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Journal articles on the topic 'Generalized Neo Balancing Sequence'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Chailangka, Natdanai, and Apisit Pakapongpun. "On a Certain Sequence of Sequence t-Neo Balancing Numbers." International Journal of Mathematics and Computer Science 20, no. 1 (2024): 45–48. http://dx.doi.org/10.69793/ijmcs/01.2025/pakapongpun.

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2

S., Sriram, and Veeramallan P. "A NOTE ON NEO BALANCING SEQUENCE, GENERALIZED RECURSIVE SEQUENCES AND PYTHAGOREAN TRIPLES." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 08 (2022): 2852–54. https://doi.org/10.5281/zenodo.7012592.

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We proved theorems about creating Pythagorean Triples from generalized recursive sequences in this study. Pythagorean triples are a very old concept that has made significant progress in recent mathematical studies. Pythagorean triples can be generated using Neo balancing sequences and generalized recursive sequences, and vice-versa. For greater understanding, a general procedure is presented with appropriate illustrations.

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3

Mehraban, Elahe, and Mansour Hashemi. "Coding theory on the generalized balancing sequence." Notes on Number Theory and Discrete Mathematics 29, no. 3 (2023): 503–24. http://dx.doi.org/10.7546/nntdm.2023.29.3.503-524.

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4

Rihane, S. E. "On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers." Carpathian Mathematical Publications 13, no. 1 (2021): 259–71. http://dx.doi.org/10.15330/cmp.13.1.259-271.

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The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is called a Lucas-balancing number. For an integer $k\geq 2$, let $(F_n^{(k)})_n$ be the $k$-generalized Fibonacci sequence which starts with $0,\ldots,0,1,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. The purpose of this paper is to show that 1, 6930 are the only balancing numbers and 1, 3 are the only Lucas-bala

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5

Costa, Eudes Antonio, Elen Viviani Pereira Spreafico, and Paula Maria Machado Cruz Catarino. "A note on the generalized bi-periodic Lucas-balancing numbers." BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS 6 (June 16, 2025): 1–15. https://doi.org/10.14393/bejom-v6-2025-75273.

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In this study, we introduce a new class of integers called the sequence of generalized bi-periodic Lucas-balancing numbers, which extends the well-known sequence of Lucas-balancing numbers. We present several fundamental properties, including the deduction of the corresponding generating function, as well as homogeneous and non-homogeneous recurrence relations associated with this new sequence. We also formulate generalized versions of Binet's formulas for these numbers. In addition, we investigated the validity of several classical identities within this new context, such as the Tagiuri-Vajda

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6

Nikiema, Salifou, and Japhet Odjoumani. "Lucas generalized numbers in Narayana's cows sequence." Gulf Journal of Mathematics 15, no. 1 (2023): 84–92. http://dx.doi.org/10.56947/gjom.v15i1.1381.

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Let {Nn}n≥0 be the Narayana's cows sequence given by N0 = 0, N1 = N2 = 1 and Nn+3 = Nn+2 + Nn, for integers n ≥ 0 and let {Un}n ≥ 0 be the generalized Lucas sequence with parameters integers a ≥1, b =±1 given by U0 = 0, U1 = 1 and Un+2 = aUn+1 + bUn, for integers n ≥ 0. In this paper we give effective bounds for the Diophantine equation Nm =Un, in positive unknowns m and n. We then solve explicitly that equation with Fibonacci, Pell and Balancing sequences cases.

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7

Yılmaz, Nazmiye, Esra Kırmızı Çetinalp, and Ömür Deveci. "The quaternion-type cyclic-balancing sequence in groups." Notes on Number Theory and Discrete Mathematics 31, no. 2 (2025): 201–10. https://doi.org/10.7546/nntdm.2025.31.2.201-210.

