更多相关文摘 
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