On generalized bihyperbolic Mersenne numbers [PDF]
Mathematica Bohemica, 2023 In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
doaj +2 more sources
Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]
PLoS ONE, 2023 An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov +2 more
doaj +2 more sources
The Challenge of Time-to-Event Analysis for Multiple Events: A Guided Tour From Time-to-First-Event to Recurrent Time-to-Event Analysis. [PDF]
Biom JABSTRACT Clinical trials often compare a treatment to a control group concerning multiple possible combined time‐to‐event endpoints like hospital‐free survival. Thereby, the first endpoint may occur more than once (“recurrent”), whereas the second endpoint is absorbing. Inclusion of all observed events in the analysis can increase the power and provide
Schmeller S +4 more
europepmc +2 more sources
Learned pseudo-random number generator: WGAN-GP for generating statistically robust random numbers. [PDF]
PLoS ONE, 2023 Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary ...
Kiyoshiro Okada +3 more
doaj +2 more sources
Application of Statistical Shape Models to Standard Lumbar MRI for Stenosis Treatment Stratification: Severe Versus Normal Stenosis [PDF]
JOR SpineStatistical shape models (SSMs) derived from standard 2D lumbar MRIs capture coordinated morphological features that distinguish severe from normal spinal stenosis. Both intervertebral disc and combined models provide strong discriminatory power, comparable to or exceeding traditional anatomical measurements.
Foltz M +4 more
europepmc +2 more sources
Validation of the collapsed-cone superposition for whole-body patient-specific dosimetry in [177Lu]Lu-PSMA-617 radionuclide therapy. [PDF]
Med PhysAbstract Background Patient‐specific dosimetry in radiopharmaceutical therapy (RPT) offers a promising approach to optimize the balance between treatment efficacy and toxicity. The introduction of 360° CZT gamma cameras enables the development of personalized dosimetry studies using whole‐body single photon emission computed tomography and computed ...
Terro A +7 more
europepmc +2 more sources
The specifics of the Galois field GF(257) and its use for digital signal processing [PDF]
Scientific ReportsAn algorithm of digital logarithm calculation for the Galois field $$GF(257)$$ G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 ...
Akhat Bakirov +4 more
doaj +2 more sources
Mathematics, 2019 In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit ...
Yanpeng Zheng +2 more
exaly +3 more sources
Mersenne version of Brocard-Ramanujan equation
Journal of New Results in Science, 2023 In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
doaj +1 more source
Fermat and Mersenne numbers in $k$-Pell sequence
Математичні Студії, 2021 For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
doaj +1 more source