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In this research, several types of definitions of the quaternion-type cyclic-balancing sequence are presented. The Cassini formula and generating function of these sequences are also obtained for all types. The quaternion-type cyclic-balancing sequences modulo m, the first step to transferring this topic to group theory, are examined. These sequences in finite groups are then defined. Eventually, the lengths of periods for these sequences of the generalized quaternion group are calculated.

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8

Chung, Chan-Liang, and Chunmei Zhong. "Melham’s sums for some Lucas polynomial sequences." Notes on Number Theory and Discrete Mathematics 30, no. 2 (2024): 383–409. http://dx.doi.org/10.7546/nntdm.2024.30.2.383-409.

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A Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials. We define the (a,b)-type Lucas polynomial sequences and prove that their Melham’s sums have some interesting divisibility properties. Results in this paper generalize the original Melham’s conjectures.

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9

Dou, Jianping, Jun Li, and Xia Zhao. "A novel discrete particle swarm algorithm for assembly line balancing problems." Assembly Automation 37, no. 4 (2017): 452–63. http://dx.doi.org/10.1108/aa-08-2016-104.

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Purpose The purpose of this paper is to develop a feasible sequence-oriented new discrete particle swarm optimization (NDPSO) algorithm with novel particles’ updating mechanism for solving simple assembly line balancing problems (SALBPs). Design/methodology/approach In the NDPSO, a task-oriented representation is adopted to solve type I and type II SALBPs, and a particle directly represents a feasible task sequence (FTS) as a permutation. Then, the particle (permutation) is updated as a whole using the geometric crossover based on the edit distance with swaps for two permutations. Furthermore,

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10

Siton, Yarden, and Alon Kuperman. "Generalization of Split DC Link Voltages Behavior in Three-Phase-Level Converters Operating with Arbitrary Power Factor with Restricted Zero-Sequence Component." Electronics 12, no. 19 (2023): 4063. http://dx.doi.org/10.3390/electronics12194063.

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This article examines the impact of a power factor on the behavior of partial DC link voltages in three-phase three-level AC/DC (or DC/AC) converters operating without additional balancing hardware. We consider the case in which the controller utilizes a bandwidth-restricted (DC in steady state) zero-sequence component to achieve average partial DC link voltage equalization since the injection of high-order zero-sequence components is impossible or forbidden. An assessment of partial split DC-link capacitor voltage behavior (particularly that of ripple magnitudes and phases) is necessary for,

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11

VLASENKO, Valentyn. "FORMATION AND IMPLEMENTATION OF AN EFFECTIVE CASH FLOW MANAGEMENT PROCESS AT SMALL AND MEDIUM-SIZED BUSINESS ENTERPRISES UNDER CONDITIONS OF ECONOMIC REVIVAL." MODELING THE DEVELOPMENT OF THE ECONOMIC SYSTEMS, no. 4 (November 28, 2024): 312–19. https://doi.org/10.31891/mdes/2024-14-41.

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The methodological and applied principles of formation and implementation of an effective cash flow management process at small and medium-sized business enterprises under conditions of economic recovery are substantiated. The author's interpretation of the category content of «enterprise cash flow management process» is proposed as a set of financial measures to implement the operational, financial and investment activities of enterprise with the aim of forming a sufficient amount of cash and other means of payment, which involves planning and forecasting, organizing the receipt and movement

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12

Katerna, Olga, Nina Avanesova, Olha Hetman, Nadiia Antypenko, and Hanna Krivoruchko. "SUBSTANTIATION OF MANAGEMENT INNOVATIONS IN THE PROCESSES OF CREATION OF PROJECT VALUES AT ENTERPRISES." Economics and Finance 9, no. 3 (2021): 34–51. http://dx.doi.org/10.51586/2311-3413.2021.9.3.34.51.

