New bounds on the signed total domination number of graphs

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turan, we present a sharp lower bound on this parameter for graphs with no complete graph of order r+1 as a subgraph. Also, we prove that n-2(s-s') is an upper bound on the signed total domination number of any tree of order n with s support vertices and s' support vertives of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur

The Signed Roman Domatic Number of a Digraph

Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v]$ consists of $v$ andall inner neighbors of $v$, and every vertex $u\in V(D)$ for which $f(u)=-1$ has an innerneighbor $v$ for which $f(v)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct signedRoman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le 1$ for each$v\in V(D)$, is called a {\em signed Roman dominating family} (of functions) on $D$. The maximumnumber of functions in a signed Roman dominating family on $D$ is the {\em signed Roman domaticnumber} of $D$, denoted by $d_{sR}(D)$. In this paper we initiate the study of signed Romandomatic number in digraphs and we present some sharp bounds for $d_{sR}(D)$. In addition, wedetermine the signed Roman domatic number of some digraphs. Some of our results are extensionsof well-known properties of the signed Roman domatic number of graphs

Double Roman domination and domatic numbers of graphs

A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function‎ ‎$f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$‎, ‎then the vertex $v$ must have at least two‎ ‎neighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$‎, ‎and if $f(v)=1$‎, ‎then the vertex $v$ must have‎ ‎at least one neighbor $u$ with $f(u)\ge 2$‎. ‎The weight of a double Roman dominating function $f$ is the sum‎ ‎$\sum_{v\in V(G)}f(v)$‎, ‎and the minimum weight of a double Roman dominating function on $G$ is the double Roman‎ ‎domination number $\gamma_{dR}(G)$ of $G$‎. ‎A set $\{f_1,f_2,\ldots,f_d\}$ of distinct double Roman dominating functions on $G$ with the property that‎ ‎$\sum_{i=1}^df_i(v)\le 3$ for each $v\in V(G)$ is called in \cite{v} a double Roman dominating family (of functions)‎ ‎on $G$‎. ‎The maximum number of functions in a double Roman dominating family on $G$ is the double Roman domatic number‎ ‎of $G$‎. ‎In this note we continue the study of the double Roman domination and domatic numbers‎. ‎In particular‎, ‎we present‎ ‎a sharp lower bound on $\gamma_{dR}(G)$‎, ‎and we determine the double Roman domination and domatic numbers of some‎ ‎classes of graphs

Nucleation and phase selection in undercooled melts: Magnetic alloys of industrial relevance (MAGNEPHAS)

Studies of phase selection and microstructure evolution in high-performance magnetic materials are an urgent need for optimization of production routes. Containerless solidification experiments by electromagnetic levitation and drop tube solidification were conducted in undercooled melts of Fe-Co, Fe-Ni soft magnetic, and Nd-Fe-B hard magnetic alloys. Melt undercooling under microgravity was achieved in the TEMPUS facility during parabolic flight campaigns. For Fe-Co and Fe-Ni alloys significant effects of microgravity on metastable phase formation were discovered. Microstructure modifications as well as metastable phase formation as function of undercooling and melt flow were elucidated in Nd-Fe-B. Modeling of solidification processes, fluid flow and heat transfer provide predictive tools for microstructure engineering from the melt. They were developed as a link between undercooling experiments under terrestrial and microgravity conditions and the production routes of magnetic materials

Study protocol for the Cities Changing Diabetes programme: a global mixed-methods approach

INTRODUCTION: Urban living has been shown to affect health in various ways. As the world is becoming more urbanised and almost two-thirds of people with diabetes now live in cities, research into the relationship between urban living, health and diabetes is key to improving the lives of many. The majority of people with diabetes have type 2 diabetes, a subset linked to overweight and obesity, decreased physical activity and unhealthy diets. Diabetes has significant consequences for those living with the condition as well as their families, relationships and wider society. Although care and management are improving, complications remain common, and diabetes is among the leading causes of vision loss, amputation, neuropathy and renal and cardiovascular disease worldwide. We present a research protocol for exploring the drivers of type 2 diabetes and its complications in urban settings through the Cities Changing Diabetes (CCD) partnership programme. METHODS AND ANALYSIS: A global study protocol is implemented in eight collaborating CCD partner cities. In each city, academic institutions, municipal representatives and local stakeholders collaborate to set research priorities and plan implementation of findings. Local academic teams execute the study following the global study protocol presented here. A quantitative Rule of Halves analysis obtains measures of the magnitude of the diabetes burden, the diagnosis rates in each city and the outcomes of care. A qualitative Diabetes Vulnerability Assessment explores the urban context in vulnerability to type 2 diabetes and identifies social factors and cultural determinants relevant to health, well-being and diabetes. ETHICS AND DISSEMINATION: The protocol steers the collection of primary and secondary data across the study sites. Research ethics board approval has been sought and obtained in each site. Findings from each of the local studies as well as the result from combined multisite (global) analyses will be reported in a series of core scientific journal papers

Ultrafast far-infrared optics of carbon nanotubes

The optical properties of single-wall carbon nanotube sheets in the far-infrared (FIR) spectral range from few THz to several tens of THz have been investigated with terahertz spectroscopy both with static measurements elucidating the absorption mechanism in the FIR and with time-resolved experiments yielding information on the charge carrier dynamics after optical excitation of the nanotubes. We observe an overall depletion of the dominating broad absorption peak at around 4THz when the nanotubes are excited by a short visible laser pulse. This finding excludes particle-plasmon resonances as absorption mechanism and instead shows that interband transitions in tubes with an energy gap of ~10meV govern the far-infrared conductivity. A simple model based on an ensemble of two-level systems naturally explains the weak temperature dependence of the far-infrared conductivity by the tube-to-tube variation of the chemical potential. Furthermore, the time-resolved measurements do not show any evidence of a distinct free-carrier response which is attributed to the photogeneration of strongly bound excitons in the tubes with large energy gaps. The rapid decay of a featureless background with pronounced dichroism is associated with the increased absorption of spatially localized charge carriers before thermalization is completed

Temperature dependence of ultrafast phonon dynamics in graphite

Nonequilibrium optical phonons are generated in graphite following the excitation of electron-hole pairs with a femtosecond laser pulse. Their energy relaxation is probed by means of terahertz pulses. We find that the hot-phonon lifetime increases by a factor of 2 when the sample temperature decreases from 300 to 5 K. These results suggest that the energy relaxation in graphite at room temperature and above is dominated by the anharmonic decay of hot A′1phonons at the K point into acoustic phonons with energies of about 10 meV

On the Signed 22-independence Number of Graphs

In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area