Results 61 to 70 of about 594,288 (306)
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
Advanced Engineering Materials, EarlyView.This article investigates residual stress formation during single‐spot nanosecond laser ablation of stainless steel. Experimental validation and a parametric study using finite element simulations are employed to analyze thermal effects, ablation dynamics, and stress evolution.
Yutaka Tsumura +7 more
wiley +1 more source
A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
doaj +1 more source
Advanced Functional Materials, EarlyView.This research applies advanced laser beam shaping (LCoS‐SLM) to fabricate the Ti‐6Al‐4V alloy via laser powder bed fusion. A tailored beam is used to prevent martensite formation and create a dual α+β microstructure by controlling cooling rates.
Reza Esmaeilzadeh +8 more
wiley +1 more source
Kesetaraan Uji Pepin dan Lucas-lehmer [PDF]
, 2015 Pepin test provides a necessary and sufficient condition for a Fermat number to be a prime. Lucas-Lehmer test provides a necessary and sufficient condition for a Mersenne number to be a prime.
Gemawati, S. (Sri) +2 more
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Fast Neutron Detector Based on Hybrid 2D Perovskite Thin Films
Advanced Functional Materials, EarlyView.This work presents the direct detection of fast neutrons using flexible hybrid 2D perovskite (PEA2PbBr4) thin‐film detectors. Thanks to their high low‐Z elements content and good charge transport, these materials enable efficient neutron detection. The thin film configuration allowed the operation at low voltage, and offer scalability, flexibility, and
Ilaria Fratelli +11 more
wiley +1 more source
The terms in Lucas sequences divisible by their indices [PDF]
, 2009 For Lucas sequences of the first kind (u_n) and second kind (v_n) defined as usual for positive n by u_n=(a^n-b^n)/(a-b), v_n=a^n+b^n, where a and b are either integers or conjugate quadratic integers, we describe the set of indices n for which n divides
Smyth, Chris
core +4 more sources
Advanced Functional Materials, EarlyView.A metal halide perovskite‐based photoanode integrated with a CoNiFe layered double hydroxide (LDH) cocatalyst is reported for selective glucose oxidation reaction (GOR), achieving simultaneous and unassisted photoelectrochemical hydrogen production. This system delivers high photocurrent density, excellent Faradaic efficiency of GOR, and strong techno ...
Shujie Zhou +12 more
wiley +1 more source
Incomplete Tribonacci–Lucas Numbers and Polynomials [PDF]
Advances in Applied Clifford Algebras, 2014 In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Necati Taskara, Nazmiye Yilmaz
openaire +3 more sources
Solusi Bilangan Bulat suatu Persamaan Diophantine melalui Bilangan Fibonacci dan Bilangan Lucas [PDF]
, 2015 This article discusses the Diophantine equations in the form x 2 + axy + by 2 = c. The values of a, b, and c are constructed by Fibonacci number Fn and Lucas number L n.
Gemawati, S. (Sri) +2 more
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