Results 1 to 10 of about 25,702 (163)
On perfect powers in $k$-generalized Pell sequence [PDF]
Mathematica Bohemica, 2023 Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar +2 more
doaj +4 more sources
Perfect Matchings and Perfect Powers [PDF]
Journal of Algebraic Combinatorics, 2003 In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers. In this paper we present an approach that allows proving them in a unified way. We use this approach to prove a conjecture of James Propp stating that the number of tilings of the so-called Aztec
Mihai Adrian Ciucu
exaly +4 more sources
Sieve algorithms for perfect power testing [PDF]
Algorithmica, 1993 Many tests for primality of \(n\) first require the elimination of the case where \(n\) is a perfect \(k\)-th power. This is negligible compared with the main primality routines, so it is usually ignored. There is a rich variety of methods including Newton's root extraction with starting value found by counting digits, modular tests for \(k\) power and
Eric Bach 0001, Jonathan P. Sorenson
exaly +4 more sources
A Further Generalization of limn→∞n!/nn=1/e{\lim _{n \to \infty }}\root n \of {n!/n} = 1/e
Annales Mathematicae Silesianae, 2022 It is well-known, as follows from the Stirling’s approximation n!∼2πn(n/e)nn! \sim \sqrt {2\pi n{{\left( {n/e} \right)}^n}}, that n!/n→1/en\root n \of {n!/n \to 1/e}.
Farhadian Reza, Jakimczuk Rafael
doaj +1 more source
Photonics, 2022 We proposed an infrared narrowband metamaterial perfect absorber (MPA) which is induced by toroidal dipole resonance in a dielectric-metal hybrid system.
Yuepei Cai, Yong Huang, Keyong Zhu
doaj +1 more source
A UNIQUE PERFECT POWER DECAGONAL NUMBER [PDF]
Bulletin of the Australian Mathematical Society, 2021 AbstractLet $\mathcal {P}_s(n)$ denote the nth s-gonal number. We consider the equation $$ \begin{align*}\mathcal{P}_s(n) = y^m \end{align*} $$ for integers $n,s,y$ and m. All solutions to this equation are known for $m>2$ and $s \in \{3,5,6,8,20 \}$ . We consider the case $s=10$ , that of decagonal numbers. Using a descent argument and the
openaire +4 more sources
ON PERFECT POWERS IN LUCAS SEQUENCES [PDF]
International Journal of Number Theory, 2005 Let (un)n≥0be the binary recurrence sequence of integers given by u0= 0, u1= 1 and un+2= 2(un+1+ un). We show that the only positive perfect powers in this sequence are u1= 1 and u4= 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
Bugeaud, Yann +3 more
openaire +1 more source
The Annals of "Dunărea de Jos" University of Galaţi. Fascicle XVIII, Philosophy, 2021 This study addresses fundamental ideas about the elements water, fire, earth, wind, and in the subsidiary of these elements addresses the dual perspective of the light and dark veil from a psycho-metaphilosophical point of view. Philosophical notions are
Vasile R. TODORAN
doaj +1 more source
Robust nonlinear control of wind turbine driven doubly fed induction generators
Heritage and Sustainable Development, 2020 This paper presents the active and reactive powers control of a doubly fed induction generator (DFIG) connected to the grid utility and driven by a wind turbine, this machine allowing a large speed variation and so a large range of wind is achieved ...
Hamza Mesai Ahmed, Youcef Djeriri
doaj +1 more source
On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
doaj +1 more source