Log in

Relevant bibliographies by topics / Faa di Bruno formula / Journal articles

To see the other types of publications on this topic, follow the link: Faa di Bruno formula.

Journal articles on the topic 'Faa di Bruno formula'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 32 journal articles for your research on the topic 'Faa di Bruno formula.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Mishkov, Rumen L. "Generalization of the formula of Faa di Bruno for a composite function with a vector argument." International Journal of Mathematics and Mathematical Sciences 24, no. 7 (2000): 481–91. http://dx.doi.org/10.1155/s0161171200002970.

Full text

Abstract:

The paper presents a new explicit formula for thenth total derivative of a composite function with a vector argument. The well-known formula of Faa di Bruno gives an expression for thenth derivative of a composite function with a scalar argument. The formula proposed represents a straightforward generalization of Faa di Bruno's formula and gives an explicit expression for thenth total derivative of a composite function when the argument is a vector with an arbitrary number of components. In this sense, the formula of Faa di Bruno is its special case. The mathematical tools used include differential operators, polynomials, and Diophantine equations. An example is shown for illustration.

APA, Harvard, Vancouver, ISO, and other styles

2

Constantine, G. M., and T. H. Savits. "A Multivariate Faa di Bruno Formula with Applications." Transactions of the American Mathematical Society 348, no. 2 (1996): 503–20. http://dx.doi.org/10.1090/s0002-9947-96-01501-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Shabat, Alexey Borisovich, and Magomed Khochalaevich Efendiev. "On applications of Faà-di-Bruno formula." Ufimskii Matematicheskii Zhurnal 9, no. 3 (2017): 131–36. http://dx.doi.org/10.13108/2017-9-3-131.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Sarsengeldin, Merey, and Stanislav Kharina. "Method of the integral error functions for the solution of the one- and two-phase Stefan problems and its application." Filomat 31, no. 4 (2017): 1017–29. http://dx.doi.org/10.2298/fil1704017s.

Full text

Abstract:

The analytical solutions of the one- and two-phase Stefan problems are found in the form of series containing linear combinations of the integral error functions which satisfy a priori the heat equation. The unknown coefficients are defined from the initial and boundary conditions by the comparison of the like power terms of the series using the Faa di Bruno formula. The convergence of the series for the temperature and for the free boundary is proved. The approximate solution is found using the replacement of series by the corresponding finite sums and the collocation method. The presented test examples confirm a good approximation of such approach. This method is applied for the solution of the Stefan problem describing the dynamics of the interaction of the electrical arc with electrodes and corresponding erosion.

APA, Harvard, Vancouver, ISO, and other styles

5

Savits, Thomas H. "Some statistical applications of Faa di Bruno." Journal of Multivariate Analysis 97, no. 10 (November 2006): 2131–40. http://dx.doi.org/10.1016/j.jmva.2006.03.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Gzyl, Henryk. "Multidimensional extension of Faa di Bruno's formula." Journal of Mathematical Analysis and Applications 116, no. 2 (June 1986): 450–55. http://dx.doi.org/10.1016/s0022-247x(86)80009-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Mortini, Raymond. "The Fàa di Bruno formula revisited." Elemente der Mathematik 68, no. 1 (2013): 33–38. http://dx.doi.org/10.4171/em/216.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Johnson, Warren P. "The Curious History of Faa di Bruno's Formula." American Mathematical Monthly 109, no. 3 (March 2002): 217. http://dx.doi.org/10.2307/2695352.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Abel, Ulrich. "A new Faà di Bruno type formula." Elemente der Mathematik 70, no. 2 (2015): 49–54. http://dx.doi.org/10.4171/em/274.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Wenchang *, Chu. "The Faà di Bruno formula and determinant identities." Linear and Multilinear Algebra 54, no. 1 (January 2006): 1–25. http://dx.doi.org/10.1080/03081080412331281005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Jha, Sumit Kumar. "A formula for the number of non-negative integer solutions of a1x1 + a2x2 + ··· + amxm = n in terms of the partial Bell polynomials." Notes on Number Theory and Discrete Mathematics 27, no. 2 (June 2021): 64–69. http://dx.doi.org/10.7546/nntdm.2021.27.2.64-69.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Dawid, A. P., S. Kotz, N. L. Johnson, and C. B. Read. "Encyclopedia of Statistical Sciences, Vol. 3. Faa di Bruno's Formula- Hypothesis Testing." Biometrics 41, no. 1 (March 1985): 341. http://dx.doi.org/10.2307/2530670.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Corcino, Roberto Bagsarsa, Charles Montero, Maribeth Montero, and Jay Ontolan. "The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers." European Journal of Pure and Applied Mathematics 12, no. 3 (July 25, 2019): 1122–37. http://dx.doi.org/10.29020/nybg.ejpam.v12i3.3494.

