1936年, 第1卷, 第1期　刊出日期：1936-05-15

  

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  A PROBLEM WITH VARIABLE END POINTS IN THE CALCULUS OF VARIATIONS

  胡坤升

  数学学报. 1936, 1(1): 1-14. https://doi.org/10.12386/A1936sxxb0001

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  <正> 1.INTRODUCTION.Let g be an extremal arc with conjugateend points for the integral(?)In case n=1,the question whether or not g actually minimizes Ⅰrelative to arcs joining the ends of g has been discussed by Kneser(~1),Osgood(~2), Lindeberg(~3),and others by studying the shape of the en-velope of the extremals passing through an end point of g.In thecase n=2,Hahn(~4) has reduced the problem to that of an ordinaryminimum of a function of two variables by using a family of brokenextremals joining the ends of g.The method of Hahn is generaland can be extended in several directions as has been recently doneby Morse(~5)
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  A TAUBERIAN GAP THEOREM OF HARDY AND LITTLEWOOD

  NORBERT WIEXER

  数学学报. 1936, 1(1): 15-22. https://doi.org/10.12386/A1936sxxb0002

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  <正> The theorem here discussed resembles typical Tauberian theoremsin being a partial inver of Abel's theoem on power series,butdiers in the uature of the auxiliary hypothesis imposed to permitthe inversion.The classical Tauberian theorem of Hardy and littlewood
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  ON WARING'S PROBLEM WITH POLYNOMIAL SUMMANDS

  华罗庚

  数学学报. 1936, 1(1): 23-61. https://doi.org/10.12386/A1936sxxb0003

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  <正> (?)is an integral-valued poly-nomial with α_0>0 and there do not exist two integers u and ι(>1)such that
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  ON THE AFFINE MANNHEIM CURVES

  方德植

  数学学报. 1936, 1(1): 62-69. https://doi.org/10.12386/A1936sxxb0004

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  <正> In the theory of the affine differential geometry of curves inspace as developed by E.Salkowski the coordinates of a curveare given by three linearly independent solutions of the differentiale(?)tion,
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  TRANSCENDENCY OF FUNCTIONS SATISFYING RICCATI DIFFERENTIAL EQUATION

  陈建功

  数学学报. 1936, 1(1): 70-80. https://doi.org/10.12386/A1936sxxb0005

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  <正> 1.The object of the present Paper is to establish the followingTHEOREM.Let Let R(x)≠0,S(x) and,T(x) be three rationalfunctions.(?)function II(x) satisfying the Riccati differentialcquatton
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  ZUR STUFENTHEORIE DER QUASI-ALGEBRAISCH-ABGESCHLOSSENHEIT KOMMUTATIVER KRPER

  曾炯之

  数学学报. 1936, 1(1): 81-92. https://doi.org/10.12386/A1936sxxb0006

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  <正> E.Artin hat wohl zuerst bemer(?),dass die Theorie der Al-gebren als eine. Theoric diophantischer Gleich(?)gon in K(?)pent betrachtet werden kaum.Vor allen(?)tier D(?)von Gleichungen mit (?)Nach Artin nennenwir einen K(?)rper K quasi-algeb(?)jede homo-gene Gleichtung ,deren Unbekam(?)tenzahl gr(?)ssor als der (Grad ist,eine
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  ON THE POINCARE'S GROUPS AND THE EXTENDED UNIVERSAL COVERINGS OF CLOSED ORIENTABLE TWO-MANIFOLDS

  江泽涵

  数学学报. 1936, 1(1): 93-153. https://doi.org/10.12386/A1936sxxb0007

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  <正> Ⅰ.POINCARES GROUPS AND REDUCED CHAINS1.ⅠNTRODUCTION.Let M be a closed orientable two-mani-fold of genus p>1 and M its universal covering (?)berlagerung).Nielsen (?) has begun with an M in non-Euclidian hyperbolic planerepresented inside the unit circle in the complex plane,and thenadjoined to M the points of the unit cilcle.This M plus the pointsof the unit circle form what we shall call, in the present paper,thecanonical representation of an abstract“extended” universal coveringfor p>1.By means of geometrical considerations of M plus theunit circle,and group-theoretic considerations of the Poincares groupof M*, he has investigated finally the continuous transformations ofM* into itself and the fixed point problem.
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  ON INTERPOLATION AND APPROXIMATION BY RATIONAL FUNCTIONS WITH PREASSIGNED POLES

  申又枨

  数学学报. 1936, 1(1): 154-173. https://doi.org/10.12386/A1936sxxb0008

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  <正> 1. INTRODUCTION. It is the purpose of this paper to presentsome results,on the problem of interpolation and approximation toa functiou f(z),analytic on a closed limited point set E in thecomplex z-plane whose complement K is connected and regular inthe sense that Green's fumction for K exists,by rational functionsf_n(z) of respective degrees n,n=1,2,…of the form
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  ON CERTAIN CONFIGURATIONS(T)OF FINIKOFF AND THE TRANSFORMATIONS OF CALAPSO

  苏步青

  数学学报. 1936, 1(1): 174-206. https://doi.org/10.12386/A1936sxxb0009

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  <正> ⅠNTRODUC(?)NIn a recent paper the author has published the result, ofsome,investigations on the periodic sequences of Laplace of periodfour with a stratifiable couple of diagonal congruences.Thedeterinination of these soquences of Laplace requires the integrationof the classical partial differential equation