A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has a fundamental rack which contains more information than the fundamental group. Racks provide an elegant and complete algebraic framework in which to study links and knots in 3{manifolds, and also for the 3{...

E. R. van Dam gave an example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the cyclotomic scheme of class 45 on GF(212). The aim of this paper is to present a new example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the c...

Almost all finite graphs have the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We survey some recently discovered families of explicit finite n-e.c. graphs, and present a new construction of strongly regular n-e.c. arising from affine planes.

In this paper, we study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for three tournaments as well as extremal families for each tournament. We use Razborov’s semidefinite method for flag algebras to prove the upper bounds.

We give an alternative proof of the fact that a planar function cannot exist on groups of even order. The argument involved leads us to define a class of functions which we call semi-planar. Through the introduction of an incidence structure we construct semi-biplanes using semi-planar functions. The method involved represents a new approach to constructing semi-biplanes and provides infinite c...

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal su...

A characterization of critical sets and their images for suitable proper Whitney functions in the plane is given. More precisely, necessary and suucient conditions are provided for the existence of proper Whitney extensions F of f : C ! R 2 such that C is the critical set of F. This result relies strongly on theorems of Blank and Troyer.

We consider strongly starlikeness of order α of functions f(z)= z+an+1zn+1 +··· which are analytic in the unit disc and satisfy the condition of the form ∣∣∣∣f ′(z) ( z f(z) )1+μ −1 ∣∣∣∣< λ, 0< μ < 1, 0< λ< 1.

BACKGROUND The soluble transferrin receptor (sTfR) is established as a test for iron deficiency (ID). In chronic lymphocytic leukemia (CLL), sTfR is not reliable for screening for ID as the latter is strongly dependent on tumor burden. METHODS We investigated whether the influence of the tumor load can be excluded or minimized using the sTfR/log ferritin ratio (TfR-F-Index) and the C-reactive...