The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model...

We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative a...

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v|W ) = (d(v,w1), d(v, w2), . . . , d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The setW is a resolving set for G if distinct vertices of G have distinct representations. A resolving set of minimum ...

We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length ω2, the distributivity number of P(ω)/fin is ω2, whereas the distributivity number of r.o.(P(ω)/fin) 2 is ω1. This answers an old problem of Balcar, Pelant and Simon, and others.

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n vertices with maximum degree 3 is at most 1 3 n + 2. We disprove this conjecture by constructing a collection of connected graphs {Gn} with maximum degree 3 on arbitrarily large number of vertices, having zero forcing number at least 4 9 |Gn|.

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a wavelike oscillation by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Gc is defined as the ratio of potential energ...