Journal•ISSN: 0031-5303
Periodica Mathematica Hungarica
Springer Science+Business Media
About: Periodica Mathematica Hungarica is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Computer science & Diophantine equation. It has an ISSN identifier of 0031-5303. Over the lifetime, 1946 publications have been published receiving 16429 citations.
Topics: Computer science, Diophantine equation, Abelian group, Prime (order theory), Type (model theory)
Papers published on a yearly basis
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TL;DR: In this article, it was shown that a convex subset of Euclidean d-space R d is convex (concave) if the inequality F(OA + (1 O)B)
Abstract: Given subsets A and B of Euclidean d-space R a and 0 ~ 0, we set A + B -{x + Y l x E A, y E B} and OA = {Ox Ix 6 A }. Further given a convex subset g2 of R d we shall say that a set function F : 2 ~ \ {~} ~ [0, + ~ ] is convex (concave} if the inequality F(OA + (1 O)B) ~ Or(A} + (1 0 ) / ' ( B ) (>=.) holds for all It ~ A, B c_ D, and all 0 < 0 < 1. Here we shall s tudy such set functions of the special form given in the following
451 citations
TL;DR: The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences, arithmetic functions and the greatest prime factor func- tion and mixed problems.
Abstract: 68 unsolved problems and conjectures in number theory are presented and brie y discussed. The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences), arithmetic functions, the greatest prime factor func- tion and mixed problems.
425 citations
TL;DR: For this modified UCB algorithm, an improved bound on the regret is given with respect to the optimal reward for K-armed bandits after T trials.
Abstract: In the stochastic multi-armed bandit problem we consider a modification of the UCB algorithm of Auer et al. [4]. For this modified algorithm we give an improved bound on the regret with respect to the optimal reward. While for the original UCB algorithm the regret in K-armed bandits after T trials is bounded by const · $$
\frac{{K\log (T)}}
{\Delta }
$$
, where Δ measures the distance between a suboptimal arm and the optimal arm, for the modified UCB algorithm we show an upper bound on the regret of const · $$
\frac{{K\log (T\Delta ^2 )}}
{\Delta }
$$
.
297 citations
255 citations
TL;DR: In this article, the class of all graphs G which satisfy the Ramsey number G→(G>>\s 1, G>>\s 2) is defined, and the asymptotic behavior of the Ramsey numbers is investigated.
Abstract: Let denote the class of all graphsG which satisfyG→(G
1,G
2). As a way of measuring minimality for members of
, we define thesize Ramsey number ř(G
1,G
2) by
. We then investigate various questions concerned with the asymptotic behaviour ofř.
237 citations