The linear programmimg formulations of graph domination and graph packing are duals. Likewise, fractional efficient domination for a graph G has as its dual the parameter discussed in this paper, namely the minimum weight of a real-valued function f : V(G) -+ [0, (0) such that the sum of the weights in each closed neighborhood is at least its cardinality. The fractional and integer "closed neig...

LET f (z,w) ≡ f0(z)w + f1(z)w + · · · + fn(z) ∈ C[z,w]. Classically, the equation f (z,w) = 0 was said to define w as an (n-valued) algebraic function of z, provided that f0(z) was not identically 0 and that f (z,w) was squarefree and without factors of the form z− c. Then, indeed, the singular set B = {z: there are not n distinct solutions w to f (z,w) = 0} is finite; and as z varies in any si...

Abstract— In this paper, input impedance of a vertical rod under lightning stroke is first computed by applying the method of moments (MoM) on the Maxwell’s equations. The circuit model is then achieved through applying modified vector fitting (MVF) on the computed input impedance. After then the equivalent circuit is again extracted for a few values of soil conductivity and rod radius. Finally...

We show that every henselian valued field L of residue characteristic 0 admits a proper subfield K which is dense in L. We present conditions under which this can be taken such that L|K is transcendental and K is henselian. These results are of interest for the investigation of integer parts of ordered fields. We present examples of real closed fields which are larger than the quotient fields o...