Articles
Journal of Algebra and its Applications (17936829)
We change Chermak-Delgado measure slightly so that it can be used for compact groups as well. Corresponding to this new measure, a lattice of open subgroups is obtained. Then we prove that if this lattice is non-empty in a compact group G, then G has a characteristic open abelian subgroup N such that [G: N] ≤ [G: A]2 for every abelian subgroup A G. This is a generalization of the well-known Chermak-Delgado Theorem. © 2026 World Scientific Publishing Company.
GPS Solutions (10805370)(1)pp. 73-85
The study of long-term GNSS time series provides valuable insights for researchers in the field of earth sciences. Understanding the trends in these time series is particularly important for geodynamic researchers focused on earth crust movements. Functional and stochastic models play a crucial role in estimating trend values within time series data. Various methods are available to estimate variance components in GNSS time series. The least squares variance component estimation (LS-VCE) method stands out as one of the most effective approaches for this purpose. We introduce an innovative method, which streamlines calculations and simplifies equations, and therefore significantly boosting the processing speed for diagonal(ized) cofactor matrices. The method can be applied to the GNSS time series of linear stochastic models consisting of white noise, flicker noise and random walk noise. Moreover, unlike the conventional approaches, our method experiences high computational efficiency even with an increase in the number of colored noise components in time series data. For GNSS time series, this variable transformation has been applied to both univariate and multivariate modes, preserving the optimal properties of LS-VCE. We conducted simulations on daily time series spanning 5, 10, 15, and 20 years, employing two general and fast modes with one and two colored noise components plus white noise. The computation time for estimating variance components was compared between the two modes, revealing a notable decrease in processing time with the fast mode. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Parvaresh, F.,
Sobhani, R.,
Abdollahi, A.,
Bagherian, J.,
Jafari, F.,
Khatami bidgoli, M. IEEE Transactions on Information Theory (00189448)71(6)pp. 4156-4166
In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has been proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, . . . , n} with the minimum distance at least d ∈ {1, . . . ,(Formula presented)} under the Kendall τ-metric. By presenting an algorithm and two theorems, we improve the known lower and upper bounds for P(n,d) . In particular, we show that P(n,d)=4 for all n ≥ 6 and (Formula presented) (Formula presented) < d ≤ (Formula presented) (Formula presented) . Additionally, we prove that for any prime number n and integer r ≤ − (Formula presented) , P(n,3) ≤ (n-1)! (Formula presented) (Formula presented) . This result greatly improves the upper bound of P(n,3) for all primes n ≥ 37 . © 1963-2012 IEEE.
