Results 41 to 50 of about 1,424 (225)

A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$

Journal of Innovative Applied Mathematics and Computational Sciences, 2021
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan, Erkan Taşdemir, Can Murat Dikmen   +2 more
doaj  

Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source

A note on hybrid convolutions involving Balancing and Lucas-Balancing numbers

Applied Mathematical Sciences, 2018
Robert Frontczak
openalex   +2 more sources

A note on k-tridiagonal matrices with the balancing and Lucas-balancing numbers.

, 2015
In this note, we consider one type of k-tridiagonal matrix family whose permanents and determinants are specified to the balancing and Lucas-balancing numbers. Moreover, we provide some properties between Chebyshev polynomial properties and the given number sequences.
Fatih Yılmaz, Emrullah Kırklar
openalex   +3 more sources

Almost repdigits in balancing and Lucas-balancing sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
doaj   +1 more source

On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers

Mathematics
This study introduces two new sequences: the incomplete Edouard and the incomplete Edouard–Lucas numbers. In addition, we establish some of the properties, identities, and recurrence relations of these sequences. The relations of these new sequences with
Elen Viviani Pereira Spreafico, Eudes Antonio Costa, Paula Catarino   +2 more
doaj   +1 more source

Use of a Molecular Signature Response Classifier to Inform Treatment Selection Improves Clinical Disease Activity Among Patients with Rheumatoid Arthritis Initiating a Biologic or Targeted Synthetic Disease‐modifying Antirheumatic Drug

Arthritis Care &Research, Accepted Article.
Objective We assessed the effectiveness of PrismRA to improve clinical outcomes among patients with rheumatoid arthritis (RA) initiating treatment with a biologic or targeted synthetic disease‐modifying antirheumatic drug (b/tsDMARD) Methods PrismRA incorporated 19 gene expression features and 4 clinical features to assess a patient's likelihood of ...
Fenglong Xie, Timothy Beukelman, Nicholas P McCormick, Jeffrey R Curtis   +3 more
wiley   +1 more source

Interaction between Molten Al‐Killed Mn–B Steel and Carbon‐Bonded MgO Refractories Based on Recyclates

Advanced Engineering Materials, EarlyView.
High‐temperature interactions between low‐sulfur Al‐killed Mn–B steel and MgO–C refractories (0 and 50 wt% recyclates) are studied via finger immersion tests (1600 °C). Surface‐active elements influence infiltration. MgO/CaS layer forms, along with spinel and calcium silicate.
Matheus Roberto Bellé, Lukas Neubert, Anton Yehorov, Till M. J. Stadtmüller, Christos G. Aneziris, Olena Volkova   +5 more
wiley   +1 more source

CO2 Reduction on Copper‐Nitrogen‐Doped Carbon Catalysts Tuned by Pulsed Potential Electrolysis: Effect of Pulse Potential

Advanced Functional Materials, EarlyView.
This study demonstrates that pulsed potential electrolysis significantly improves CO2 reduction performance on copper‐nitrogen doped carbon electrodes. The formation of cationic copper sites and metallic clusters as a function of applied intermittent potential leads to notable selectivity changes compared to potentiostatic reduction.
Dorottya Hursán, Janis Timoshenko, Andrea Martini, Hyo Sang Jeon, Eduardo Ortega, Martina Rüscher, Arno Bergmann, Aram Yoon, Uta Hejral, Antonia Herzog, Clara Rettenmaier, Felix T. Haase, Philipp Grosse, Beatriz Roldan Cuenya   +13 more
wiley   +1 more source

On the Balancing-bilinear system of difference equations: solutions via some number sequences and global stability

Miskolc Mathematical Notes
In the current paper, we present a new class of systems called the Balancing-bilinear system of difference equations to investigate some theoretical proprieties.
Ahmed Ghezal, Imane Zemmouri
doaj   +1 more source