A family of sets is intersecting if every pair its intersect. star a with some element (a center) in each sets. The classical result Erdős, Ko, and Rado (1961) states that r-subsets [n] r≤n/2 has size at most star. Let G be graph, α(G) independence number, μ(G) the smallest maximal independent set G. We say r-EKR if, among all maximum-sized families vertices G, there In 2005 Holroyd Talbot conj...

We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl [5]. For some k ≥ 2, let F be a k-wise intersecting family of r-subsets of an n element set X, i.e. for any F1, . . . , Fk ∈ F , ∩ k i=1Fi 6= ∅. If r ≤ (k − 1)n k , then |F| ≤ ( n−1 r−1 ) . We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and o...

[email protected] TEX , L ATEX , AND B I B T EX F I L ES ARE a common method of collaboration for computer science professionals. It is widely assumed by users that LaTeX files are safe; that is, that no significant harm can come of running LaTeX on an arbitrary computer. Unfortunately, this is not the case. In this article we describe how to exploit LaTeX to build a virus that spreads between docum...

The enzymatic kinetic resolution (EKR) of racemic alcohols or esters is a broadly recognized methodology for the preparation these compounds in optically active form. Although EKR approaches have been developed enantioselective transesterification vast number secondary hydrolysis their respective esters, to date, there no report bio- chemo-catalytic asymmetric synthesis non-racemic possessing 1...

The purpose of this study was to investigate the agreement between the clinical history method (CHM), Orbscan IIz, and Pentacam in estimating corneal power after myopic excimer laser surgery. Fifty five patients who had myopic LASIK/PRK were recruited into this study. One eye of each patient was randomly selected by a computer-generated process. At 6 months after surgery, postoperative corneal ...

Previous studies have found that G-protein-coupled receptor 116 (GPR116) is a regulator of breast cancer metastasis. However, the role of GPR116 in colorectal carcinoma (CRC) carcinogenesis and progression is unknown. In this study, We found GPR116 expression was significantly up-regulated in CRC specimens compared with corresponding non-cancerous tissues. Increased GPR116 expression in CRC was...