Results 61 to 70 of about 255,828 (280)
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 +13 more
core +3 more sources
Graphene‐Based Wearable Textile Triboelectric Nanogenerators and Biomechanical Sensors
Advanced Materials Technologies, EarlyView.This study presents a wearable textile‐based triboelectric nanogenerator (T‐TENG) using sprayed graphene enhanced with a PVA adhesion layer. The graphene‐based electrode demonstrates high electrical conductivity and robustness to multiple bends. The fabricated T‐TENG provides stable and efficient output, with strong responsiveness to biomotion.
Hongyang Dang +4 more
wiley +1 more source
On the emergence of the Quanta Prime sequence
Arab Journal of Basic and Applied SciencesThis paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj +1 more source
On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
مجلة بغداد للعلوم, 2023 In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
B. Malini Devi, S. Devibala
doaj +1 more source
Tribonacci and Tribonacci-Lucas Sedenions
, 2018 The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.Comment: 17 pages, 1 ...
Soykan, Yüksel
core +1 more source
Advanced Materials Technologies, EarlyView.A compact incubation platform enables long‐term cultivation of biological samples directly on diamond quantum sensors for NV widefield magnetometry. The 3D‐printed biocompatible chamber provides a temperature controlled, CO2${\rm CO}_2$ and humidity rich environment while accommodating total internal reflection excitation geometry.
Andre Pointner +9 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 +2 more
doaj +1 more source
Lucas congruences for the Ap\'ery numbers modulo $p^2$
, 2020 The sequence $A(n)_{n \geq 0}$ of Ap\'ery numbers can be interpolated to $\mathbb{C}$ by an entire function. We give a formula for the Taylor coefficients of this function, centered at the origin, as a $\mathbb{Z}$-linear combination of multiple zeta ...
Krattenthaler, Christian +2 more
core
Advanced Robotics Research, EarlyView.Visual teach‐and‐repeat (VTR) navigation allows robots to learn and follow routes without building a full metric map. We show that navigation accuracy for VTR can be improved by integrating a topological map with error‐drift correction based on stereo vision.
Fuhai Ling, Ze Huang, Tony J. Prescott
wiley +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