Full text

Abstract:

This paper derives another form of explicit formula for $(r,\beta)$-Bell numbers using the Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms of the $r$-Whitney numbers of the second kind and the ordinary Lah numbers. As a consequence, a relation between $(r,\beta)$-Bell numbers and the sums of row entries of the product of two matrices containing the $r$-Whitney numbers of the second kind and the ordinary Lah numbers is established. Moreover, a $q$-analogue of the explicit formula is obtained.

APA, Harvard, Vancouver, ISO, and other styles

14

BULTEL, JEAN-PAUL. "A ONE-PARAMETER DEFORMATION OF THE NONCOMMUTATIVE LAGRANGE INVERSION FORMULA." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1395–414. http://dx.doi.org/10.1142/s0218196711006662.

Full text

Abstract:

We give a one-parameter deformation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder–Frabetti–Krattenthaler for the antipode of the noncommutative Faá di Bruno algebra. Namely, we obtain a closed formula for the antipode of the one-parameter deformation of this Hopf algebra discovered by Foissy.

APA, Harvard, Vancouver, ISO, and other styles

15

Qi, Feng. "Simplifying coefficients in a family of nonlinear ordinary differential equations." Acta et Commentationes Universitatis Tartuensis de Mathematica 22, no. 2 (January 2, 2019): 293–97. http://dx.doi.org/10.12697/acutm.2018.22.24.

Full text

Abstract:

By virtue of the Faá di Bruno formula, properties of the Stirling numbers and the Bell polynomials of the second kind, the binomial inversion formula, and other techniques in combinatorial analysis, the author finds a simple, meaningful, and signicant expression for coefficients in a family of nonlinear ordinary differential equations.

APA, Harvard, Vancouver, ISO, and other styles

16

Qi, Feng. "Simple forms for coefficients in two families of ordinary differential equations." Global Journal of Mathematical Analysis 6, no. 1 (March 30, 2018): 7. http://dx.doi.org/10.14419/gjma.v6i1.9778.

Full text

Abstract:

In the paper, by virtue of the Faá di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion formula for the Stirling numbers of the first and second kinds, the author finds simple, meaningful, and significant forms for coefficients in two families of ordinary differential equations.

APA, Harvard, Vancouver, ISO, and other styles

17

FERGER, Dietmar. "Moment equalities for sums of random variables via integer partitions and Faa di Bruno's formula." TURKISH JOURNAL OF MATHEMATICS 38 (2014): 558–75. http://dx.doi.org/10.3906/mat-1301-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Wang, Yan, Muhammet Cihat Dağli, Xi-Min Liu, and Feng Qi. "Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials." Axioms 10, no. 1 (March 18, 2021): 37. http://dx.doi.org/10.3390/axioms10010037.

Full text

Abstract:

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

APA, Harvard, Vancouver, ISO, and other styles

19

Qi, Feng. "Simplifying coefficients in differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials." Boletim da Sociedade Paranaense de Matemática 39, no. 4 (January 1, 2021): 73–82. http://dx.doi.org/10.5269/bspm.41758.

Full text

Abstract:

In the paper, by virtue of the Fa\'a di Bruno formula and identities for the Bell polynomials of the second kind, the author simplifies coefficients in a family of ordinary differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials.

APA, Harvard, Vancouver, ISO, and other styles

20

Xia, Yuxuan, and Zhenyu Cui. "An exact and explicit implied volatility inversion formula." International Journal of Financial Engineering 05, no. 03 (September 2018): 1850032. http://dx.doi.org/10.1142/s2424786318500329.

Full text

Abstract:

In this paper, we develop an exact and explicit (model-independent) Taylor series representation of the implied volatility based on the novel applications of an extended Faà di Bruno formula under the operator calculus setting, and the Lagrange inversion theorem. We rigorously establish that our formula converges to the true implied volatility as the truncation order increases. Numerical examples illustrate the remarkable accuracy and efficiency of the formula. The formula distinguishes from previous literature as it converges to the true exact implied volatility, is a closed-form formula whose coefficients are explicitly determined and do not involve numerical iterations.

