Roman Domination Dot-critical Graphs

A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value ${f(V(G))=\sum_{u \in V(G)}f(u)}$ . The Roman domination number, γ _R (G), of G is the minimum weight of a Roman dominating function on G. In this paper, we study graphs for which contracting any edge decreases the Roman domination number.     

The Selfconsistent Pauli Equation

 We deal with consistent first order non-relativistic corrections (i.e. in the small parameter , where c is the speed of light) of the Dirac–Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ɛ) approximation of the Dirac equation. We suggest a coupling to the “magnetostatic”O(ɛ) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch the semiclassical/nonrelativistic limits of this model.     

Modelling dependence structure with Archimedean copulas and applications to the iTraxx CDS index

In this paper we model the dependence structure between credit default swap (CDS) and jump risk using Archimedean copulas. The paper models and estimates the different relationships that can exist in different ranges of behaviour. It studies the bivariate distributions of CDS index spreads and the kurtosis of equity return distribution. To take into account nonlinear relationships and different structures of dependency, we employ three Archimedean copula functions: Gumbel, Clayton, and Frank. We adopt nonparametric estimation of copula parameters and we find an extreme co-movement of CDS and stock market conditions. In addition, tail dependence indicates the extreme co-movements and the potential for a simultaneous large loss in stock markets and a significant default risk. Ignoring the tail dependence would lead to underestimation of the default risk premium.     

On an open problem concerning total domination critical graphs

A graph G   with no isolated vertex is total domination vertex critical if for any vertex v$v$ of G   that is not adjacent to a vertex of degree one, the total domination number of G-v$G-v$ is less than the total domination number of G  . We call these graphs _γt${\gamma }_t$-critical. If such a graph G has total domination number k, we call it k  -_γt${\gamma }_t$-critical. We verify an open problem of k  -_γt${\gamma }_t$-critical graphs and obtain some results on the characterization of total domination critical graphs of order n=Δ(G)(_γt(G)-1)+1$n=\Delta (G)({\gamma }_t(G)-1)+1$.     

$${\varvec{}}$$-Jorda homomorphisms ad pseudo $${\varvec{}}$$-Jorda homomorphisms o Baach algebras

Let \(n\in \mathbb {N}\), A and B be Banach algebras and let B be a right A-module. We say that a linear mapping \(\varphi :A\longrightarrow B\) is a pseudo n-Jordan homomorphism if there exists an element \(w\in A\) such that \(\varphi (a^nw)=\varphi (a)^n\cdot w\), for every \(a\in A\) and \(n\ge \) 2. In this paper, among other things, we show that under some conditions if a linear mapping \(\varphi \) is a (pseudo) n-Jordan homomorphism, then it is a (pseudo) \((n + 1)\)-Jordan homomorphism. Additionally, we investigate automatic continuity of surjective pseudo n-Jordan homomorphisms under some conditions.     

Global Existence for Capillary Water Waves

Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space‐time resonance method and commuting vector fields. © 2015 Wiley Periodicals, Inc.     

Molecular dynamics simulation of manipulation of metallic nanoclusters on stepped surfaces

Molecular dynamics simulations are carried out to investigate the manipulation of metallic clusters on stepped surfaces. Five surface forms are considered in the simulations. The system parts are made of pure transition metals and Sutton-Chen many-body potential is used as interatomic potential. The conditions which are subjected to change in the tests include: materials used for particles and substrate, and surface step conditions. In addition to qualitative observations, two criteria which represent the particle deformation and substrate abrasion are utilized as evaluation tools and are computed for each case. Simulation results show the effect of the aforementioned working conditions on the particle behavior as well as changes in the pushing forces. Obtaining this sort of knowledge is highly beneficial for further experiments in order to be able to plan the conditions and routines which guarantee better success in the manipulation process.     

光学发射光谱法测量氩气微空心阴极放电中特性参数

针对微空心阴极放电(MHCD)装置,通过在氩气中添加少量氮气,分析氮分子第一正带系N2(B3ΠgA3u+)发射光谱的方法测量了MHCD中的气体温度,通过氩气中混有的少量氢气,分析Hβ谱线Stark加宽得到电子数密度。研究表明,MHCD在极小的体积和很高的功率密度下维持放电,致使发生了明显的气体加热现象,气体温度可高于700 K,并且随着放电室压强和放电电流呈有规律的变化,具有较好的可控性,电子数密度的量级为1014～1015cm-3。通过对不同条件下等离子体特性参数的诊断和分析,得到了其量级和变化规律,对MHCD的广泛研究和应用提供了重要的实验数据和技术支持。