… proof that cr(K5,n) = Z(5, n). We explore in depth the role of antipodal vertices in optimal
drawings of K5,n, for n even. We prove that if n ≡ 2 (mod 4), then every optimal drawing of K5,n …

… monotone drawing of \(G\). For these two notions of the crossing number, optimal drawings
do … Given a signature function \(\sigma \) with no forbidden 4-tuples and 5-tuples we apply the …

… A K satisfies AK <A and range AK C range K. Now let Be NND(k) be another matrix with B <
A and range B C_ range K. … leads to determinant optimal designs for sample size n. Gaffke (…

… crossings in drawings of \(K_{n}\), and use it to prove that \(\nu _{2}(K_{n}) = Z(… (n\) odd we
provide a family of size \(2^{(n-5)/2}\) of non sphere-homeomorphic crossing optimal drawings. …

… Then, we regard the optimal layout of vertices as the state in … The parameter k ij is the strength
of the spring between Pi and Pj… Figure 5(a) and 5(b) show the picture of two initial states in …

… optimal 2-planar drawing consists of a subset of planar edges forming faces of size five (ie,
pentagons), and each face is filled up with five … In the following we prove that \(5n-10\) is also …

… The method was used by Tvergaard [5] in 1973 and has had a … -of-the-art today for shape
design is that shape optimization is … element as a body occupying a domain K~ in !~ 3 and …

… (K in art..) It is one of the letters of augmentation [occurring in … of youth but not been rendered
decrepit by K and in the CK,) when [… ($ in art., and K.) he must despair like as he despairs of …

… Imagine, for example, an ideal experiment which … a collection of (say) J X K means is to
assume a model that implies … factorially combined with K levels of stimulus type and n subjects. Ifit …

… investigated at five levels: 4, 5, 6, 7 and 8 in the optimization of a spectrophotometric method.
… are, in this way, more efficient and economical then their corresponding 3 k designs, mainly …