## American Journal of Mathematics, Volume 41 |

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algebraic asymptotic Axiom basis points belongs Bertini involution coefficients condition congruent conic conies continuous function Cremona transformation cubic curves curves of order cusps defining equations denote derivatives determinant differential equations distinct double line double point Equilibrium point exists a motion expression F-points finite fixed point follows function fundamental points Geiser genus given Hence Hessian hyperplane sections integral invariant involution Jacobian limit point linear system locus matrix mod Px modular invariant modulo Px multiplicity nodes obtained orbits of Class Oscillating Satellite pairs parameters pencil of cubics plane point correspondences point in common point-set polar cubic polynomial principal minor projection Proof quadratic quadratic form quadric residual curve residual image respectively saltus equation satisfied sections of F seminvariants sextic simple basis points simple intersections simple points solutions Steinerian subset surface F symmetroid tacnode tangent Theorem triple point types values vanish variable

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Page 303 - ... through any two given points. I have not however determined whether every such space is descriptive. Definitions. — A point P is said to be a limit point of a point-set M if, and only if, every region that contains P contains at least one point of M distinct from P. The boundary of a point-set M is the set of all points [X\ such that every region that contains X contains at least one point of M and at least one point that does not belong to M. If M is a set of points, M' denotes the point-set...

Page 326 - XVIII in progress. $5 per volume. (Foreign postage, fifty cents.) Johns Hopkins University Circular, including the President's Report, Annual Register, and Medical Department Catalogue.

Page 326 - XLI in progress. $6 per volume. (Foreign postage, fifty cents.) American Journal of Philology. Edited by BL GILDERSLEEVE and CWE MILLET;, managing Editor.

Page 268 - A most useful feature is that the determinant of a product of matrices is equal to the product of...

Page 267 - В 1 a. HB PHILLIPS. Functions of matrices. It is the purpose of the present paper to study the functions represented by polynomials or convergent series in a matrix or a finite number of matrices. As the work is concerned mainly with the roots of the matrices, the fundamental facts about the roots are first briefly developed (p.

Page 303 - ... that satisfies 22 satisfies also 23, but not conversely. In every space satisfying 22 there exists infinitely many open curves through any two given points. I have not however determined whether every such space is descriptive. Definitions. — A point P is said to be a limit point of a point-set M if, and only if, every region that contains P contains at least one point of M distinct from P. The boundary of a point-set M is the set of all points [X] such that every region that contains X contains...

Page 239 - Hence any modular invariant can be expressed in one and but one way as a linear homogeneous function of the characteristic invariants. Moreover, the number of linearly independent modular invariants equals the number of classes. For example, using (19), we see that a complete set of linearly independent modular invariants of the quadratic form qm modulo p (p > 2) is given by (23) /0, Ar, A* (r= 1, ...,m-1), Dk (k = 1, . . ., p-1).

Page 134 - Mathieu1 who showed how the problem could be reduced to the solution of certain ordinary linear differential equations. But he found these equations to be so unmanageable that he contented himself with approximating to their solutions for the special case of an ellipsoid of revolution.

Page 302 - Hilbert's hypotheses are far more general. Without doubt this is still not entirely satisfactory, since though the form of the group is supposed any whatever, its matter, that is to say the plane which undergoes the transformations, is still subjected to being a number-manifold in Lie's sense. Nevertheless, this is a step in advance, and besides Hilbert analyzes better than anyone before him the idea of number-manifold and gives outlines which may become the germ of an assumptional theory of analysis...

Page 184 - ... to coincide with x. This remark applies also to similar situations below. ' The functions u(g, x) and l(g, x) are often, though not quite unobjectionably, called the 'maximum' and the 'minimum