<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)
<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
<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,
<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
<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
<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.
<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
<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
