1937年, 第2卷, 第2期　刊出日期：1937-06-15

  

• 全选
  |

论文
• Select
  PROJECTIVE DIFFERENTIAL GEOMETRY

  ;

  数学学报. 1937, 2(2): 143-151. https://doi.org/10.12386/A1937sxxb0010

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> By hypothesis the curve C_m has with C a contact of order m+1;the constant term and the coefficient of the term s in the expansion off/s~m must vanish,namely,
• Select
  CONTRIBUTIONS TO THE PROJECTIVE THEORY OF CURVES IN SPACE OF N DIMENSIONS(First Memoir)

  苏步青

  数学学报. 1937, 2(2): 153-173. https://doi.org/10.12386/A1937sxxb0011

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> In the present paper we propose to establish certain theoremsconcerning plane sections of the circumscribed developable of a curvein the projective n-dimensional space s_n((?)3).The planes in considera-tion are supposed to be in the osculating spaces s_3 of the curve.Forthe planes of other kinds the corresponding sections must have a singularpoint of higher order and consequently require more complicated repre-sentation,as we have shown in other places.The allied problemwill be considered in a subsequent paper.
• Select
  ON A GENERALIZED WARING PROBLEM II

  华罗庚

  数学学报. 1937, 2(2): 175-191. https://doi.org/10.12386/A1937sxxb0012

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Introduction.Let P(h) be an integral-valued polynomial of theK-th degree and with positive first coefficient,Let G(P(h.)) be theleast value of integers such that the Diophantine equation
• Select
  SOME NEW GEOMETRICAL SIGNIFICANCES OF THE PROJECTIVE CURVATURES AND THE CURVATURE FORM OF A SPACE CURVE

  方德植

  数学学报. 1937, 2(2): 193-197. https://doi.org/10.12386/A1937sxxb0013

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Su has recently established the projective theory of space curvesby a purely geometrical method and has shown among other thingsthat the projective invariants of a curve can simply be expressed by cer-tain double ratios.In my former paper I have interpreted the curvatureform by the Von Staudt's double ratios of the tangent of the space curveC at a point infinitely near an ordinary point P with respect to unda-mental tetrahedron of Sannia at P.
• Select
  DER DUAL DER GRUNDFORMEL IN INTEGRALGEOMETRIE

  吴大任

  数学学报. 1937, 2(2): 199-204. https://doi.org/10.12386/A1937sxxb0014

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Eine grundlegende Formel in Integralgeometrie ist die sogenannte,,kinematiscke Hauptformed.“Diese Formel wurde zuerst tüb Komplexeund sparer auch fur stetig gekrümmte Fl(?)cher im Euklidiscben Raumvoll W.BLASCHKE bewiesen,Im lctzten Falle wurde sie aus einer Dich-tenformel hergeleitet,die man,,die kinematische Grundformel für be(?)egteFl(?)chen“oder kurz,,die Grundformel“nennt.Ich habe gezeigt,dassgenau dieselbe Grundformel im elliptischen Raum gilt und dass sie indiesem Falle in einer dualen Weise sich erkl(?)ren l(?)sst.Man bekommtdadurch sofort den Dual der Grundformel,welche im elliptischen Raumalso nichts Neues als die Grundformel selbst liefert.Es soll der Zweck
• Select
  NOTE ON THE DIOPHANTINE EQUATION

  柯召

  数学学报. 1937, 2(2): 205-207. https://doi.org/10.12386/A1937sxxb0015

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Dr.Erd(?)s conjectured that the Diophantine equation(1)x~x y~y=z~zhas no integer solution, if,x>1,y>1.z>1.In the present note,Ⅰshall prove that his conjecture is correct ouly (?)(x,y)=1 and(1)has intinitely many solutions when (x,y)>1.
• Select
  ON THE MEYER'S THEOREM AND THE DECOMPOSITION OF QUADRATIC FORMS

  柯召

  数学学报. 1937, 2(2): 209-224. https://doi.org/10.12386/A1937sxxb0016

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Meyer proved in 1883 theTheorem M.ecery indetiuite quadratie form in more than fourrep(?)sents zero with the rariables not all zero.
• Select
  ON THE REPRESENTATIONS OF THE COMPLEX 3-DIMENSIONAL AND THE REAL 4-DIMENSIONAL ORTHOGONAL GROUPS AND THEII SOMORPHISM

  李华宗

  数学学报. 1937, 2(2): 225-233. https://doi.org/10.12386/A1937sxxb0017

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> It is well-known that the camplex linear unimodular group G_2 ofa 2-dimensional affine space E_2 is a representation of the real orthogonalgToup G_4 of a 4-dimensional euclidean space R.In this paper it isshown that the same group G,is also a representation of the complexorthogonal group G_3 of a 3-dimensional euclidean space R_3,and that anisomorphism between G_4 and G_3 can be established.
• Select
  SUR LES ENSEMBLES FERMES PUNCTIFORMES

  周绍濂

  数学学报. 1937, 2(2): 235-237. https://doi.org/10.12386/A1937sxxb0018

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> 1.La presente Note a pour but de donner le théorème suivant:Etant danné un ensemble spatial fermé punctiforme E et deuxpaints quelconque A et B n'appartenant pas àE.on peut toujours joindreles deux,points A et B par un are simple de longuer bornée rencon-trant pas E.
• Select
  ON THE PLANE SECTIONS OF THE TANGENT SURFACE OF A SPACE CURVE

