Article history: Received 28 January 2013 Available online 27 September 2014

Let n i , k i be positive integers , i 5 1 , . . . , d , satisfying n i > 2 k i . Let X 1 , . . . , X d be pairwise disjoint sets with u X i u 5 n i . Let * be the family of those ( k 1 1 ? ? ? 1 k d )-element sets which have exactly k i elements in X i , i 5 1 , . . . , d . It is shown that if ̂ ’ * is an intersecting family then u ̂ u / u * u < max i k i / n i , and this is best possible . The ...

I described a new UUTD grading system, including HN and UD, based on magnetic resonance urography (MRU) [6] . Herein I describe a new comprehensive classification system for lower and upper urinary tract dysfunction in patients with NB ( table 1 ). In table 1 , LUTD is described according to the Guidelines of the European Association of Urology (EAU) [2] and the terminology of the International...

A cross-intersecting Erdős-Ko-Rado set of generators of a finite classical polar space is a pair (Y,Z) of sets of generators such that all y ∈ Y and z ∈ Z intersect in at least a point. We provide upper bounds on |Y | · |Z| and classify the crossintersecting Erdős-Ko-Rado sets of maximum size with respect to |Y | · |Z| for all polar spaces except some Hermitian polar spaces.

Ahlswede and Khachatrian's diametric theorem is a weighted version of their complete intersection theorem, which is itself a well known extension of the t-intersecting Erd˝ os-Ko-Rado theorem. The complete intersection theorem says that the maximum size of a family of subsets of [n] = {1,. .. , n}, every pair of which intersects in at least t elements, is the size of certain trivially intersect...

Let S(n) be the symmetric group on n points. A subset S of S(n) is intersecting if for any pair of permutations π, σ in S there is a point i ∈ {1, . . . , n} such that π(i) = σ(i). Deza and Frankl [9] proved that if S ⊆ S(n) is intersecting then |S| ≤ (n− 1)!. Further, Cameron and Ku [4] show that the only sets that meet this bound are the cosets of a stabilizer of a point. In this paper we giv...

1. Two vector bundles E and F over the finite connected CW complex X are /-equivalent, if their sphere-bundles S(E) and S(F) are of the same fiber-homotopy type. If they become /-equivalent after a suitable number of trivial bundles is added to both of them they are stably /-equivalent. This note concerns itself with a new stable /-invariant 6(E), which was suggested by the recent work of Atiya...

Correspondence and Galley proofs: 14 Shin-ichi Hisasue, M.D. 15 Department of Urology, Sapporo Medical University School of 16 Medicine, S1-W16, Chuo-ku, Sapporo, Hokkaido, Japan 060-8543 17 Tel: 81-(0)11-611-2111 ext. 3472, Fax: 81-(0)11-612-2709 18 E-mail: [email protected] 19 20 Financial support: This work was supported in part by 21 grants-in-aid for scientific research (12671547 and 16...