Summary of Papers as of August 2014
نویسنده
چکیده
• Published 1. Rectilinear equilateral sets in Rn, Geombinatorics, 20 (2011) 151–167. Kusner (1983) conjectured that the maximum size of a set whose elements are pairwise equidistant under the `1-norm in Rn is 2n. If true, this would be sharp. The conjecture has been proved for n = 3 (in 1998) and n = 4 (in 2000). Recently, Alon and Pudlak gave an upper bound of O(n lnn). These proofs are very involved and use ideas from embeddings of metric spaces, approximation theory, etc. However, in the words of the authors, their methods won’t solve the full conjecture. We show that the Kusner conjecture is true if there exists an equidistant set of size 3n/2 on the surface of the generalized-octahedron with radius 1 in Rn. Related to this, we show that the maximum size of an equidistant set on the surface of the unit generalized-octahedron without its extreme point is at most n, and this is sharp. Also, we show that if F is a family of the unit generalized-octahedrons such that every two members of F intersect, then every three members of F must intersect. We are working on extending this result to showing that a same F with at least 2n+ 1 members must be an intersecting family. This would be enough to prove the Kusner conjecture.
منابع مشابه
ECAI Computer Games Workshop 2014
From August 20 to August 22, the 21st European Conference on Artificial Intelligence was held in Prague, Czech Republic. In the two days preceding, 13 workshops were additionally held. On the first day (Monday, August 18) the Computer Games Workshop was held, chaired by Tristan Cazenave, Mark Winands, and Yngvi Björnsson at the Czech Technical University in Prague. A total of 20 papers were sub...
متن کاملمقالههای بین‌المللی پراستناد علوم پزشکی کشور در پایگاه اسکوپوس: 2010 تا 2014
Introduction: Scientific output of the Islamic Republic of Iran in Medical Sciences has been increased during recent years as reflected in Scopus database. Moreover, highly cited papers of researchers, institutions and countries can be used in order to study the citation impact and quality of scientific output. The current study investigates the quality of Medical Sciences’ scholarly outp...
متن کاملاتانازی در تاریخ پزشکی در غرب و جهان اسلام
" Euthanasia " originally is aGreek word. It meansgood deathor dyingcomfortably . But now itisamedical term . It`s commonsense is the " Act or method of causing death painlessly, in order to end suffering as a way to deal with persons dying of incurable,Painful disease . In the West,talkaboutbeing rightorwrongon thisissue, especiallyfrom theperspective of religionand...
متن کاملاندازهگیری فلزات جیوه، سرب، آرسنیک، کادمیوم و کروم در نمک و آب دریاچه مهارلو (استان فارس) در فصول مختلف سال
Background and purpose: Today, environmental pollutions are of the most important issues and hazardous in food safety around the world. Given the importance of salt and water in dietary, and extracting them from Maharloo Lake, Iran, this study aimed to investigate the concentrations of heavy metals, as environmental pollutions, in salt and water of this lake at different seasons. Materials and...
متن کاملIDSA Ebola Summary—August 2014
We write to provide an update on the evolving Ebola outbreak in West Africa. Of particular relevance for infectious disease specialists is information on the identification and care of possible imported cases of Ebola virus disease (EVD) in the United States. This communication is current as of August 21, 2014, and contains links to the sources where anticipated updates will be found in the nea...
متن کامل