  熊全治

  数学学报. 1937, 2(2): 239-245. https://doi.org/10.12386/A1937sxxb0019

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> 1.Introduction.Let the tangent surface of an analytic curve Cin ordinary space be cut by a plane through a tangent at an ordinarypoint O of C,then the plane section thus obtained has a point of in-flexion at O,provided that the plane is not osculating to C at O.Thisis a well-known fact.Prof.Bompiani has enriched the projectivedifferential geometry of a plane curve at the neighbourhood of a point ofinflexion by introducing various covariant osculants.Prof.Su hasgiven some remarkable properties of the loci of the cusp-tangent t ofthe seven-point cusped cubic of the plane section of the tangent surfacemade by a variable plane n through a tangent of C at O.Prof.Lanehas investigated the loci of the osculants and various points and linesintroduced by Prof.Bompiani.The object of this note is to obtain someproperties of other loci related to the same problem as considered byProf.Su.
• Select
  THE GEOMETRY OF HIGHER PATH-SPACES

  陈省身

  数学学报. 1937, 2(2): 247-276. https://doi.org/10.12386/A1937sxxb0020

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> IntroductionThe geometry in a space R_n(x~1,…, x~n)in whit.h there is givena system of differential equations of the r-th order:(?)has recently been studied by various writers.It seems to me thatthe most natural way to study this problem is to formulate the problemas a problem of equivalence.By solving complelely the problem ofequivalence the geometry in the space is automatically defined.By theuse of the general method of Cartan the problem of equivalence and thedefinition of a geometry trom a geometric object become two aspects ofthe same problem.We want to illustrate this point clearly in the (?)s-eussion of the present problem.
• Select
  CONTRIBUTIONS TO THE PROJECTIVE THEORY OF CURVES IN SPACE OF N DIMENSIONS(Second Memoir)

  苏步青

  数学学报. 1937, 2(2): 277-289. https://doi.org/10.12386/A1937sxxb0021

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> In a recent paper of the same title we studied the plane sectionsof the circumscribed developable of a curve in the projective n-dimen-sional space Sn(n(?)3) confining ourselves to the consideration of theplanes contained in the osculating space S_3(P) at an ordinary point Pof the curve.In particular, the plane section x_3 made by a planethrough the tangent of the curve at P has an inflexion at P and conse-quently admits an invariant point O_6,namely,the cusp of the cubic whichhas with x_3 a contact of order 6 at P.We have established among otherthings that when the plane π turns about the tangent the correspondingpoint O_6 describes a twisted cubic Г_3 in the osculating space S_3(P) ofthe curve at P.
• Select
  CESRO MEANS CONNECTED WITH THE ALLIED SERIES OF A FOURIER SERIES

  周鸿经

  数学学报. 1937, 2(2): 291-300. https://doi.org/10.12386/A1937sxxb0022

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> 1.Introduction.It is classical that,if the Fourier series of a function ψ(t) ofbounded variation is (?) sin nt,the sequence (?) is bounded.This resultcannot be improved.“For,the function (?) whoseFourier series is (?) sin nt is of bounded variation;but we have(?).We know,however,that,if ψ(t) is of bounded varia-tion in (0, 2π),the sequence (?) converges(c,β) to 2π~(-1)ψ(+0) for everyα>0.In this paper Ⅰ shall give some results concerning the convergence(C) of the sequence (?),by studying the Ces(?)ro means ψ(t) of ψ(t).
• Select
  ON AN EXPONENTIAL SUM

  华罗庚

  数学学报. 1937, 2(2): 301-312. https://doi.org/10.12386/A1937sxxb0023

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> The main object of this paper is to prove the following theoremLet f(x)be a polynomial of the k-th degree with integer coeffi-cients
• Select
  SOME“ANZAHL”THEOREMS FOR GROUPS OF PRIME-POWER ORDERS

  华罗庚;段学复

  数学学报. 1937, 2(2): 313-319. https://doi.org/10.12386/A1937sxxb0024

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> In the theory of p-groups,or groups whose orders are powers ofa prime p,there are a number of the so-called“Anzahl”theoremswhich relate to the number of sub-groups with a certain property.Weshall define a group(?)of order p~n as of rank δ,if the highest order ofthe elements of (?) is equal to p~(n—δ).By means of this notion the “Anzahl”theorem due to Miller can be restated as follows:
• Select
  ON ELECTRIC NETWORKS

  周炜良

  数学学报. 1937, 2(2): 321-339. https://doi.org/10.12386/A1937sxxb0025

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> Consider an electric network N with n conductors F_1,F_2,…,F_n,of resistances.R_1,R_2:…,R_n respectively,and d+1 jumctions P_1,P_2,…,P_(d-1).Let a direction be assigned to each conductor in a quitearbitrary way.To each junction P_i we shall associate a row n—vector,that is a (?),n)-matrix(P_(i1), P(i2), "",P_(in)),where p_(ij)is equal to+1.-1.or 0 according as F_j is directed toward P_i,direated away from P_i.or not connected with P_i The d+1 vectors thus defined shall be denof-ed again by Ⅰ_i~′,P_2…,P_2…,P_(d+1).Since the relation(?)evidently
• Select
  A CORRECTION

  江泽涵

  数学学报. 1937, 2(2): 341-342. https://doi.org/10.12386/A1937sxxb0026

  摘要 ( ) PDF全文 ( )   可视化   收藏

  <正> In my paper entitled'On the Poincaré's groups and the extendeduniversal coverings of closed orientable two-manifolds”,the conversepart of (i) of Number 7 is not valid and should be omitted.The firstplace where this conve(?)se part was used is in the proof of(iii)ofNumber 7.To make the correction,at the end of(i)of Number 5 wereplace“not reduced.”by“not reduced, but (u_(1,1)) (u_(1,2))is reduced”,and to(iii)of Number 5 we add“When u_(1,2) is not the(2p-1)st f.e.