Even More Real World Data Regarding ChEVAR Continuing to Show Consistent Results

Finite groups have even more centralizers

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...

Even Find Mistakes in Data Are Coming to the Aid of Professionals in an Ever-more-complex World

Modeling Real-World Data Sets

Traditionally, the performance of algorithms is evaluated using worst-case analysis. For a number of problems, this type of analysis gives overly pessimistic results: Worst-case inputs are rather artificial and do not occur in practical applications. In this lecture we review some alternative analysis approaches leading to more realistic and robust performance evaluations. Specifically, we focu...

Measuring Real-World Data Availability

This paper examines how server marketing claims of high reliability (e.g., 99.999%) stack up against real world data measurements. Our goals were to: measure discretionary NFS data availability, compare data availability between standalone and clustered systems, and draw some conclusions about best practices for customers. We explain our methodology for measuring, filtering, and categorizing av...

finite groups have even more centralizers

for a finite group $g$‎, ‎let $cent(g)$ denote the set of centralizers of single elements of $g$‎. ‎in this note we prove that if $|g|leq frac{3}{2}|cent(g)|$ and $g$ is 2-nilpotent‎, ‎then $gcong s_3‎, ‎d_{10}$ or $s_3times s_3$‎. ‎this result gives a partial and positive answer to a conjecture raised by a‎. ‎r‎. ‎ashrafi [on finite groups with a given number of centralizers‎, ‎algebra‎ ‎collo...