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The project value management model proposed in the work reveals a certain sequence of actions and tools for identifying, balancing, creating, checking relevance, and tracking the long-term consequences of using the project value, largely solves unresolved theoretical issues, provides not only the formation of conditions for ensuring the project value in all its manifestations and for a wide range of stakeholders but also tracking of the long-term results and creation of a knowledge base in the post-project period, which increases the efficiency of the project activities of the company and its

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13

Chailangka, Natdanai, and Apisit Pakapongpun. "On the generalization neo balancing sequence and some applications." Journal of Applied Research on Science and Technology (JARST), March 4, 2025. https://doi.org/10.60101/jarst.2024.257946.

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We investigate the generalization of sequence neo balancing numbers and their recurrence relations by extending the catalyst of certain sequences in balancing numbers to any integer k in the sequence neo balancing numbers. We derive the Diophantine equation for sequence neo balancing numbers in terms of k, which corresponds to the Diophantine equation for neo balancing numbers. We derive the Diophantine equation for the sequence neo balancing numbers and solve it via Pell's equation and Brahmagupta's identity. We examine the square root term in the derived Diophantine equation for the sequence

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14

Sriram, S. "A Note on Neo Balancing Sequence, Generalized Recursive Sequences and Pythagorean Triples." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 08 (2022). http://dx.doi.org/10.47191/ijmcr/v10i8.05.

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We proved theorems about creating Pythagorean Triples from generalized recursive sequences in this study. Pythagorean triples are a very old concept that has made significant progress in recent mathematical studies. Pythagorean triples can be generated using Neo balancing sequences and generalized recursive sequences, and vice-versa. For greater understanding, a general procedure is presented with appropriate illustrations.

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15

Soykan, Y¨uksel. "A Study on Generalized Balancing Numbers." Asian Journal of Advanced Research and Reports, September 7, 2021, 78–100. http://dx.doi.org/10.9734/ajarr/2021/v15i530401.

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In this paper, we investigate properties of the generalized balancing sequence and we deal with, in detail, namely, balancing, modified Lucas-balancing and Lucas-balancing sequences. We present Binet’s formulas, generating functions and Simson formulas for these sequences. We also present sum formulas of these sequences. We provide the proofs to indicate how the sum formulas, in general, were discovered. Of course, all the listed sum formulas may be proved by induction, but that method of proof gives no clue about their discovery. Moreover, we consider generalized balancing sequence at negativ

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16

Adédji, Kouèssi Norbert, Roméo Jésugnon Adjakidjè, and Alain Togbé. "Mulatu Numbers as Products of Three Generalized Lucas Numbers." Mathematica Pannonica, September 26, 2024. http://dx.doi.org/10.1556/314.2024.00014.

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Let 𝑀𝑘 be the 𝑘-th Mulatu number. Let 𝑟, 𝑠 be non-zero integers with 𝑟 ≥ 1 and 𝑠 ∈ {−1, 1}, let {𝑈𝑛}𝑛≥0 be the generalized Lucas sequence and {𝑉𝑛}𝑛≥0 its companion given respectively by 𝑈𝑛+2 = 𝑟𝑈𝑛+1 + 𝑠𝑈𝑛 and 𝑉𝑛+2 = 𝑟𝑉𝑛+1 + 𝑠𝑉𝑛, with 𝑈0 = 0, 𝑈1 = 1, 𝑉0 = 2, 𝑉1 = 𝑟. In this paper, we give effective bounds for the solutions of the following Diophantine equations 𝑀𝑘 = 𝑈𝓁𝑈𝑚𝑈𝑛 and 𝑀𝑘 = 𝑉𝓁𝑉𝑚𝑉𝑛, where 𝓁, 𝑚, 𝑛 and 𝑘 are nonnegative integers and 𝓁 ≤ 𝑚 ≤ 𝑛. Then, we explicitly solve the above Diophantine equations for the Fibonacci, Pell, Balancing sequences and their companions respectively.

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17

Aziz, Shahkaar, Muhammad Waqas, Sobia Ahsan Halim, et al. "Exploring whole proteome to contrive multi-epitope-based vaccine for NeoCoV: An immunoinformtics and in-silico approach." Frontiers in Immunology 13 (August 3, 2022). http://dx.doi.org/10.3389/fimmu.2022.956776.

