For a graph G and integer r ≥ 1 we denote the collection of independent r-sets of G by I (r)(G). If v ∈ V (G) then I (r) v (G) is the collection of all independent r-sets containing v. A graph G, is said to be r-EKR, for r ≥ 1, iff no intersecting family A ⊆ I (r)(G) is larger than maxv∈V (G) |I v (G)|. There are various graphs which are known to have his property: the empty graph of order n ≥ ...

Given a set of n real numbers, if the sum of the elements of every subset of size larger than k is negative, what is the maximum number of subsets of nonnegative sum? In this note we show that the answer is (n−1 k−1 ) + (n−1 k−2 ) + · · ·+ (n−1 0 ) + 1, settling a problem of Tsukerman. We provide two proofs; the first establishes and applies a weighted version of Hall’s theorem, and the second ...

Let X be a proper variety defined over a field K. Following [Ma], we say that two points x, x′ ∈ X(K) are R-equivalent if they can be connected by a chain of rational curves defined over K (cf. (4.1)). In essence, two points are R-equivalent if they are “obviously” rationally equivalent. Several authors have proved finiteness results over local and global fields (cubic hypersurfaces [Ma], [SD],...

be a positive definite quadratic form with determinant D R and integer coefficients a ;Call it an even form if all a ; ; are even ., an odd form if at least one a ;; is odd . Then Í,, is called non-decomposable, if it cannot be expressed as a sum of two non-negative quadratic forms with integer coefficients . Mordell 1 ) proved that f, can always be decomposed into a sum of five squares of line...

In terms of the notion of a specific class of ranked semilattices, called regular quantum matroids, we prove the Erdiis-Kc-Rado-type results in a unified way for the association schemes J,(n,d) of vector spaces and H,(n,d) of bilinear forms, together with their Delsarte t-designs, respectively. @ 1999 Elsevier Science B.V. All rights reserved

Learner corpora consist of texts produced by second language (L2) learners. I We present ALeS Ko, a learner corpus of Chinese L2 learners of German and discuss the multi-layer annotation of the left sentence periphery notably the Vorfeld.

conclusions urodynamic studies in children should be performed in preferred voiding position for each kid considering the culture and voiding habits. unfamiliar voiding position may turn the uroflowmetry to a stressful experience for child that make him uncooperative and cause misleading results. results comparison of uroflowmetric indexes between different genders and voiding positions showed ...

BACKGROUND Urinary stone incidence in pregnancy has been reported in a wide range, from 1 in 200 to 1 in 2000 cases. OBJECTIVES The aim of this study was to investigate the efficacy and safety of ureteroscopic treatment and its results and complications for pregnant women with urinary stones. PATIENTS AND METHODS From 2003 till 2011, 113 pregnant patients with symptomatic urolithiasis were ...

INTRODUCTION The SCAN genitourinary cancer workgroup aimed to develop Singapore Cancer Network (SCAN) clinical practice guidelines for neoadjuvant and adjuvant chemotherapy for muscle-invasive bladder cancer (MIBC). MATERIALS AND METHODS The workgroup utilised a modified ADAPTE process to calibrate high quality international evidence-based clinical practice guidelines to our local setting. ...