Results 71 to 80 of about 9,626 (197)

Generalizing the eight levels theorem: a journey to Mersenne prime discoveries and new polynomial classes

Arab Journal of Basic and Applied Sciences
Mersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
doaj   +1 more source

Batched ranged random integer generation

Software: Practice and Experience, Volume 55, Issue 1, Page 155-169, January 2025.
Summary Pseudorandom values are often generated as 64‐bit binary words. These random words need to be converted into ranged values without statistical bias. We present an efficient algorithm to generate multiple independent uniformly‐random bounded integers from a single uniformly‐random binary word, without any bias.
Nevin Brackett‐Rozinsky, Daniel Lemire
wiley   +1 more source

On Gersenne Sequence: A Study of One Family in the Horadam-Type Sequence

Axioms
This study introduces an innovative approach to Mersenne-type numbers. This paper introduces a new class of numbers, which we call Gersenne numbers. The aim of this paper is to define the Gersenne sequence and to investigate some of their properties ...
Douglas Catulio Santos, Eudes Antonio Costa, Paula M. M. C. Catarino   +2 more
doaj   +1 more source

On the number of $N$-free elements with prescribed trace [PDF]

, 2015
In this paper we derive a formula for the number of $N$-free elements over a finite field $\mathbb{F}_q$ with prescribed trace, in particular trace zero, in terms of Gaussian periods.
Tuxanidy, Aleksandr, Wang, Qiang
core  

Securing Ports of Web Applications Against Cross Site Port Attack (XSPA) by Using a Strong Session Identifier (Session ID)

IET Cyber-Physical Systems: Theory &Applications, Volume 10, Issue 1, January/December 2025.
A cookie contains a session ID that is a unique number generated by the server. The proposed generator is suitable for all types of web applications, because it requires the smallest area of only 134 Gate Equivalent (GE) on the application specific integrated circuit (ASIC) for its execution.
Kavita Bhatia, Santosh K. Pandey, Vivek K. Singh, Deena Nath Gupta   +3 more
wiley   +1 more source

Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, I [PDF]

Notes on Number Theory and Discrete Mathematics
The aim of this work is to present a method using the cyclic sequences {Mₖ},{θₜₖ} and {ψₜₖ} in the finite fields 𝔽_ρ, with ρ a prime, that yield divisors of Mersenne, Fermat and Lehmer numbers.
A. M. S. Ramasamy
doaj   +1 more source

Probability Hypothesis Density Filter‐Based Group Target Tracking Algorithm Using Rigid‐Body Similarity Model and Measurement Fusion: Implementations Across Random Finite Set Frameworks

IET Radar, Sonar &Navigation, Volume 19, Issue 1, January/December 2025.
This paper proposes an improved group target tracking algorithm based on rigid‐body similarity model and measurement fusion, implemented across different random finite set filtering frameworks. The method outperforms traditional VLFM algorithms in the GMPHD framework and demonstrates robustness against varying clutter densities in the PMBM framework ...
Kai Chang, Haitao Wang, Tian Xia, Li Wang, Ziqiang Chen   +4 more
wiley   +1 more source

Weakly subnormal subgroups and variations of the Baer–Suzuki theorem

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract A subgroup R$R$ of a finite group G$G$ is weakly subnormal in G$G$ if R$R$ is not subnormal in G$G$ but it is subnormal in every proper overgroup of R$R$ in G$G$. In this paper, we first classify all finite groups G$G$ that contains a weakly subnormal p$p$‐subgroup for some prime p$p$.
Robert M. Guralnick, Hung P. Tong‐Viet, Gareth Tracey   +2 more
wiley   +1 more source

A Study on the k-Mersenne and k-Mersenne-Lucas Sequences

Universal Journal of Mathematics and Applications
In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas
Mine Uysal, Hakan Akkuş, Bayram Şen, Engin Özkan   +3 more
doaj   +1 more source

Measuring (meta)cognitive processes in multimedia learning: Matching eye tracking metrics and think‐aloud protocols in case of seductive details

Journal of Computer Assisted Learning, Volume 40, Issue 6, Page 2985-3004, December 2024.
Abstract Background Both learning and problem solving are major goals of complex problem solving in engineering education. The order of knowledge construction and problem solving in learning through problem solving, however, has not been explained in current literature.
Lisa Stark, Andreas Korbach, Roland Brünken, Babette Park   +3 more
wiley   +1 more source