Results 31 to 40 of about 51,391 (253)

Combinatorial sums associated with balancing and Lucas-balancing polynomials [PDF]

, 2020
The aim of the paper is to use some identities involving binomial coefficients to derive new combinatorial identities for balancing and Lucas-balancing polynomials. Evaluating these identities at specific points, we can also establish some combinatorial
Goy, Taras, Frontczak, Robert
core   +3 more sources

Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits

, 2021
See the abstract in the attached pdf.
Rayaguru, Sai Gopal, Panda, Gopal Krishna   +1 more
openaire   +3 more sources

NEW IDENTITIES FOR THE COMMON FACTORS OF BALANCING AND LUCAS-BALANCING NUMBERS [PDF]

International Journal of Pure and Apllied Mathematics, 2013
Balancing numbers n and balancers r are originally defined as the solution of the Diophantine equation 1 + 2 + ··· + (n − 1) = (n + 1) + (n + 2) + ··· + (n + r). If n is a balancing number, then 8n 2 + 1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n 2 + 1 is called a Lucas-balancing number.
P. Ray
semanticscholar   +2 more sources

Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications

Integers, 2014
See the abstract in the attached pdf.
openaire   +4 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

Productivity‐Driven Optimization of Laser Powder Bed Fusion Parameters for IN718 Superalloy: Process Control, Microstructure, and Mechanical Properties

Advanced Engineering Materials, EarlyView.
This study demonstrates how optimizing laser power, scanning speed, and hatching distance in laser powder bed fusion can boost the productivity of Inconel 718 manufacturing by up to 29% while maintaining mechanical integrity. The work delivers a validated process window and cost–time analysis, offering industry‐ready guidelines for efficient additive ...
Amir Behjat, Guido Barale, John Stavridis, Ehsan Norouzi, Jin‐Yoo Suh, Dong‐Ik Kim, Luca Iuliano, Abdollah Saboori   +7 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

Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes

AIMS Mathematics, 2019
In this article, we derive some identities involving k balancing and k-Lucas-balancing numbers of arithmetic indexes, say an + p, where a and p are some fixed integers with 0≤p≤a-1.
P. Ray
semanticscholar   +1 more source

Moving Beyond Oligoethers: Polar Side‐Chain Engineering for Aqueous Mixed Ionic–Electronic Conductors

Advanced Functional Materials, EarlyView.
We investigate how side‐chain chemistry and hydrogen bonding affect electrochemical doping in poly(propylenedioxythiophene) polymers. Replacing oligoether side chains with hydroxyl or carboxylic acid groups nearly triples electrochemical conductivity.
Joshua M. Rinehart, Anna M. Österholm, James F. Ponder Jr., Lucas Q. Flagg, Lee J. Richter, John R. Reynolds   +5 more
wiley   +1 more source

Balancing and Lucas-balancing Numbers With Real Indices [PDF]

, 2015
In this thesis, we have studied the balancing and Lucas-balancing numbers for real indices. Also we have discussed some properties of balancing numbers with real numbers.
Tanty, Sephali
core