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Frames have applications in numerous fields of mathematics and engineering.


This paper shows a number of problems in pure and applied mathematics that are solved by constructing transportation networks.


Numerical multilinear algebra (or called tensor computation), in which instead of matrices and vectors the higherorder tensors are considered in numerical viewpoint, is a new branch of computational mathematics.


Also, the mathematics mechanization method can be extended to solve other mechanism problems involving nonlinear equations symbolically.


In this study, we developed an assessment method of indicator system (AMIS) based on analytical hierarchy process (AHP), fuzzy mathematics, and the theory of nethierarchy.

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 The paper discusses the method of determinating the cam profile,with roller or platfaced follower,by means of instantaneous centers.The proposed graphical method may directly plot the cam profile without plotting its pitch curve,therefore its construction is more simplified and more accurate.The proposed analytical method may lead to the simplest formula by using elementary mathematics so as to simplify the caculating process,and consequently it is most apt to be adopted by designers.  本文研究用相对速度瞬心求滚子从动杆和平底从动杆凸轮实际轮廓的方法。这种作图法可以直接求出凸轮的实际轮廓曲线而毋须绘制其理论轮廓线,因而使作图简化精确。这种分析法可以用最浅近的数学推导得出最简单的计算公式,使计算工作简化、故宜于一般设计人员采用。  In this paper we briefly review the existing types of large radio telescopes and sug gest certain principles to be considered in future design.With these in mind,a new type of telescopes is proposed.This consists of a large central paraboloid and a number of outer rings of discrete antenna elements. Fig.1 shows the arrangement of the paraboloid and one ring.When the two are connected by “correlation technique”,the resulting radiation pattern will be D∞F_1F_2, where F_1,F_2 are the field patterns of the paraboloid... In this paper we briefly review the existing types of large radio telescopes and sug gest certain principles to be considered in future design.With these in mind,a new type of telescopes is proposed.This consists of a large central paraboloid and a number of outer rings of discrete antenna elements. Fig.1 shows the arrangement of the paraboloid and one ring.When the two are connected by “correlation technique”,the resulting radiation pattern will be D∞F_1F_2, where F_1,F_2 are the field patterns of the paraboloid and the ring respectively.By suitably chosing the radius of the paraboloid R_0,the radius of the ring α,and the number of elements in the ring n (R_0 and a being expressed in unit of the working wavelength), one may neglect the influence of the “secondary patterns” in F_2 (which occurs because the aperture of the ring is not full,but discrete).The Fourier transform of D∞F_1F_2 will then be expressed by equation (22) and shown in Fig.3,in which we take the radia tion pattern of the paraboloid to be represented by Λ_2~2 (2πR_0r). When there are N rings with radii α_1=β_1R_0,α_2=β_2R_0,……,α_N=β_NR_0,and when they are connected with the central paraboloid by “correlation technique”,the radiation pattern will be D(r)=C_0[Λ_2(2πR_0r)]~2+CΛ_2(2πR_0r)[A_1J_0(2πα_1r)+A_2J_0(2πα_2r)+ +……+A_NJ_0(2παNr)],(26) where C_0,C,A_0…A_N are constants.The transform of D(r) is then expressed by equa tions (37),(23),and (27),and may be adjusted to the form as shown in Fig.5.We see from the figure that the curve has nonzero values between the zero spatial frequency and the high frequency cutoff.Hence by the principle of “convolution correction” as pointed out by Wild in [11],the pattern may be “transformed” into a desirable one when a correcting function G is applied. To obtain such a curve as in Fig.5,that is,a curve with nonzero values below cutoff,one may choose the parameters β_m=α_m/R_0(m=1,2,…,N) so that the individual Fourier transforms corresponding to the paraboloid and successive rings will overlap in certain spatial frequency ranges.With this condition and the consideration of economy of arrangement,we may determine β_m and hence n_m [eq.