The flux of primary cosmic ray nuclei of atomic numberZ⩾2 at geomagnetic latitude 30°

The method of determining the primary flux of nuclei with atomic number Z?3 developed by Bradt and Peters, has been extended to include all nuclei of charge Z?2. It is shown that the method permits the identification of primary helium nuclei with an efficiencyν?90%. The primary α-particle flux obtained in this way is in very good agreement with that obtained by other methods and the relative flux values for nuclei of atomic number 3?Z?5 and 6?Z?9 agree with previous determinations.     

360°的来历

据说360°是古代巴比伦人的杰作.在公元前两千年之前,巴比伦人就有了长度“里”的概念,但它的1(巴)里很大(约为12公里),在此基础上逐渐又产生了“小时”的概念,他们是以人们走1(巴)里所用的时     

sin18°和cos18°的值的各种求法

sin18°和cos18°通常用几何法求解。但讀者从本文提供的各种解法中,不难体会到这是一道很好的綜合題。通过各种解法练习,会有助于我們綜合运用中学数學知識能力的提高。在求解sin18°和cos18°的各种方法中,都将遇到把cos nx表达成仅含cosx的函数这一过程。     

Kinetostatic analysis of variable lead screw mechanisms with 3° conic frustum meshing elements

The main concern of this paper is the theoretical kinetostatic analysis of a variable lead screw mechanism (VLSM) used in high speed shuttleless weaving looms. The mechanism consists of a slider-crank submechanism, with four conic frustum meshing elements (with a 3° conical angle) installed in the slider to drive the oscillatory motion of the variable lead screw. It is the spatial cam joint between the meshing elements and the screw. Then, d'Alembert's principle and theory of conjugate surfaces are applied to develop the models for the kinetostatic analysis; models for analyzing the frictional forces of various kinematic joints are also implemented. The result is a set of 27 nonlinear equations with 27 unknowns. The power equation is also applied to analyze the input and dissipated power of the VLSM, its results are also used to check the correctness of solutions to the nonlinear equation set. The VLSM is analyzed for a specified constant input speed or a measured state of motion of the crank. The results show that the peak input power and the peak input torque at constant input velocity are almost twice that of their values at nonconstant input velocities. There are obvious changes in the bearing loads when the slider is at both of its limit positions due to the change in the directions of the frictional forces.     

用几何方法求15°、75°角的三角函数值

初三几何教科书中,介绍了利用锐角分别为30°、45°的两个基本直角三角形,通过建立形与数之间的联系,直接求得30°、45°、60°等这些特殊角的三角函数值.在锐角中,15°和75°角也是较为特殊的角,利用基本的直角三角形,我们也可以求出它们的三角函数值.     

旋转90°解正方形

<正>正方形是有四条边相等、四个角都为90°的平面图形.因此,在有些正方形的解题中,将图形中的部分绕某一顶点按顺时针或逆时针方向旋转90°,就能达到使相关的边重合,促进条件与结论相对集中的效果,进而打通解决问题的途径.     

60°角思维体操

60°角是图形中的特殊角 ,含 60°角的三角形往往有许多美妙的性质 .怎样利用 60°角的条件呢 ?好 !下面让我们一起来做 60°角思维体操 .一利用 60°角构造直角三角形图 1例 1　如图 1,圆内接四边形ＡＢＣＤ中 ,∠Ａ =60° ,∠Ｂ =90° ,ＡＤ =3 ,ＣＤ =2 .(1)求ＢＣ的长 ;(2 )求四边形ＡＢＣＤ的面积 .(第十四届江苏省竞赛题 )解　延长ＡＢ、ＤＣ交于点Ｅ .∵　∠Ｄ =180° -∠ＡＢＣ =180° -90° =90°,∠Ａ = 60° ,∴　∠Ｅ =3 0°,ＡＥ =2ＡＤ =6,ＤＥ =3 3 .∴　ＥＣ =3 3 -2 .∴　ＢＣ =12 ＥＣ =32 3 -1.(2 )在Ｒｔ△ＢＣＥ中 ,Ｂ…     

不用计算器求tan22°30’与tan15°的值

在学习三角函数这一章时，老师引导我们大家通过构造特殊直角三角形，探究出了tan30°=√3/3，tan45°=1,tan60°=√3，一般的角度的正切值，书上给出了怎样用计算器来求，如果不用计算器能求出tan22°30’与tan15°的值吗？     

The1I6 state of Pr3+ in LaCl3 at 77°K

A single crystal of 5% Pr³⁺ in LaCl₃ was grown by Stockbarger’s method and its absorption spectrum at 77° K. recorded in the region 4200–5400 Å on a grating spectrograph having a dispersion of 5 Å/mm. in the first order. Polarization of the absorption lines has also been obtained. In the group of lines arising from¹I₆ ←³H₄ transition, six more lines in addition to the four previously known have been observed. Satisfactory analysis of all these ten lines is given. One additional Stark level in¹I₆ is established at 21407 cm.^?1 withμ=1. For a few lines the polarization results obtained here do not agree with those of previous workers but fit in satisfactorily in the analysis.     

The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ° = Ker θ° , where ρ° = ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.     

Sin18°求值三法

我们知道:sin18°=(5~(1/2)-1)/4,通常它是通过sin(2×18°)=cos(3×18°)利用二倍角、三倍角公式展开后解方程求得的。以下我们介绍sin18°值的另外三种求法。方法一(几何法) 如图等腰三角形ABC,两底角为72°,顶角为36°,并设腰长为a,底边长为c,过C作底边AB的垂线,则∠BCB=180°在Rt△BCD中,就有     

构造图形求sin18°

构造图形求ｓｉｎ１８°王昌元（湖北省松滋师范４３４２００）１构造如图１所示的三角形，依余弦定理易得ｃｏｓ３６°＝１—２ｘ２（１）ｃｏｓ７２°＝ｘ即２ｃｏｓ２３６°－１＝ｘ（２）由（３）得（ｘ－１）（２ｘ＋１）（４ｘ２＋２ｘ－１）＝０（４）易知，在（４...     

Study of solar flares using cosmic radio noise on 25 Mc./s. at Ahmedabad (23°02′ N., 72°38′ E.)

The paper describes observations made at Ahmedabad of sudden cosmic noise absorptions (SCNA’s) on 25 Mc./s. associated with solar flares. The frequency distributions of solar flare attenuations, their times of growth and duration, etc., have been determined and the results are compared with similar observations made by other workers. It has been found that SCNA’s of 25 Mc./s. recorded at Ahmedabad in 1956–58 have been markedly larger in size and duration than those observed in Australia on 18·3 Mc./s. in 1950–51.     

为什么tan90°无意义?

<正>当我们被问到"为什么tan 90°无意义"时,总会下意识回答"因为正切函数的函数图象在90°处取不到",但事实上这是不准确的.对于三角函数而言,是先有三角函数的概念,之后才有的三角函数图象,因此并不能通过函数图象在某一点是否取得到,来解释函数在某一点是否有意义,而需要从函数的由来入手进行解释.三角函数源于天文学、测量等实际需要,正切函数和与之联系较为紧密的余切函数的研究主要是由于日影测量而引起的.