A hilly poor noncrossing partition is a noncrossing partition with the properties : (1) each block has at most two elements, (2) in its linear representation, any isolated vertex is covered by some arc. This paper defines basic pairs as a combinatorial object and gives the number of hilly poor noncrossing partitions with n blocks, which is closely related to Maximal Davenport-Schinzel sequences...

Building on work of Dubickas and Smyth regarding the metric Mahler measure and the authors regarding extremal norms associated to the Mahler measure, the authors introduce a new set of norms associated to the Mahler measure of algebraic numbers which allow for an equivalent reformulation of problems like the Lehmer problem and the Schinzel-Zassenhaus conjecture on a single spectrum. We present ...

Orchard intensification is motivated by the desire to produce fruit early in the life of the orchard to rapidly recover establishment costs. Intensification is possible using dwarfing rootstocks that control tree size, induce early cropping and produce large quantities of fruit compared to the amount of wood produced. Therefore, this study attempts to compare some yield and fruit properties of ...

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold giv...

study of morphological traits of red fleshed apples is a critical step to improve the quality andcommercializing of them. in order to study genetic diversity of iranian red fleshed apples, a total of 17morphological characteristics were assessed for eight genotypes of red- fleshed (‘haji qermez’, ‘goushtqermez’, ‘shahroud-10’, ‘arous gousht qermz’, ‘b.9’, ‘qazvin 1, 2, 3’) and 12 iranian and fo...

The Josephson effect and superconducting proximity effect were observed in superconductor-graphenesuperconductor SGS Josephson junctions with coherence lengths comparable to the distance between the superconducting leads. By comparing the measured gate dependence of the proximity induced subgap features multiple Andreev reflections and of the supercurrent to theoretical predictions, we find tha...

The well-known randomized consensus algorithm by Aspnes and Herlihy for asynchronous shared-memory systems was proved to work, even against a strong adversary, under the assumption that registers it uses are atomic registers. With registers, every read or write operation is instantaneous (and thus indivisible). As pointed out Golab et al. (2011), however, works with does not necessarily work if...