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...

We consider way k tape alternating pushdown automata k apa and way k tape alternating nite automata k afa We say that an alternating automaton accepts a language L with f n bounded maximal respectively minimal leaf size if arbitrary re spectively at least one accepting tree for any w L has no more than f jwj leaves The main results of the article are the following For way k tape alternating cou...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

We consider the convergence properties for alternating projection algorithm (a.k.a alternating projections) which has been widely utilized to solve many practical problems in machine learning, signal and image processing, communication and statistics since it is a gradient-free method (without requiring tuning the step size) and it usually converges fast for solving practical problems. Although...

Hydrophilic/hydrophobic patterning is a powerful strategy to control folding in non-natural polymers/oligomers. In this contribution, we present a novel strategy for the preparation of alternating hydrophilic/hydrophobic patterned non-natural peptide foldamers. This strategy relies on the post-modification of a reactive peptide precursor that can be prepared via standard solid phase peptide syn...

There is evidence that sleep bruxism is an arousal-related phenomenon. In non-REM sleep, transient arousals recur at 20- to 40-second intervals and are organized according to a cyclic alternating pattern. Polysomnographic recordings from six subjects (two females and four males) affected by sleep bruxism (patients) and six healthy age-and gender-matched volunteers without complaints about sleep...

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...