let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...

Let X be a smooth curve defined over Q̄, let a, b ∈ P(Q̄) and let fλ(x) ∈ Q̄(x) be an algebraic family of rational maps indexed by all λ ∈ X(C). We study whether there exist infinitely many λ ∈ X(C) such that both a and b are preperiodic for fλ. In particular, we show that if P,Q ∈ Q̄[x] such that deg(P ) 2 + deg(Q), and if a, b ∈ Q̄ such that a is periodic for P (x)/Q(x), but b is not preperiodic f...

For us, G-bundles are taken in the fppf topology (or, equivalently, the étale topology). Remember that BunG depends on the choice of X, even though the notation suppresses this! Last time, Francois proved that BunGLn is an algebraic stack: • It satisfies descent in the fppf (equivalently, étale) topology; i.e., it’s a stack; • Its diagonal morphism is representable by an algebraic space (implyi...

One way to view Theorem 1.1 is as a statement that the algebraic structure of a finitely generated profinite group somehow also encodes the topological structure. That is, if one wishes to know the open subgroups of a profinite group G, a topological property, one must only consider the subgroups of G of finite index, an algebraic property. As profinite groups are compact topological spaces, an...

We present unpublished work of D. Carter, G. Keller, and E. Paige on bounded generation in special linear groups. Let n be a positive integer, and let A = O be the ring of integers of an algebraic number field K (or, more generally, let A be a localization OS−1). If n = 2, assume that A has infinitely many units. We show there is a finite-index subgroup H of SL(n, A), such that every matrix in ...

We present unpublished work of D. Carter, G. Keller, and E. Paige on bounded generation in special linear groups. Let n be a positive integer, and let A = O be the ring of integers of an algebraic number field K (or, more generally, let A be a localization OS−1). If n = 2, assume that A has infinitely many units. We show there is a finite-index subgroup H of SL(n, A), such that every matrix in ...

Answering structural queries of XML with index is an important approach of efficient XML query processing. Among existing structural indexes for XML data, F&B index is the smallest index that can answer all branching queries. However, an F&B index for less regular XML data often contains a large number of index nodes, and hence a large amount of main memory. If the F&B index cannot be accommoda...

the risks of fire and explosion in oil and gas industry need to be managed. the objectives of the present study were to assess the risk of fire and explosion in iso-max unit of tehran oil refinery using dow’s fire and explosion index and to study the influences of the controlling methods. the latest version of dow fire and explosion index guideline was applied to calculate the fire and explosio...

Any vertex labeling f : V → {0, 1} of the graph G = (V,E) induces a partial edge labeling f ∗ : E → {0, 1} defined by f ∗(uv) = f(u) if and only if f(u) = f(v). The balance index set of G is defined as {|f ∗−1(0)− f ∗−1(1)| ∣∣ |f−1(0) − f−1(1)| ≤ 1}. In this paper, we propose a new and easier approach to find the balance index set of a graph. This new method makes it possible to determine the b...