A finite abelian group G is said to have the Hajós-k-property (k>1) if from any decomposition of into a direct product of its subsets, it follows that one of these subsets is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai. Using some properties of the cyclotomic polynomials, we will show that the cyclic groups of orders p and groups of type (p, q), where p a...

We construct finitely generated groups with strong fixed point properties. Let Xac be the class of Hausdorff spaces of finite covering dimension which are mod-p acyclic for at least one prime p. We produce the first examples of infinite finitely generated groups Q with the property that for any action of Q on any X ∈ Xac, there is a global fixed point. Moreover, Q may be chosen to be simple and...

We show that for all integers t ≥ 8 and arbitrarily small > 0, there exists a graph property Π (which depends on ) such that -testing Π has non-adaptive query complexity Q = Θ̃(q2−2/t), where q = Θ̃( −1) is the adaptive query complexity. This resolves the question of how beneficial adaptivity is, in the context of proximity-dependent properties ([9]). This also gives evidence that the canonical t...

We study higher syzygies of a ruled surface X over a curve of genus g with the numerical invariant e. Let L ∈ PicX be a line bundle in the numerical class of aC0 + bf . We prove that for 0 ≤ e ≤ g − 2, L satisfies Property Np if a ≥ p + 2 and b − ae ≥ 3g − e + p and for e ≥ g − 1, L satisfies Property Np if a ≥ p + 2 and b − ae ≥ 2g + 1 + p. By using these facts, we obtain Mukai type results. F...

Absac A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case Q) entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [2] or fc-colorability [4]. A famous conjecture of Karp [11] says that every non-trivial monotone graph property is elusive. We prove that a n...

Note that, by (4 .4) and (4 .5), (7 .6) holds for all nonnegatíve p. Substituting from (7 .6) in (6 .1) and (6 .2) and evaluating coefficients of xm, we obtain the following two identities. r-1 m (p + q)T rP~+4) = pTrpm + ~,(q) + T (P)-L q r, m pq E a l i r-a-1, m-j s-0 j-0 r-1 m-1 pq ~-~ T(P)Tr(9a-l. m-i-1 a L-0 i-0 r-1 m (r + i)Tr m+q) _ (r + 1)Tr + p (r-s)T (P)T (q) a. j r-8-1, M-j 8-0 j-0 r...

This paper presents an approximation of navigation problem under unknown environment using reinforcement learning. The motivation is to represent a robot that can move in a world with streets and intersections. Each intersection has a different quantity of streets (irregular blocks). The selected algorithms were Q-Learning and Value Iteration. The robot was programmed only with Q-Learning and w...

This article considers an Fq-conic contained in Fq-subplane of PG(2,q3), and shows that it corresponds to a normal rational curve the Bruck-Bose representation PG(6,q). The main result characterises which curves PG(6,q) correspond via Fq-conics PG(2,q3). interest are called 3-special, property describes how extension meets transversal lines regular 2-spread representation. proof uses geometric ...

Differential privacy is a widely accepted concept of preservation, and the Laplace mechanism famous instance differentially private mechanisms used to deal with numerical data. In this paper, we find that differential does not take linear property queries into account, resulting in unexpected information leakage. Specifically, makes it possible divide one query two queries, such as $q(D)=q(D_{1...

ion property for the main clause is greater than or equal to the cardinality of the than clause property. The latter is obtained by taking the boolean meet of the property corresponding to the common noun argument of the hypothetical determiner in the than clause and the noun-phrase abstraction property of the than clause. So our example would be paraphraseable as: ‘the number of books bought b...