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Relevant bibliographies by topics / Bell polynomial

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Academic literature on the topic 'Bell polynomial'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Bell polynomial"

1

Kim, Dae San, Taekyun Kim, Hyekyung Kim та Jongkyum Kwon. "Some Identities on λ-Analogues of Lah Numbers and Lah-Bell Polynomials". European Journal of Pure and Applied Mathematics 17, № 3 (2024): 1385–402. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5288.

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In recent years, some applications of Lah numbers were discovered in the real world problem of telecommunications and optics. The aim of this paper is to study the λ-analogues of Lah numbers and Lah-Bell polynomials which are λ-analogues of the Lah numbers and and Lah-Bell polynomials. Here we note that λ-analogues appear when we replace the falling factorials by the generalized falling factorials in the defining equations. By using generating function method, we study some properties, explicit expressions, generating functions and Dobinski-like formulas for those numbers and polynomials. We a

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Bretti, Gabriella, Pierpaolo Natalini, and Paolo Emilio Ricci. "A new set of Sheffer–Bell polynomials and logarithmic numbers." Georgian Mathematical Journal 26, no. 3 (2019): 367–79. http://dx.doi.org/10.1515/gmj-2019-2007.

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Abstract In a recent paper, we have introduced new sets of Sheffer and Brenke polynomial sequences based on higher order Bell numbers. In this paper, by using a more compact notation, we show another family of exponential polynomials belonging to the Sheffer class, called, for shortness, Sheffer–Bell polynomials. Furthermore, we introduce a set of logarithmic numbers, which are the counterpart of Bell numbers and their extensions.

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Natalini, Pierpaolo, and Paolo Ricci. "New Bell–Sheffer Polynomial Sets." Axioms 7, no. 4 (2018): 71. http://dx.doi.org/10.3390/axioms7040071.

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In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results by Dattoli and Ben Cheikh on the monomiality principle, showing the possibility to derive explicitly the main properties of Sheffer polynomial families starting from the basic elements of their generating functions. The introduction of iterated exponential and logarithmic functions allows to construct new sets of Bell–Sheffer polynomia

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Chai, Xue-Dong, and Chun-Xia Li. "The integrability of the coupled Ramani equation with binary Bell polynomials." Modern Physics Letters B 34, no. 32 (2020): 2050371. http://dx.doi.org/10.1142/s0217984920503716.

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Binary Bell polynomial approach is applied to study the coupled Ramani equation, which is the generalization of the Ramani equation. Based on the concept of scale invariance, the coupled Ramani equation is written in terms of binary Bell polynomials of two dimensionless field variables, which leads to the bilinear coupled Ramani equation directly. As a consequence, the bilinear Bäcklund transformation, Lax pair and conservation laws are systematically constructed by virtue of binary Bell polynomials.

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Ramírez, W., C. Cesarano, S. Wani, S. Yousuf, and D. Bedoya. "About properties and the monomiality principle of Bell-based Apostol-Bernoulli-type polynomials." Carpathian Mathematical Publications 16, no. 2 (2024): 379–90. http://dx.doi.org/10.15330/cmp.16.2.379-390.

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This article investigates the properties and monomiality principle within Bell-based Apostol-Bernoulli-type polynomials. Beginning with the establishment of a generating function, the study proceeds to derive explicit expressions for these polynomials, providing insight into their structural characteristics. Summation formulae are then derived, facilitating efficient computation and manipulation. Implicit formulae are also examined, revealing underlying patterns and relationships. Through the lens of the monomiality principle, connections between various polynomial aspects are elucidated, unco

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Thiyam, Bhaktaraj, and Md Indraman Khan. "Analytical Insights into the Modified Fractional Bell Polynomial with Mittag-Leffler Parameter." International Journal of Research in Science and Technology 14, no. 2 (2024): 1–12. http://dx.doi.org/10.37648/ijrst.v14i02.001.

