Kano et al. proved that if P0, P1, . . . , Pk−1 are pairwise disjoint collections of points in general position, then there exist spanning trees T0, T1, . . . , Tk−1, of P0, P1, . . . , Pk−1, respectively, such that the edges of T0 ∪ T1 ∪ · · · ∪ Tk−1 intersect in at most (k − 1)n − k(k − 1)/2 points. In this paper we show that this result is asymptotically tight within a factor of 3/2. To prov...

Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısica Computacional, Universidade de Coimbra, P-3004-516 Coimbra, Portugal Theoretical Physics Group, Dept of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada T1K 3M4 and Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Ef...

the aim of this study is to determine whether there is a role of podoplanin and glutathione s-transferases t1 (gst-t1) expression in laryngeal squamous cell carcinoma. the study was completed with 33 patients and gene expression analysis was performed by qrt–pcr. the podoplanin and gst-t1 expression patterns were analyzed to determine their correlation with clinicopathologic parameters of laryn...

Synthesis of guanosine 3'-phosphodiesters of 1, N6-ethenoadenosine-2-sulfonate or 1, N6-etheno-2-azaadenosine can be done readily with ribonuclease N1. There is a 10-fold difference in quantum yield between the phosphodiesters and the starting fluorescent nucleosides. This difference provides the basis for the development of a fluorescent assay for nuclease.

Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, . . . , 4 are the theories “ZFC + φ1 + φ2”, “ZFC + ¬φ1 + φ2”, “ZFC + φ1 + ¬φ2”, and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, . . . , 4, Ai =df {δ < κ | δ is an inaccessible cardinal which is not a limit of inaccessible...

Background MOLLI is a method of producing a T1 map at end diastole by using the electrocardiogram (ECG) under respiratory arrest to obtain consecutive inversion recovery images with an arbitrary number of MOLLI cycles. Since a variety of heart rates are presumed clinically, it is important to understand their effects on the T1 value and the error of measurement. We investigated the error of mea...

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Background The recently published method SMART1Map[1] has proposed a new true T1 measurement technique. It consists in a 2D saturation-recovery prepared balancedSSFP sequence which allows different acquisition schemes depending on the number of repetition (shot) used. Single-shot acquisition duration is short but cardiac motion blur can occur due to long acquisition window duration. Two-shot ac...