APA, Harvard, Vancouver, ISO, and other styles

21

Leipnik, Roy B., and Charles E. M. Pearce. "The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term." ANZIAM Journal 48, no. 3 (January 2007): 327–41. http://dx.doi.org/10.1017/s1446181100003527.

Full text

Abstract:

AbstractThe Faà di Bruno formulæ for higher-order derivatives of a composite function are important in analysis for a variety of applications. There is a substantial literature on the univariate case, but despite significant applications the multivariate case has until recently received limited study. We present a succinct result which is a natural generalization of the univariate version. The derivation makes use of an explicit integralform of the remainder term for multivariate Taylor expansions.

APA, Harvard, Vancouver, ISO, and other styles

22

Qi, Feng, Da-Wei Niu, and Bai-Ni Guo. "Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers." Tatra Mountains Mathematical Publications 72, no. 1 (December 1, 2018): 67–76. http://dx.doi.org/10.2478/tmmp-2018-0022.

Full text

Abstract:

Abstract In the paper, the authors apply Faà di Bruno formula, some properties of the Bell polynomials of the second kind, the inversion formulas of binomial numbers and the Stirling numbers of the first and the second kind, to significantly simplify coefficients in two families of ordinary differential equations associated with the higher order Frobenius–Euler numbers.

APA, Harvard, Vancouver, ISO, and other styles

23

Hespel, Christiane. "Iterated derivatives of the output of a nonlinear dynamic system and Faà di Bruno formula." Mathematics and Computers in Simulation 42, no. 4-6 (November 1996): 641–57. http://dx.doi.org/10.1016/s0378-4754(96)00040-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Qi, Feng, Muhammet Cihat Dağlı, and Dongkyu Lim. "Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers." Open Mathematics 19, no. 1 (January 1, 2021): 833–49. http://dx.doi.org/10.1515/math-2021-0079.

Full text

Abstract:

Abstract In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate Narumi numbers and polynomials, and derive explicit formulas for the Narumi numbers and polynomials and for (degenerate) Cauchy numbers.

APA, Harvard, Vancouver, ISO, and other styles

25

FIGUEROA, HÉCTOR, and JOSÉ M. GRACIA-BONDÍA. "COMBINATORIAL HOPF ALGEBRAS IN QUANTUM FIELD THEORY I." Reviews in Mathematical Physics 17, no. 08 (September 2005): 881–976. http://dx.doi.org/10.1142/s0129055x05002467.

Full text

Abstract:

This paper stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an elementary invitation to the subject as well. The rest of Sec. 1 is devoted to the basics of Hopf algebra theory and examples in ascending level of complexity. Section 2 turns around the all-important Faà di Bruno Hopf algebra. Section 2.1 contains a first, direct approach to it. Section 2.2 gives applications of the Faà di Bruno algebra to quantum field theory and Lagrange reversion. Section 2.3 rederives the related Connes–Moscovici algebras. In Sec. 3, we turn to the Connes–Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Sec. 3.1, we describe the first. Then in Sec. 3.2, we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Sec. 3.3, general incidence algebras are introduced, and the Faà di Bruno bialgebras are described as incidence bialgebras. In Sec. 3.4, deeper lore on Rota's incidence algebras allows us to reinterpret Connes–Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained. The structure results for commutative Hopf algebras are found in Sec. 4. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota–Baxter map in renormalization.

APA, Harvard, Vancouver, ISO, and other styles

26

Steward, David R., Philippe Le Grand, Igor Janković, and Otto D. L. Strack. "Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2089 (October 30, 2007): 223–48. http://dx.doi.org/10.1098/rspa.2007.0138.

Full text

Abstract:

A general framework for analytic evaluation of singular integral equations with a Cauchy kernel is developed for higher order line elements of curvilinear geometry. This extends existing theory which relies on numerical integration of Cauchy integrals since analytic evaluation is currently published only for straight lines, and circular and hyperbolic arcs. Analytic evaluation of Cauchy integrals along straight elements is presented to establish a context coalescing new developments within the existing body of knowledge. Curvilinear boundaries are partitioned into sectionally holomorphic elements that are conformally mapped from a local curvilinear Z -plane to a straight line in the -plane. Cauchy integrals are evaluated in these planes to achieve a simple representation of the complex potential using Chebyshev polynomials and a Taylor series expansion of the conformal mapping. Bell polynomials and the Faà di Bruno formula provide this Taylor series for mappings expressed as inverse mappings and/or compositions. Examples illustrate application of the general framework to boundary-value problems with boundaries of natural coordinates, Bezier curves and B-splines. Strings formed by the union of adjacent curvilinear elements form a large class of geometries along which Dirichlet and/or Neumann conditions may be applied. This provides a framework applicable to a wide range of fields of study including groundwater flow, electricity and magnetism, acoustic radiation, elasticity, fluid flow, air flow and heat flow.