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In this paper, we will define the Modified Fractional Bell Polynomial by incorporating the Mittag Leffler function of one parameter. The Existence and convergence of the Modified Fractional Bell Polynomial will be established by extending the classical results of Bell Polynomial and Mittag Leffler function of one parameter in the fractional calculus. Additionally, we explore the inverse of the Modified Fractional Bell Polynomial, providing a step-by-step proof of its existence. This result enhances the applicability of the polynomial by allowing a unique mapping from each output to a set of in

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Kim, Byung Moon, Taekyun Kim, Jin-Woo Park та Taha Ali Radwan. "Identities on Changhee Polynomials Arising from λ -Sheffer Sequences". Complexity 2022 (7 червня 2022): 1–16. http://dx.doi.org/10.1155/2022/5868689.

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In this paper, authors found a new and interesting identity between Changhee polynomials and some degenerate polynomials such as degenerate Bernoulli polynomials of the first and second kind, degenerate Euler polynomials, degenerate Daehee polynomials, degenerate Bell polynomials, degenerate Lah–Bell polynomials, and degenerate Frobenius–Euler polynomials and Mittag–Leffer polynomials by using λ -Sheffer sequences and λ -differential operators to find the coefficient polynomial when expressing the n -th Changhee polynomials as a linear combination of those degenerate polynomials. In addition,

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Pathan, M. A., Hemant Kumar, Taekyun Kim, and J. Lopez-Bonilla. "ON THE CHARACTERISTIC POLYNOMIAL OF CHEBYSHEV MATRICES." jnanabha 53, no. 02 (2023): 145–50. http://dx.doi.org/10.58250/jnanabha.2023.53217.

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We exhibit that the coeficients of the characteristic polynomial of any matrix Anxn can be written in terms of the complete Bell polynomials, and this result is applied to Chebyshev matrices which generates the concept of Associated Polynomials of Chebyshev.

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He, Tian-Xiao, and José L. Ramírez. "The dual of number sequences, Riordan polynomials, and Sheffer polynomials." Special Matrices 10, no. 1 (2021): 153–65. http://dx.doi.org/10.1515/spma-2021-0153.

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Abstract In this paper we introduce different families of numerical and polynomial sequences by using Riordan pseudo involutions and Sheffer polynomial sequences. Many examples are given including dual of Hermite numbers and polynomials, dual of Bell numbers and polynomials, among other. The coefficients of some of these polynomials are related to the counting of different families of set partitions and permutations. We also studied the dual of Catalan numbers and dual of Fuss-Catalan numbers, giving several combinatorial identities.

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Czyżycki, Tomasz, Jiří Hrivnák, and Jiří Patera. "Generating Functions for Orthogonal Polynomials of A2, C2 and G2." Symmetry 10, no. 8 (2018): 354. http://dx.doi.org/10.3390/sym10080354.

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The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical uni

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Book chapters on the topic "Bell polynomial"

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Campbell, Geoffrey B. "Determinants, Bell Polynomial Expansions for Vector Partitions." In Vector Partitions, Visible Points and Ramanujan Functions. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003174158-31.

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Schimming, R., and S. Z. Rida. "The Bell Differential Polynomials." In Applications of Fibonacci Numbers. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5020-0_40.

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Natalini, Pierpaolo, Sandra Pinelas, and Paolo Emilio Ricci. "General Sets of Bell-Sheffer and Log-Sheffer Polynomials." In Differential and Difference Equations with Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_42.

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Birmajer, Daniel, Juan B. Gil, Peter R. W. McNamara, and Michael D. Weiner. "Enumeration of Colored Dyck Paths Via Partial Bell Polynomials." In Lattice Path Combinatorics and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11102-1_8.

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Novaes, Douglas D. "An Equivalent Formulation of the Averaged Functions via Bell Polynomials." In Trends in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55642-0_25.

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Atkins, Peter, Julio de Paula, and James Keeler. "Vibrational motion." In Atkins’ Physical Chemistry. Oxford University Press, 2022. http://dx.doi.org/10.1093/hesc/9780198847816.003.0037.

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This chapter focuses on molecular vibration, which plays a role in the interpretation of thermodynamic properties. It introduces the ‘harmonic oscillator’, a simple but very important model for the description of vibrations. The chapter shows that the energies of an oscillator are quantized and that an oscillator may be found at displacements that are forbidden by classical physics. The energy levels of a quantum mechanical harmonic oscillator are evenly spaced. The chapter then explains how the wavefunctions of a quantum mechanical harmonic oscillator are products of a Hermite polynomial and

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Censor, Yair, and Stavros A. Zenios. "Decompositions in Interior Point Algorithms." In Parallel Optimization. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195100624.003.0008.

