An R~-universally extending ordered field of power N, is constructed for each regular power N,, where 0 < of -< On and Zt~<~ 2• <-X,. When ,R, is inaccessible, the structure is either a (set) model of J. H. Conway's ordered field No or an isomorphic copy of No depending on whether or not S~. is a set or a proper class. An early version of this paper was delivered to the Joint Colloquium on Hist...

For accurate and efficient use of wind power, it is important to know the statistical characteristics, availability, diurnal variation, and prediction of wind speed. Prediction of wind power permits the scheduling of the connection or the disconnection of wind turbines to achieve optimal operating costs. In this paper, a simple and accurate method for predicting wind speed based on weather-sens...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

We prove two results on the stability spectrum for Lω1,ω . Here S m i (M) denotes an appropriate notion (at or mod) of Stone space of m-types over M . Theorem A. Suppose that for some positive integer m and for every α < δ(T ), there is an M ∈ K with |S i (M)| > |M |iα(|T |). Then for every λ ≥ |T |, there is an M with |S i (M)| > |M |. Theorem B. Suppose that for every α < δ(T ), there is Mα ∈...