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Neo-Coronavirus (NeoCoV) is a novel Betacoronavirus (β-CoVs or Beta-CoVs) discovered in bat specimens in South Africa during 2011. The viral sequence is highly similar to Middle East Respiratory Syndrome, particularly that of structural proteins. Thus, scientists have emphasized the threat posed by NeoCoV associated with human angiotensin-converting enzyme 2 (ACE2) usage, which could lead to a high death rate and faster transmission rate in humans. The development of a NeoCoV vaccine could provide a promising option for the future control of the virus in case of human infection. In silico pred

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18

Li, Kaixing, Yanbin Li, Saifan Gong, Jing Tong, Yonggang Liu, and Wujiao Xu. "Numerical investigation on meshing temperature of multicomponent nylon gears by incorporating viscoelasticity." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, March 16, 2023, 146442072311609. http://dx.doi.org/10.1177/14644207231160907.

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This study concerns a numerical analysis of the meshing temperature for a multicomponent nylon gear by incorporating typical viscoelastic responses of polymers. Firstly, the generalized Maxwell model parameters were calibrated by the dynamic mechanical analysis to capture the viscoelasticity of polyamide 66. Next, the finite element model predicting the meshing temperature was established, including the heat generation analysis model, which calculates the generation of the frictional and hysteretic heat, and the heat propagation analysis model, which simulates the heat transmission. Different

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19

Subramanian, Vasantharaj, and Indragandhi Vairavasundaram. "Comparative analysis of dual second-order generalized integrator-phase locked loop based series hybrid filter and static synchronous compensator for load voltage compensation and power quality improvement with grid synchronization in islanded microgrid." Circuit World, June 7, 2022. http://dx.doi.org/10.1108/cw-05-2021-0157.

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Purpose The purpose of this study is to eliminate voltage harmonics and instantly measure the positive sequence fundamental voltage during unbalanced grid conditions, the dual second-order generalized integrator-phase locked loop used in series hybrid filter structures is often used in grid synchronisation in three-phase networks. The preferred series active hybrid power filter simultaneously compensates for voltage balancing and current harmonics generated by non-linear loads. Design/methodology/approach This paper examines the use of renewable energy–based microgrid (MG) to support linear an

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20

Ruan, Shengfeng, and Christina R. Bourne. "Escherichia coli cells evade inducible parE toxin expression by reducing plasmid copy number." Microbiology Spectrum, May 3, 2024. http://dx.doi.org/10.1128/spectrum.03973-23.

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ABSTRACT Plasmids play important roles in microbial ecosystems, serving as carriers of antibiotic resistance and virulence. In the laboratory, they are essential tools for genetic manipulation and recombinant protein expression. We uncovered an intriguing survival phenotype in a fraction of the bacterial population while using plasmid-mediated arabinose-inducible gene expression to monitor the production of toxic ParE proteins. This phenotype was not correlated with changes to the plasmid sequence and could not be rescued by increasing arabinose uptake. Instead, survival correlates with a mark

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21

Zhang, Boyang, Shili Lin, Luis Moraes, et al. "Methane prediction equations including genera of rumen bacteria as predictor variables improve prediction accuracy." Scientific Reports 13, no. 1 (2023). http://dx.doi.org/10.1038/s41598-023-48449-y.

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AbstractMethane (CH4) emissions from ruminants are of a significant environmental concern, necessitating accurate prediction for emission inventories. Existing models rely solely on dietary and host animal-related data, ignoring the predicting power of rumen microbiota, the source of CH4. To address this limitation, we developed novel CH4 prediction models incorporating rumen microbes as predictors, alongside animal- and feed-related predictors using four statistical/machine learning (ML) methods. These include random forest combined with boosting (RF-B), least absolute shrinkage and selection

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