(30)]. Table 1 gives the values of β and n as required in such design.In the sixth column of the table,we also give the halfpower beam widths of the resulting patterns when they are corrected to Λ_1~2 (2πR_1r),where R_1=(β_N+1)R_0/2 (unit:R_0/2 minute of arc). For the sake of illustration,we take the total number of the rings N as 6.Denote the Fourier transform of radiation pattern D by (?),which curve is sketched in Fig.5. In the figure,the amplitude of (?) being modified to conform with the curve (?)_1~2 in order to suppress secondary lobes.The reverse transform of (?) is shown in Fig.6,which is the resulting radiation pattern.From it we see that the halfpower beam width is about (200/R_0)′,the secondary lobe is tolerable,but rather broad. For correcting the pattern to Λ_1~2 (Fig.9),one has to find the correcting function G. As was done by Wild in [11],we have calculated the functions (?)=(?) and G in the case of zenith distance z=0.(Figs.7 and 8) Such calculations may be extended to other zenith distances,but the mathematics will be much more tedious. This type of radio telescope has the following essential characters: (1)It may be looked upon as the extension of a large paraboloid in the sense of improving the resolution and the collecting area.The field of application is wider than most of the usual types of large radio telescopes. (2)The system of antennas is good for wide range of wavelength variation. (3)At any stage,it always permits further developement by addition of outer rings. (4)It is advantageous to have the central paraboloid as large as practicable,since the resolving power is proportional to the factor (β_N+1)R_0.For given β_N,the total num ber of elements required in the rings is the same for any R_0. (5)Away from the zenith,while the resolution in horizontal direction remains the same,that in vertical direction gradually deteriorates with the ihcrease of zenith distance. For N=6,the main lobe expands 1.8 times at z=60°,and 3.2 times at z=75°. (6)Beam swinging and scanning present some technical difficulties Owing to the path differences between different elements being functions of both azimuth and eleva tion. (7)The “convolution corrections” of the radiation pattern are different for dif ferent zenith distances.  本文从讨论现有各种大型射电望远镜系统出发,根据技术条件和研究工作的发展趋势,提出在设计中应当考虑的因素.按照这些考虑,提出了由一个中央大型抛物面天线和多个环状分布分立天线组合而成的系统,导出这种组合的设计公式,并以环的数目 N=6为例,计算了具体的天线方向图形空间谱,并算出为了调整方向图形所需的改正曲线,以及通过两种改正方法所得到的图形.这种系统有着多用途的特点.同时它可以适用于很宽的波长范围,而且通过增加环数可以得到不断的发展.文中讨论了这些特点,提出了一些问题,并且对实现这种方案的技术条件作了简要的叙述.  1135 observations of MR Cyg in yellow light were obtained on 19 nights from September to November, 1975, using the 60cm reflector at Xinglung station. The determination of the time of primary minimum by the method of Kwee and van Woerden gives the result JD. 2442729. 09916. In an attempt to solve the light curve by Kopal's iterative method we met the difficulty of non convergence and this has successfully been overcome by using the new method of LuChenZou. According to our analysis the primary minimum should... 1135 observations of MR Cyg in yellow light were obtained on 19 nights from September to November, 1975, using the 60cm reflector at Xinglung station. The determination of the time of primary minimum by the method of Kwee and van Woerden gives the result JD. 2442729. 09916. In an attempt to solve the light curve by Kopal's iterative method we met the difficulty of non convergence and this has successfully been overcome by using the new method of LuChenZou. According to our analysis the primary minimum should be a partial eclipse of transit type. The usual practice of using the (OC)criterion alone in selecting an optimum photome tric solution is shown to be rather misleading so far as the relevant analysis rests on the basis of the observational accuracy of present day photoelectric photometry. A partial remedy thereby is achieved in the new method by making use of the depth equation too. Further computer study along this line is under way. All calculations in this study were carried out on the DJS21 Computer of the Computing Station of the Institute of Mathematics, Academia Sinica.  对密近双星MR Cyg进行黄光光电观测,得到完整的光变曲线,采用陆陈邹的解轨方法,用电子计算机算得测光轨道根数,对解的结果和测光解轨方法进行了讨论.   << 更多相关文摘 
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