Relevant bibliographies by topics / Generalized Neo Balancing Sequence

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Academic literature on the topic 'Generalized Neo Balancing Sequence'

Author: Grafiati
Published: 5 June 2025
Last updated: 24 June 2025

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Journal articles on the topic "Generalized Neo Balancing Sequence"

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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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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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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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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-balancing numbers which are a term of $k$-generalized Fibonacci sequence. This generalizes the result from [Fibonacci Quart. 2004, 42 (4), 330-340].
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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, d'Ocagne, Catalan, and Cassini identities, considering the two different cases of the discriminant value of the equation polynomial associated with the recurrence relation. These extensions contribute to a structural and algebraic deepening of the properties of Lucas-balancing numbers.
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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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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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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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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, the fragment mutation with adaptive mutation probability is incorporated into the NDPSO to improve exploration ability. Findings Case study illustrates the effectiveness of the NDPSO. Comparative results between the NDPSO and existing real-encoded PSO (CPSO) and direct discrete PSO (DDPSO) against benchmark instances of type I SALBP and type II SALBP show promising higher performance of the proposed NDPSO. Originality/value A novel particles’ updating mechanism for FTS-encoded particle is proposed to solve the SALBPs. The comparative results indicate that updating of FTS as a whole seems superior to existing updating of FTS by fragment with respect to exploration ability for solving SALBPs. The novel particles’ updating mechanism is also applicable to generalized assembly line balancing problems.
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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, e.g., minimizing the values of DC link capacitances and selecting reference voltage values. Previous studies assessed the abovementioned behavior analytically for operation under a unity power factor based on third-harmonic-dominated split partial voltages’ ripple nature. However, it is shown here that deviation from the unity power factor introduces additional (to the third harmonic) non-negligible harmonic content, increasing partial voltage ripple magnitudes and shifting their phase (relative to the mains voltages). As a result, the third-harmonic-only assumption is no longer valid, and it is then nearly impossible to derive corresponding analytical expressions. Consequently, a numerical approach is used in this work to derive a generalized expression of normalized ripple energy as a function of the power factor, which can then easily be utilized for assessments of split DC link voltage behaviors for certain DC link capacitances and reference voltages. Simulations and experimental results validate the proposed methodology applied to a 10 kVA T-type converter prototype.
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Book chapters on the topic "Generalized Neo Balancing Sequence"

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Michie, D., and R. Camacho. "Building Symbolic Representations of Intuitive Real-time Skills from Performance Data." In Machine Intelligence 13. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198538509.003.0015.

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Abstract Real-time control skills are ordinarily tacit—their possessors cannot explicitly communicate them. But given sufficient sampling of a trained expert’s input—output behaviour, machine learning programs have been found capable of constructing rules which, when run as programs, deliver behaviours similar to those of the original exemplars. These ‘clones’ are in effect symbolic representations of subcognitive behaviours. After validation on simple pole-balancing tasks, the principles have been successfully generalized in flight-simulator experiments, both by Sammut and others at UNSW, and by Camacho at the Turing Institute and Oxford. A flight plan switches control through a sequence of logically concurrent sets of reactive behaviours. Each set can be thought of as a committee of subpilots who are respectively specialized for rudder, elevators, rollers, thrust, etc. The chairman (the flight plan) knows only the mission sequence, and how to recognize the onset of each stage. This treatment is essentially that of the ‘blackboard model’, augmented by machine learning to extract subpilot behaviours (seventy-two behaviours in Camacho’s auto-pilot for a simulated F–16 combat plane). A ‘clean-up’ effect, first noted in the polebalancing phase of this enquiry, results in auto-pilots which fly the F–16 under tighter control than the human from whom the behavioural records were sampled.
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Conference papers on the topic "Generalized Neo Balancing Sequence"

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Han, L. H., and T. J. Lu. "Mechanical Properties Measurement of Electroactive Polymers." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58115.

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Electroactive polymers (EAPs), such as piezoelectric polymer, polyelectrolyte gels, dielectric elastomer and conducting polymer etc., are emerging as a new type of actuation materials for a broad range of actuator and transducer applications, because of their higher strain, higher response and higher efficiency. Acrylic elastomer films have demonstrated higher specific energy density (0.4J/g) and more than 100% actuated strains, and have been recommended for the artificial muscle actuators. Much research has been carried out to investigate the actuation properties of EAP films, however, little information is available for the mechanical properties of EAP films, which are crucial for designing EAP actuators. This work focuses on developing a means of characterizing the mechanical properties of EAP thin film materials, describing the mechanical behavior with the suitable constitutive models and determining the material parameters for the development of actuators. To measure the mechanical properties of EAP films, a uniaxial testing system is developed, which consists of a small-scale force transducer, a CCD camera, a National Instruments card and a laser displacement transducer. The loading and unloading cycles on film specimens are controlled by an Instron Machine. The applied force and the total are stored in the computer by the National Instrument card. A sequence of 2D images are recorded by the CCD camera to capture the deformation process of the film sample. Then, the displacements of the marks on the film surface vertical to the thickness plane are calculated from the sequential images by image analysis techniques. There are several well-known models available to describe the mechanical behaviors of the EAP films, such as Neo-Hookean, Mooney-Rivlin and Ogden models etc. To determine the most suitable constitutive models and corresponding material constants, a generalized method based on finite element analysis is proposed and implemented by interfacing with ABAQUS finite element package. The kernel of the method is to minimize the difference between the measured displacement field and the computed displacement field. A global optimisation algorithm, simulated annealing (SA), is used to minimize the objective. The experimental investigation on the mechanical properties of the dielectric elastomer film (VHB4910) is presented as an example to demonstrate the functions of the testing system and the developed method. The developed testing system and method can also be used for characterizing the mechanical properties of other EAP film materials.
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