A method for computing the Disjoint-Sum-Of-Products (DSOP) form of Boolean functions is described. The algorithm exploits the property of the most binate variable in a set of cubes to compute a DSOP form. The technique uses a minimized Sum-Of-Products (SOP) cube list as input. Experimental results comparing the size of the DSOP cube list produced by this algorithm and those produced by other me...

In The continuously increasing enrolment of higher education has created some employment problems. It is very meaningful that we scientifically forecast and analysis the graduates employment trends. Based on the basic principle of Grey Model with First Order Differential Equation and one Variable (GM(1,1)) and Power Function x   Transformation, in this paper, a new Variable Weights Buffer Fir...

Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalit...

For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M1(G) = ∑ v∈V (G) dG(v) 2 where dG(v) is the degree of vertex v in G. The alternative expression for M1(G) is ∑ uv∈E(G)(dG(u)+dG(v)). Very recently, Eliasi, Iranmanesh and Gutman [7] introduced a new graphical invariant ∏∗ 1(G) = ∏ uv∈E(G)(dG(u) + dG(v)) as the multiplicative version of ...

The general sum-connectivity index is a molecular descriptor defined as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text], and α is a real number. Let X be a graph; then let [Formula: see text] be the graph obtained from X by adding a new vertex [Formula: see text] corresponding to each edge of X and joining [Formula: see text] to the end vertices...

We propose a new power index based on the minimum sum representation (MSR) of a weighted voting game. The MSR offers a redesign of a voting game, such that voting power as measured by the MSR index becomes proportional to voting weight. The MSR index is a coherent measure of power that is ordinally equivalent to the Banzhaf, Shapley-Shubik and Johnston indices. We provide a characterization for...

The general sum-connectivity index of a graph G is χα(G) = ∑ uv∈E(G) (d(u)+d(v)), where d(u) denotes the degree of vertex u ∈ V (G), and α is a real number. In this paper, we show that in the class of graphs G of order n ≥ 3 and minimum degree δ(G) ≥ 2, the unique graph G having minimum χα(G) is K2 + Kn−2 if −1 ≤ α < α0 ≈ −0.867. Similarly, if we impose the supplementary condition for G to be t...

We compare multivariate aging notions of conditionally independent lifetimes with corresponding univariate aging notions of their one-dimensional marginal distributions. Let G(t|θ) (t ≥ 0) be a one-dimensional survival function indexed by θ; for simplicity’s sake, we assume here that θ is a non-negative scalar quantity; let, furthermore, Π be a probability distribution over [0,∞) and consider t...

which is a Riemann sum for ∫ b a g 2(s) ds. By the way: since we are assuming that g is deterministic, ∫ b a g(s)dw(s) is a Gaussian random variable. (Proof: recall that a sum of Gaussians is Gaussian; therefore ∑ i g(si)[w(si+1) − w(si)] is Gaussian. Now use the fact that a limit of Gaussians is Gaussian.) Since we know its mean and variance, we have completely characterized this random variable.