Facts,methods, programmes and paradigms

The concept of OR has widened at the Swedish Defence Research Institute (FOA) as at many other places during the last ten years. It has grown from academically faithful frameworks of science and mathematics into many other subjects and also into practical, purposeful activities with a weaker academic affiliation. Holism has been promoted “the hardway” and not only by inspiration from the Ackoff alarms. The awareness of work processes and working paradigms has likewise grown by the simulataneous stimulation from modern OR-literature and as uneasy bureaucratic context.The following taxonomy has a solid foundation in how OR is actually performed at the Institute:

     

20.

An algebraic study of BIB designs: A complete solution for v = 6 and k = 3     

A Hedayat  G.B Khosrovshahi 《Journal of Combinatorial Theory, Series A》1981,30(1):43-52

The set of all distinct blocks of a BIB design is referred to as the support of the design. The family of BIB designs with v = 6 and k = 3 is studied in depth from the view of possible support sizes. Via a linear algebraic technique it is shown that: (i) a BIB design with v = 6 and k = 3 exists if and only if the support size belongs to {10, 14, 16, 17, 18, 19, 20}; (ii) the minimum block size, b, needed to obtain a BIB design with support size $\text{b}{}^1$ is given by:

System/facts:	subject	object
method:	creativity	analysis
purpose/process:	interactive	advisory
paradigm:	intuitive	rational

     

$\text{b}{}^1$	10	14	16	17	18	19	20
$\text{b}$	10	20	20	30	40	30	20

An algebraic study of BIB designs: A complete solution for v = 6 and k = 3

The set of all distinct blocks of a BIB design is referred to as the support of the design. The family of BIB designs with v = 6 and k = 3 is studied in depth from the view of possible support sizes. Via a linear algebraic technique it is shown that: (i) a BIB design with v = 6 and k = 3 exists if and only if the support size belongs to {10, 14, 16, 17, 18, 19, 20}; (ii) the minimum block size, b, needed to obtain a BIB design with support size $\text{b}{}^1$ is given by: