The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,≺), with the order relation ≺ corresponding to the spacetime causal relation. Spacetime in CST is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. In order to obtain a well define...

We extend some theoretical results in the frame of concurrency theory, which were presented in [1]. In particular, we focus on partially ordered sets (posets) as models of nonsequential processes [2] and we apply the same construction as in [1] of a lattice of subsets of points of the poset via a closure operator defined on the basis of the concurrency relation, viewed as lack of causal depende...

A classical-like combinatorial interpretation of the Fibonomial coefficients is proposed following [1,2]. It is considered to be in the spirit classicalcombinatorial interpretation like binomial Newton and Gauss q-binomial coefficients or Stirling number of both kinds are. (See ref. [3,4] and refs. given therein). It also concerns choices. Choices of specific sub-posets from a non-tree poset sp...

A useful nanophotocatalyst (La,S-TiO2) was prepared by a sol-gel method and characterized by UV–vis diffuse reflectance spectroscopy (DRS), X-ray diffraction (XRD), photoluminescence emission spectroscopy (PL) and scanning electron microscopy (FESEM). The results showed that the La,S-TiO2, which calcined at 550 °C, contained only anatase phaseand its crystal size was 23 nm...

Various authors have studied a natural operation (under various names) on the order ideals (equivalently antichains) of a finite poset, here called rowmotion. For certain posets of interest, the order of this map is much smaller than one would naively expect, and the orbits exhibit unexpected properties. In very recent work (inspired by discussions with Berenstein) Einstein and Propp describe h...

We study some poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the right, or increasing the size of some part by one. The resulting poset N was studied by the author in [5] in relation to non-commutative term orders, and then in [6], where some results about generating functions for standard path...

Clean hydrogen is the major energy carrier for power production. The conversion of CO to CO2 and zero emission during hydrogen energy production causes high capital cost. It is a matter of prestige to optimize the process in order to make zero emission and cost effective production of clean hydrogen energy and electric power. In this era, coal gasification is th...