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Abstract In 1984 N. Karmarkar of AT&T Bell Laboratories introduced an interior point algorithm for linear programming. The algorithm has a polynomial time complexity bound and has been established, following extensive computational experimentation, as a viable competitor to the classic simplex algorithm for the solution of large-scale linear programs. A flurry of re search activities followed Karmarkar’s work and several interior point algorithms were developed for linear programming, convex quadratic programming, convex programming, linear complementarity problems, and nonlinear complemen

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"Bell polynomials." In Special Matrices of Mathematical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799838_0013.

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Mező, István. "The Bell polynomials." In Combinatorics and Number Theory of Counting Sequences. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9781315122656-3.

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Conference papers on the topic "Bell polynomial"

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Khan, Waseem Ahmad, Samir El-Nakla, and Daniel Bedoya. "Evaluate properties of Bell-based Frobenius-Sigmoid polynomials and applications in computer modeling." In 2024 6th International Symposium on Advanced Electrical and Communication Technologies (ISAECT). IEEE, 2024. https://doi.org/10.1109/isaect64333.2024.10799529.

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Mishra, Sumit, Sanjay Moulik, and Ved Prakash. "Invalid Scenarios of External Cluster Validity Indices: An Analysis Using Bell Polynomial." In 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2021. http://dx.doi.org/10.1109/smc52423.2021.9659242.

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Nohutcu, Gökçe Yıldız, and Kübra Erdem Biçer. "Bell Collocation Method to Solve High Order Fredholm-Volterra Integro Differential Equations." In 8th International Students Science Congress. ULUSLARARASI ÖĞRENCİ DERNEKLERİ FEDERASYONU (UDEF), 2024. https://doi.org/10.52460/issc.2024.035.

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In this study, a new numerical method has been developed to solve high-order Fredholm-Volterra integro-differential equations under mixed conditions. In this method, Bell polynomials, their derivatives, and collocation points are used to transform the problem into a matrix equation system. When this equation system is solved, approximate solutions are obtained in the form of a truncated Bell series. To demonstrate the reliability and applicability of the numerical method, some numerical examples are provided. These examples are further analyzed based on the residual error function, and the res

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Wang, Dan, Shu-Li Liu, Yong Geng, and Xiao-Li Wang. "Exact solutions of a generalized (2+1)-dimensional soliton equation via Bell polynomials." In 2021 40th Chinese Control Conference (CCC). IEEE, 2021. http://dx.doi.org/10.23919/ccc52363.2021.9550677.

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Alnajar, Omar, and Maslina Darus. "Coefficient estimates for subclasses of bi-univalent functions related to Gegenbauer polynomials and an application of bell distribution." In 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS5). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0228336.

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Sahib, Eman Ahmed Abdul, Enass H. Flaieh, and Ali Abdulabbas Gatea Alkhafaji. "Data-driven approach for predicting remaining useful life of belt-conveyor systems using polynomial curve fitting model." In 4TH INTERNATIONAL CONFERENCE ON INNOVATION IN IOT, ROBOTICS AND AUTOMATION (IIRA 4.0). AIP Publishing, 2025. https://doi.org/10.1063/5.0254220.

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Westrom, Clyde, Rachel Tanczos, Kevin Adanty, and Sean Shimada. "Predicting Head Injury Criterion in Real-World Frontal Impacts." In WCX SAE World Congress Experience. SAE International, 2025. https://doi.org/10.4271/2025-01-8709.

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<div class="section abstract"><div class="htmlview paragraph">Research on modeling head injury metrics and head acceleration waveforms from real-world collisions has been limited compared to vehicle crash pulses. Prior studies have used rectangular, triangular, polynomial, half-sine, and haversine pulse functions to model vehicle crash pulses and have employed more complex approximations for head injury metrics. This study aimed to develop a method to predict 15 ms Head Injury Criterion (HIC<sub>15</sub>) in frontal passenger vehicle impacts using these simple pulse fun

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