Results 71 to 80 of about 255,151 (329)

Lucas Numbers and Cryptography [PDF]

, 2012
We know that the Fibonacci numbers are the numbers from Fibonacci sequence. It was discovered by Leonardo de Fibonacci de Pisa. The Fibonacci series was derived from the solution to a problem about rabbits.
Thokchom, Chhatrajit Singh
core  

Relationship between Vieta-Lucas polynomials and Lucas sequences

, 2022
Let $w_n=w_n(P,Q)$ be numerical sequences which satisfy the recursion relation \begin{equation*} w_{n+2}=Pw_{n+1}-Qw_n. \end{equation*} We consider two special cases $(w_0,w_1)=(0,1)$ and $(w_0,w_1)=(2,P)$ and we denote them by $U_n$ and $V_n$ respectively. Vieta-Lucas polynomial $V_n(X,1)$ is the polynomial of degree $n$.
openaire   +2 more sources

From Sample to Mixed Reality: A Translational 3D MALDI Imaging Platform for Advanced 3D Spatial Omics Analysis of 3D Cell Culture Disease Models

Advanced Science, EarlyView.
A comprehensive technology platform enables high‐fidelity, volumetric MALDI imaging of 3D cell cultures by integrating custom embedding molds, a semi‐automated computational framework for 3D reconstruction, voxel‐instead of pixel‐based biomarker discovery, and immersive mixed reality data exploration.
Stefania Alexandra Iakab, Jonas Cordes, Thomas Enzlein, Florian Keller, Kevin Kastner, Theresa Mulholland, Björn Christian Fröhlich, Lars Gruber, James Lucas Cairns, Stefan Schmidt, Mathias Hafner, Richard Schneider, Johannes Betge, Frank Fischer, Julian Reichwald, Rüdiger Rudolf, Carsten Hopf   +16 more
wiley   +1 more source

Horadam–Lucas Cubes

Axioms
In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them.
Elif Tan, Luka Podrug, Vesna Iršič Chenoweth   +2 more
doaj   +1 more source

On fourth-order jacobsthal quaternions

Journal of Mathematical Sciences and Modelling, 2018
In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
doaj   +1 more source

Binomial coefficients, Catalan numbers and Lucas quotients

, 2010
Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^
C. J. Smyth, E. B. Vinberg, H. Pan, L. L. Zhao, R. Crandall, R. L. Graham, R. P. Stanley, W. Jänichen, Z. H. Sun, Z. W. Sun, Z. W. Sun, Z. W. Sun, Z. W. Sun, ZhiWei Sun   +13 more
core   +3 more sources

The Square Terms in Lucas Sequences

Journal of Number Theory, 1996
Let \(P\) and \(Q\) be relatively prime odd integers and define the sequences \(\{U_n\}\) and \(\{V_n\}\) by \(U_n = PU_{n - 1} - QU_{n - 2}\) with \(U_0 = 0\), \(U_1 = 1\) and \(V_n = PV_{n - 1} - QV_{n - 2}\) with \(V_0 = 2\), \(V_1 = P\). The main results of the paper are the following. (i) If \(V_n\) is a square, then \(n = 1,3\) or 5.
Ribenboim, Paulo, McDaniel, Wayne L.
openaire   +1 more source

Ruddlesden–Popper Structured Sr3Fe2O7−δ as Redox‐Activated CO2 Sorbents for Green Hydrogen Production

Advanced Energy and Sustainability Research, EarlyView.
A‐site and B‐site doped strontium ferrite‐type Ruddlesden–Popper oxides are evaluated as CO2 sorbents for glycerol‐based hydrogen production via sorption‐enhanced steam reforming. A Sr1.4Ca0.6Fe0.9Ni0.1O4−δ composition forms an active Sr3Fe2O7 phase, achieving ≈95 vol% H2 purity and over sixfold longer CO2 prebreakthrough time (tpb) than its perovskite
Mahe Rukh, Runxia Cai, Seyedamin Razavi, Sam Portillo, Yuge Yao, Luke Neal, Fanxing Li   +6 more
wiley   +1 more source

A Sequence Bounded Above by the Lucas Numbers

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018
In this work, we consider the sequence whosenthterm isthe number of h-vectors of length n. The set of integer vectors E(n)isintroduced. For, n>=2,the cardinality ofE(n)is the nthLucasnumber Lnisshowed.
Ali Aydoğdu, Engin Özkan, Aykut Göçer   +2 more
doaj   +1 more source

Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj   +1 more source