On the maximum number of diagonals of a circuit in a graph

For a graph G, let ?(G) denote the maximum number k such that G contains a circuit with k diagonals.Theorem. For any graph G with minimum valency$\text{n? 3, ?(G) ?}\text{1}\text{2}\text{(n+1)(n-2)}$.If the equality holds and G is connected, then either G is isomorphic to K_n+1 or G is separable and each of its terminal blocks is isomorphic to K_n+1, or K_n+1 with one edge subdivided.     

Model-Year Architectures for Rapid Prototyping

The Rapid Prototyping of Application-Specific Signal Processors (RASSP) program is changing the way engineers design embedded signal processors by providing a process that will reduce by at least a factor of four both the time-to-market and cost, and improve design quality. To achieve these improvements, Lockheed Martin's Advanced Technology Laboratories (ATL) is using a methodology that stresses hardware and software reuse, and model-year architectures that enable interoperability and upgrades through open interface standards. This paper describes ATL's model-year architecture, which defines a framework for reuse to enable low-cost technology upgrades for embedded processors. This approach can be applied to a wide range of military and commercial applications.     

Derivatives of the Hurwitz Zeta function for rational arguments

The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivatives of ζ(s,a) at negative odd s and rational a. For several of these rational arguments, closed-form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function.     

Ozonolytic cleavage of cycloalkenes to terminally differentiated products

Conditions are reported which convert cycloalkenes to terminally differentiated products through the intermediacy of α-alkoxy hydroperoxides.