Notations M Riemannian manifold. N 0 normal neighborhood of the origin in T p M. N p normal neighbourhood of p, N p = exp N 0. s p geodesic symmetry with respect to p. f Φ d Φ f = f • Φ. X Φ d Φ X. K(S) sectional curvature of M at p along the section S. D r s set of tensor fields of type (r, s). I(M) the set of all isometries on M Definition 1 (normal neighborhood) A neighborhood N p of p in M ...

By an absolute neighborhood retract (ANR) I mean a separable metrizable space which is a neighborhood retract of every separable metrizable space which contains it and in which it is closed. This generalization of Borsuk's original definition was given by Kuratowski for the purpose of enlarging the class of absolute neighborhood retracts to include certain spaces which are not compact. The spac...

Knowledge bases are useful resources for many natural language processing tasks, however, they are far from complete. In this paper, we define a novel entity representation as a mixture of its neighborhood in the knowledge base and apply this technique on TransE—a well-known embedding model for knowledge base completion. Experimental results show that the neighborhood information significantly ...

We apply a heuristic method based on counting points over finite fields to the Poincaré center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for Żo la̧dek’s conjecture about general degree 3 non linearities. Introduction In 1885 Poincaré asked when the differential equation y = − x+ p(x, y) y + q(x, y) =...

We apply a heuristic method based on counting points over finite fields to the Poincaré center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain some new information about general degree 3 non linearities. Introduction In 1885 Poincaré asked when the differential equation y = − x+ p(x, y) y + q(x, y) =: − P (x, y) Q(x, ...

Definition 1. (directly density-reachable): A point p is directly density-reachable from a point q wrt. Eps, MinPts if 1. p ∈ NEps(q) and 2. |NEps(q)| ≥MinPts NEps(q) represents the Eps-neighborhood of the point q which includes all points whose distance to the point q is less than or equal to Eps. From the statement (2), it can be understood that there is a cluster if and only if there is a co...

Abstract Pythagorean fuzzy sets (briefly, PFSs) were created as an upgrade to intuitionistic IFSs) which helped address some problems that IFSs couldn’t solve. The definition of q-rung orthopair q-ROFS) is then declared generalize and solve PFS IFS failures. Using the concept PF $$\beta $$ β -neighborhood, Zh...

It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is O ( n log n ǫ ) . In this paper we propose a family of self-regular proximity based predictorcorrector (SR-PC) IPM for LO in a lar...