Let G be a graph and F ⊆ V (G). Then F is called an induced forest of G if 〈G〉 contains no cycle. The forest number, f(G), of G is defined by f(G) := max{|F | : F is an induced forest of G}. It was proved by the second author in [6] that if G is an r-regular graph of order n, then f(G) ≤ b nr−2 2(r−1)c. It was also proved that the bound is sharp by constructing an r-regular graph H of order n w...

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form Lem = Φ(F ) , F = FαβF αβ . We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axi...

Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f (0) = 0, then for g ∈ K, f (z) + αzf (z) ≺ g(z) + αzg (z) in E implies that f (z) ≺ g(z) in E, where α > 0 is a real number and the symbol " ≺ " stands for subordination.

We show that the property of F-regularity does not deform, and thereby settle a longstanding open question in the theory of tight closure. Specifically, we construct a three dimensional N-graded domain R which is not F-regular (or even F-pure), but has a quotient R=tR which is F-regular. Examples are constructed over fields of characteristic p > 0, as well as over fields of characteristic zero.

Period-doubling cascades are among the most prominent features of many smooth one-parameter families of maps, F : R×M → M, where M is a locally compact manifold without boundary, typically R . In particular, we investigate F (μ, ·) for μ ∈ J = [μ1, μ2], when F (μ1, ·) has only finitely many periodic orbits while F (μ2, ·) has exponential growth of the number of periodic orbits as a function of ...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...