J. Browkin defined in his recent paper (Math. Comp. 73 (2004), pp. 1031–1037) some new kinds of pseudoprimes, called Sylow p-pseudoprimes and elementary Abelian p-pseudoprimes. He gave examples of strong pseudoprimes to many bases which are not Sylow p-pseudoprime to two bases only, where p = 2 or 3. In this paper, in contrast to Browkin’s examples, we give facts and examples which are unfavora...

Abstract By using a jump transformation associated to the Romik map, we define new continued fraction algorithm called odd-odd fraction, whose principal convergents are rational numbers of odd denominators and numerators. Among others, it is proved that all best approximating rationals numerators an irrational number given by vice versa.

A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. A strong stable set of a graph G is a stable set that intersects all maximal cliques of G. We present a linear-time algorithm that, for any vertex of a Meyniel graph, find a strong stable set containing this vertex.

Abstract The timing and ecological impacts of the Deccan Traps large igneous province eruption are vigorously debated. Pre–Cretaceous-Paleogene (KPg) boundary volcanism have been widely identified in marine sediments, but direct evidence terrestrial remains rare. We used mercury concentrations isotopic compositions, a proxy for volcanic activity, to assess on environments. studied two drill cor...

A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge’s Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd, eb}. We prove that a Berge graph with no induced chair (chair-free) is perfect or, equivalently, that the Strong Perfect...

Elasticity typically refers to a material's ability store energy, whereas viscosity tendency dissipate it. In this review, we discuss fluids and solids for which is not the case. These materials display additional linear response coefficients known as odd elasticity. We first introduce elasticity from continuum perspective, with an emphasis on their rich phenomenology, including transverse resp...

A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of pla...

In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, deaf and dumb, and oblivious). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a determini...

In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, deaf and dumb, and oblivious). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a determini...