Pion Compton scattering and bremsstrahlung

The pion-polarizability functions are structure functions of pion-Compton scattering. They can be assessed in high-energy pion-nucleus bremsstrahlung reactions, $\pi^- +A\to\pi^- +\gamma +A$. We present numerical expectations for pion-nucleus bremsstrahlung cross sections in the Coulomb region, i.e. the small-angle region where the nuclear scattering is dominated by the Coulomb interaction. We investigate the prospects of measuring the polarizability functions for pion-Compton c.m. energies from threshold up to 1 GeV. A meson-exchange model is used for the pion-Compton amplitude.Comment: 20 pages, 11 figure

Hard pion bremsstrahlung in the Coulomb region

Hard high-energy pion-nucleus bremsstrahlung, $\pi^- +A\to\pi^- +\gamma +A$, is studied in the Coulomb region, i.e. the small-angle region where the nuclear scattering is dominated by the Coulomb interaction. Special attention is focussed on the possibility of measuring the pion polarizability in such reactions. We study the sensitivity to the structure of the underlying the pion-Compton amplitude through a model with $\sigma$, $\rho$, and a_1 exchanges. It is found that the effective energy in the virtual pion-Compton scattering is often so large that the threshold approximation does not apply.Comment: 18 pages, 5 figure

Coulomb-nuclear interference in pion-nucleus bremsstrahlung

Pion-nucleus bremsstrahlung offers a possibility of measuring the structure functions of pion-Compton scattering from a study of the small-momentum-transfer region where the bremsstrahlung reaction is dominated by the single-photon-exchange mechanism. The corresponding cross-section distribution is characterized by a sharp peak at small momentum transfers. But there is also a hadronic contribution which is smooth and constitutes an undesired background. In this communication the modification of the single-photon exchange amplitude by multiple-Coulomb scattering is investigated as well as the Coulomb-nuclear interference term.Comment: 21 pages, 5 figures. Eqs.(51,52) corrected; some new figure

Products and Eccentric Diagraphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider the eccentric digraphs of different products of graphs, viz., cartesian, normal, lexicographic, prism, etc

Planarity of Eccentric Digraphs of graphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any othervertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is thedigraph that has the same vertex set as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider planarity of eccentric digraph of a graph

Products and Eccentric digraphs

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider the eccentric digraphs of different products of graphs, viz., cartesian, normal, lexicographic, prism, et

Eccentric Coloring in graphs

he \emph{eccentricity} $e(u)$ of a vertex $u$ is the maximum distance of $u$ to any other vertex of $G$. A vertex $v$ is an \emph{eccentric vertex} of vertex $u$ if the distance from $u$ to $v$ is equal to $e(u)$. An \emph{eccentric coloring} of a graph $G = (V, E)$ is a function \emph{color}: $V \rightarrow N$ such that\\ (i) for all $u, v \in V$, $(color(u) = color(v)) \Rightarrow d(u, v) > color(u)$.\\ (ii) for all $v \in V$, $color(v) \leq e(v)$.\\ The \emph{eccentric chromatic number} $\chi_{e}\in N$ for a graph $G$ is the lowest number of colors for which it is possible to eccentrically color \ $G$ \ by colors: $V \rightarrow \{1, 2, \ldots , \chi_{e} \}$. In this paper, we have considered eccentric colorability of a graph in relation to other properties. Also, we have considered the eccentric colorability of lexicographic product of some special class of graphs

On Edge-Distance and Edge-Eccentric graph of a graph

An elementary circuit (or tie) is a subgraph of a graph and the set of edges in this subgraphis called an elementary tieset. The distance d(ei, ej ) between two edges in an undirected graph is defined as the minimum number of edges in a tieset containing ei and ej . The eccentricity ετ (ei) of an edge ei is ετ (ei) = maxej∈Ed(ei, ej ). In this paper, we have introduced the edge - self centered and edge - eccentric graph of a graph and have obtained results on these concepts

Direct restorations and enhanced caries prevention among 20-to 60-year-olds attending Helsinki City Public Dental Service - a register-based observation

Objective Our retrospective register-based observational study evaluated age-specific aspects and changes in volume and content of direct restorative procedures, pulp cappings and enhanced caries prevention measures given to adults. Methods Data included all treatments provided for 20- to 60-year-olds visiting the Helsinki City Public Dental Service (PDS) in 2012 and 2017. For both years, the data were aggregated into 5-year age groups. Data included means of DMFT indices, number and size of direct restorations, number of specific codes for pulp cappings and enhanced prevention. Results Around half of all patients received restorations, 39,820 (50.9%) in 2012 and 43,392 (45.9%) in 2017. The greatest increase in DMFT means by age cohort was found for the 2012 age cohort of 25- to 29-year-olds and the smallest for the 2012 age cohort of 45- to 49-year-olds. In each same-age group and each age cohort, the enhanced prevention in 2017 was less frequent than in 2012. The proportion of two-surface restorations accounted for 44.7% of procedures in 2012 and 45.9% in 2017, followed by an increasing proportion of one-surface restorations, from 28.3% in 2012 to 32.9% in 2017. Associations between restoration size and age group were highly significant (p < .001). Conclusions The volume of direct restorative procedures and enhanced prevention measures were strongly age-dependent. Restorative treatment procedures were more frequent in older age groups than in younger age groups, and vice versa for enhanced prevention and pulp cappings. The magnitude of restorative treatment decreased slowly from 2012 to 2017, and overall enhanced preventive treatment was limited.Peer reviewe

Products of distance degree regular and distance degree injective graphs.

The eccentricity e (u) of a vertex u is the maximum distance of u to any other vertex in G. The distance degree sequence (dds) of a vertex v in a graph G = (V, E) is a list of the number of vertices at distance 1, 2, …, e (u) in that order, where e (u) denotes the eccentricity of u in G. Thus the sequence is the dds of the vertex vi in G where denotes number of vertices at distance j from Vi . A graph is distance degree regular (DDR) graph if all vertices have the same dds. A graph is distance degree injective (DDI) graph if no two vertices have same dds. In this paper we consider Cartesian and normal products of DDR and DDI graphs. Some structural results have been obtained along with some characterizations