Let v ( k , λ ) be the maximum number of vertices a connected -regular graph with second largest eigenvalue at most . The Alon-Boppana Theorem implies that is finite when > 2 + 4 In this paper, we show for fixed ≥ 1 there exists constant C such ≤

The inspiration for this paper is a result proved by Michael Smyth which states that Gordon Plotkin's category SFP is the largest cartesian closed category of domains. Although this category is easily enough motivated from concepts in domain theory and category theory, it is clearly harder to describe and less \elementary" than the most popular categories of domains for denotational semantics. ...

‎let $g$ be a finite group and $pi_{e}(g)$ be the set of element‎ ‎orders of $g$‎. ‎let $k in pi_{e}(g)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $g$‎. ‎set nse($g$):=${ m_{k} | k in‎ ‎pi_{e}(g)}$‎. ‎in this paper‎, ‎we prove that if $g$ is a group such‎ ‎that nse($g$)=nse($psl(2‎, ‎25)$)‎, ‎then $g cong psl(2‎, ‎25) $‎.

‎let $g$ be a finite group and $pi_{e}(g)$ be the set of element‎ ‎orders of $g$‎. ‎let $k in pi_{e}(g)$ and $m_{k}$ be the number of‎ ‎elements of order $k$ in $g$‎. ‎set nse($g$):=${ m_{k} | k in‎ ‎pi_{e}(g)}$‎. ‎in this paper‎, ‎we prove that if $g$ is a group such‎ ‎that nse($g$)=nse($psl(2‎, ‎25)$)‎, ‎then $g cong psl(2‎, ‎25) $‎.

The block economic value (BEV) of a single-metal deposit is calculated based on the metal content and the related costs. The common methods available for calculating BEV are just based upon the profitable elements, and the effects of undesirable elements on BEV are not considered. However, in multi-element deposits, the effects of other elements existing in the blocks on BEV should be considere...

This paper gives max characterizations for the sum of the largest eigen-values of a symmetric matrix. The elements which achieve the maximum provide a concise characterization of the generalized gradient of the eigenvalue sum in terms of a dual matrix. The dual matrix provides the information required to either verify rst-order optimality conditions at a point or to generate a descent direction...

We study the largest values of the rth row of Stern’s diatomic array. In particular, we prove some conjectures of Lansing. Our main tool is the connection between the Stern sequence, alternating binary expansions, and continuants. This allows us to reduce the problem of ordering the elements of the Stern sequence to the problem of ordering continuants. We describe an operation that increases th...