In this study, beginning and today expansion of universe are viewed in f(R,Φ,X) gravity. Field equations their solutions Friedmann-Lemaître-Robertson-Walker cosmologies with perfect fluid obtained by considering f(R,Φ,X)=f_0 R+f_1 X^q-V(Φ) model. Validity both gravity model for non-static space-time geometries is discussed making use the matter dynamics results such as pressure energy density. ...

We present Acacia+, a tool for solving the LTL realizability and synthesis problems. We use recent approaches that reduce these problems to safety games, that can be solved efficiently by symbolic incremental algorithms based on antichains. The reduction to safety games offers very interesting properties in practice: the construction of compact solutions (when they exist) and a compositional ap...

A strong edge-coloring φ of a graph G assigns colors to edges such that φ(e1)≠φ(e2) whenever e1 and e2 are at distance no more than 1. It is equivalent proper vertex coloring the square line G. In 1990 Faudree, Schelp, Gyárfás, Tuza conjectured if bipartite with maximum degree 3 sufficiently large girth, then has most 5 colors. 2021 this conjecture was disproved by Lužar, Mačajová, Škoviera, So...

A subset X of a finite group G is said to be prime-power-independent if each element in has prime power order and there no proper Y with 〈Y,Φ(G)〉=〈X,Φ(G)〉, where Φ(G) the Frattini subgroup G. Bpp all generating sets for have same cardinality. We prove that, Bpp, then solvable. Pivoting on some recent results Krempa Stocka (2014); (2020), this yields complete classification Bpp-groups.

We consider the notion of a Φ-zero divisor, where Φ is Young function, on discrete group. extend some results about p-divisors free groups by Linnell and Puls to divisors.

this paper investigates the nature of absolutive case and the syntactic mechanisms underlying its licensing. to this end, two recent minimalist approaches to the syntactic derivation of ergative structure will be introduced. drawing on evidence from the syntactic derivation of clauses with intransitive complex predicates in kurdish, it will be established that the absolutive case is checked by ...

We find the best possible constant C in inequality‖φ‖Lrpr⩽C‖φ‖Lppr‖φ‖BMO1−pr for all values of parameters p and r such that 1⩽p<r<+∞. To solve problem, we define explicitly compute corresponding Bellman function. This function depends on three variables has a rather complicated structure. first problem an interval then transfer our results to circle line. also obtain explicit estimates several ...