APA, Harvard, Vancouver, ISO, and other styles

27

Sidi, Avram. "A Further Property of Functions in Class B(m): An Application of Bell Polynomials." Journal of Mathematics Research 11, no. 1 (November 27, 2018): 1. http://dx.doi.org/10.5539/jmr.v11n1p1.

Full text

Abstract:

We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term infinitely many times. A function  $f(x)$ is in the class ${\bf B}^{(m)}$ if it satisfies a linear homogeneous differential equation of the form $f(x)=\sum^m_{k=1}p_k(x)f^{(k)}(x)$, with $p_k\in {\bf A}^{(i_k)}$, $i_k$ being integers satisfying $i_k\leq k$. These functions appear in many problems of applied mathematics and other scientific disciplines. They have been shown to have many interesting properties,  and their integrals $\int^\infty_0 f(x)\,dx$, whether convergent or divergent,  can be evaluated very efficiently via the Levin--Sidi $D^{(m)}$-transformation,  a most effective convergence acceleration method. (In case of divergence, these integrals  are defined in some summability sense, such as Abel summability or Hadamard finite part or a mixture of these two.) In this note, we show that if $f(x)$ is in ${\bf B}^{(m)}$, then so is $(f\circ g)(x)=f(g(x))$, where $g(x)>0$ for all large $x$ and $g\in {\bf A}^{(s)}$,  $s$ being a positive integer. This enlarges the scope of the $D^{(m)}$-transformation considerably to include functions of complicated arguments. We demonstrate  the validity of our result with an application of the $D^{(3)}$ transformation to two integrals $I[f]$ and $I[f\circ g]$, for some $f\in{\bf B}^{(3)}$ and $g\in{\bf A}^{(2)}$. The Fa\`{a} di Bruno formula and Bell polynomials play a central role in our study.

APA, Harvard, Vancouver, ISO, and other styles

28

Spindler, Karlheinz. "A short proof of the formula of Faà di Bruno." Elemente der Mathematik, 2005, 33–35. http://dx.doi.org/10.4171/em/5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Alzer, Horst, and Omran Kouba. "Applications of the Formula of Faà di Bruno: Combinatorial Identities and Monotonic Functions." Results in Mathematics 76, no. 4 (July 27, 2021). http://dx.doi.org/10.1007/s00025-021-01448-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Qi, Feng, and Bai-Ni Guo. "Some properties of the Hermite polynomials." Georgian Mathematical Journal, January 15, 2021. http://dx.doi.org/10.1515/gmj-2020-2088.

Full text

Abstract:

Abstract In this paper, by the Faà di Bruno formula and properties of Bell polynomials of the second kind, the authors reconsider the generating functions of Hermite polynomials and their squares, find an explicit formula for higher-order derivatives of the generating function of Hermite polynomials, and derive explicit formulas and recurrence relations for Hermite polynomials and their squares.

APA, Harvard, Vancouver, ISO, and other styles

31

Dinca, George, and Florin Isaia. "Superposition Operators Between Higher-order Sobolev Spaces and a Multivariate Faà di Bruno Formula: Supercritical Case." Advanced Nonlinear Studies 14, no. 1 (January 1, 2014). http://dx.doi.org/10.1515/ans-2014-0105.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Hussainy, Syed Tahir, and Lokesh D. "A study on some infinite server queues in discrete-time." Journal of Computational Mathematica 4, no. 2 (December 28, 2020). http://dx.doi.org/10.26524/cm78.

Full text

Abstract:

This work analysis some discrete-time queueing mechanisms with infinitely many servers.By using a shot noise process, general results on the system size in discrete-time are given both in transient state and in steady state. For this we use the classical differentiation formula of F´a di Bruno. First two moments of the system size and distribution of the busy period of the system are also computed.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!