Fractional pel motion compensation generally improves coding efficiency due to more precise motion accuracy and low path filtering effect in generating image at fractional pel positions. In H.264, quarter pel motion compensation is applied, where image at half pel position is generated by 6 tap Wiener filter. And the adaptive interpolation filter technique, which adaptively changes filter chara...

Let $G$ be a finite group. The intersection graph of is whose vertex set the all proper non-trivial subgroups and two distinct vertices $H$ $K$ are adjacent if only $H\cap K \neq \{e\}$, where $e$ identity group $G$. In this paper, we investigate some properties exploring topological indices such as Wiener, Hyper-Wiener, first second Zagreb, Schultz, Gutman eccentric connectivity $D_{2n}$ for $...

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

Abstract: The Hosoya polynomial of a molecular graph G is defined as ∑ ⊆ = ) ( } , { ) , ( ) , ( G V v u v u d G H λ λ , where d(u,v) is the distance between vertices u and v. The first derivative of H(G,λ) at λ = 1 is equal to the Wiener index of G, defined as ∑ ⊆ = ) ( } , { ) , ( ) ( G V v u v u d G W . The second derivative of ) , ( 2 1 λ λ G H at λ = 1 is equal to the hyper-Wiener index, d...

Abstract. A subgraph H of a graph G is gated if for every x ∈ V (G) there exists a vertex u in H such that dG(x, v) = dG(x, u) + dG(u, v) for any v ∈ V (H). The gated amalgam of graphs G1 and G2 is obtained from G1 and G2 by identifying their isomorphic gated subgraphs H1 and H2. Two theorems on the Wiener index of gated amalgams are proved. Several known results on the Wiener index of (chemica...

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...

We define an analogue of the Paley-Wiener space in the context of the Askey-Wilson function transform, compute explicitly its reproducing kernel and prove that the growth of functions in this space of entire functions is of order two and type ln q−1, providing a Paley-Wiener Theorem for the Askey-Wilson transform. Up to a change of scale, this growth is related to the refined concepts of expone...

Let G be a simple graph with vertex set and edge set . The function which assigns to each pair of vertices in , the length of minimal path from to , is called the distance function between two vertices. The distance function between and edge and a vertex is where for and. , . The Wiener index of a graph is denoted by and is defined by .In general this kind of index is called a topological index...

Let (W, H, μ) be the classical Wiener space, assume that U = IW + u is an adapted perturbation of identity where the perturbation u is an equivalence class w.r.to the Wiener measure. We study several necessary and sufficient conditions for the almost sure invertibility of such maps. In particular the subclass of these maps who preserve the Wiener measure are characterized in terms of the corres...

Abstract: Let (W,H,μ) be the classical Wiener space. Assume that U = IW + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration ofW . We give some sufficient analytic conditions on u which imply the invertibility of the map U . In particular it is shown that if u ∈ IDp,1(H) is adapted and if exp( 2‖∇u‖2 − δu) ∈ Lq(μ), where p−1 + q−1 = 1, then IW + u i...