The Wiener number W (G) of a graph G is the sum of distances between all pairs of vertices of G. If (G,w) is a vertex-weighted graph, then the Wiener number W (G,w) of (G,w) is the sum, over all pairs of vertices, of products of weights of the vertices and their distance. For G being a partial binary Hamming graph, a formula is given for computing W (G,w) in terms of a binary Hamming labeling o...

The main purpose of this paper is to prove a common fixed point theorem for two pairs of weakly compatible mappings in Menger space using implicit relation.

In this paper we obtain a unique common fixed point theorem for three pairs of weakly compatible mappings in D∗-cone metric spaces.

A permutation is called smooth if the corresponding Schubert variety smooth. Gilboa and Lapid prove that in symmetric group, multiplying reflections below a element $w$ Bruhat order compatible yields back $w$. We strengthen this result by showing such product fact determines saturated chain $e \to w$ order, property characterizes elements.

The studies of Fermi–Dirac correlations of ΛΛ and ¯ Λ ¯ Λ pairs in hadronic Z decays, Bose–Einstein correlations and colour reconnection in W-pairs decays performed by the ALEPH collaboration in e + e − annihilation at LEP are presented. The OPAL analysis of Bose–Einstein correlations in W-pair decays is also discussed.

The purpose of this paper is to prove a general fixed point theorem by altering distance for two pairs of hybrid occasionally weakly compatible mappings and to reduce the study of fixed points of pairs of mappings satisfying a contractive condition of integral type at the study of fixed point in symmetric spaces by altering distance satisfying an implicit relation.

Line spectrum pairs (LSPs) are the roots (located in the complex-frequency or -plane) of symmetric and antisymmetric polynomials synthesized using a linear prediction (LPC) polynomial. The angles of these roots, known as line-spectral frequencies (LSFs), implicitly represent the LPC polynomial and hence the spectral envelope of the underlying signal. By exploiting the duality between the time a...

We show that the pair (P(Ω),Gras(Ω)) given by the power set P = P(Ω) and by the “Grassmannian” Gras(Ω) of all subgroups of an arbitrary group Ω behaves very much like a projective space P(W ) and its dual projective space P(W ∗) of a vector space W . More precisely, we generalize several results from the case of the abelian group Ω = (W,+) (cf. [BeKi10a]) to the case of a general group Ω. Most ...