## Annals of MathematicsPrinceton University Press, 1921 - Mathematics |

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### Common terms and phrases

a₁ adjoint boundary C₁ C₂ circle circuit coefficients column conjugate consider constant continuous functions convex coördinates corresponding covariant cross-ratio curve defined denote derivatives determinant differential equations elements equal Euler Square expression ǝ log F₁ F₂ finite number follows function geodesic given Hence Hermitian metric hyperbolas identity inequalities integers integral interior intersection interval invariant J. W. ALEXANDER Laplace transform linear Math matrix modular invariants N₁ necessary and sufficient obtained pair parameter plane polygon polynomial positive proof real axis reduced respect result root of f'(z S₁ satisfied sequence sides solution sphere Stieltjes integral straight lines substitutions sufficient condition surface symmedian point t₁ tangent tensor of order theorem theory transformation triangle variables vertices x₁ y₁ z-plane zero ди

### Popular passages

Page 233 - ... enough such articles to fill the space available, and therefore wish to call the attention of authors to this lack and to the fact that, as long as the shortage continues, expository or historical articles of sufficient merit will receive prompt publication. A number of the expository articles which have already been published are available in separate form and are listed for sale on the inside of the back cover of this number of the Annals. The regular subscription price of the Annals is $3.00...

Page 233 - Price 50 cents. The gamma function in the integral calculus. By TH GRONWALL. 89 pages. Price 90 cents. Fermat's last theorem and the origin and nature of the theory of algebraic numbers. By LE DICKSON. 27 pages. Price 35 cents. Factorization of analytic functions of several variables. By WF OSGOOD. 19 pages. Price 25 cents. Investigation of a class of fundamental inequalities in the theory of analytic functions.

Page 133 - ... shall note later. By allowing all the roots of f(x) outside a Jensen circle to move out to infinity, noting what roots of f'(x) may enter or leave the circle, and counting those within the circle at the end of the process, Walsh concludes that if a Jensen circle has on or within it k roots of f (x) and is not interior to nor has a point in common with any exterior Jensen circle, then it has on or within it not more than k + 1 nor less than k — 1 roots of f'(x). In a paper not yet published...

Page 61 - ... dynamical trajectories under any positional field of force are derived by studying the differential equation of such a system. I. The oo * curves passing through a given point 0 in a given direction £ haVe associated with them their orthogonal projections in the tangent plane to the surface at 0. The locus of the foci of the osculating parabolas of the associate system is a bicircular quartic with...

Page 63 - Sz, then, as we move along the surface from 0, these quantities vary so as to satisfy the relation...

Page 18 - The locus of a point at a given distance from a given point is the circumference described from the point with the

Page 233 - According to an agreement between the Mathematical Association of America and the editors of the Annals of Mathematics, the Association contributes to the support of the Annals, and the Annals is supplied to individual members of the Association at one half of the regular price. In consequence of this agreement the volume of the Annals was increased by...

Page 61 - ... and also as one of the asymptotes to the hyperbola which is the inverse of the quartic with respect to the...

Page 177 - repeated limits of f(x, y) first with respect to x and then with respect to y, and written Lit Lt/(x, y).

Page 128 - This paper contains some geometric results concerning the relative positions of the roots of a polynomial and those of its derivative. Although not entirely restricted to real polynomials, and although the cubic is especially treated in detail, most of the results here presented are naturally connected with the following theorem of Jensen's : // circles are described whose diameters are the segments joining pairs of conjugate imaginary roots of a real polynomial f(z) , then every non-real root of...