Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

The incidence of patellar fractures accounts for almost 1% of all skeletal fractures. In case of a displaced patellar fracture, surgical intervention is often advocated for earlier stability, restoration of knee motion, and shortened morbidity. Among various fixations, the AO modified tension band technique, which incorporates two parallel Kirschner wires with an anterior tension band, is the m...

A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed achieve optimal 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation the derivative computed around initial guess. High attained constructing polynomials quotients for functional values.

Rota conjectured that, given n disjoint bases of a rank-n matroid M , there are n disjoint transversals of these bases that are all bases of M . We prove a stronger statement for the class of paving matroids.