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Bivariate Extension of the r-Dowling Polynomials and the Generalized Spivey's Formula
[article]

2020
*
arXiv
*
pre-print

In this paper, we extend the r-Dowling

arXiv:2005.08730v2
fatcat:leti7mhv2nbwtglcw66nlz2wsq
*polynomials*to their*bivariate*forms. Several properties that generalize those*of*the*bivariate**Bell*and r-*Bell**polynomials*are established. ... Finally, we obtain two forms*of*generalized Spivey's formula. ... When m = 1 and r = 0, this results to B n+1 (x, y) = n i=0 n i B i (x − 1)xy, (43) the*bivariate**extension**of*(2). ...##
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Lah-Bell numbers and polynomials
[article]

2020
*
arXiv
*
pre-print

In this paper, we introduce the Lah-

arXiv:2007.13291v1
fatcat:h27fggwzhrhfvanzz22mx4apwy
*Bell*numbers and their natural*extensions*, namely the Lah-*Bell**polynomials*, and derive some basic properties*of*such numbers and*polynomials*by using elementary methods ... In addition, we consider the degenerate Lah-*Bell*numbers and*polynomials*as degenerate versions*of*the Lah-*Bell*numbers and*polynomials*. ... The*Bell**polynomials*B n (x) are natural*extensions**of*the*Bell*numbers (see (6) , (10) ). ...##
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On Degenerate Truncated Special Polynomials

2020
*
Mathematics
*

Also, the degenerate truncated forms

doi:10.3390/math8010144
fatcat:yibr7hi5mvhodplrwqylaz65um
*of*the*bivariate*Fubini and*Bell**polynomials*and numbers are introduced and various relations and formulas for these*polynomials*and numbers, which cover several summation ... Some interesting surface plots*of*these*polynomials*in the special cases are provided. ... All authors have read and agreed to the published version*of*the manuscript. Funding: This research received no external funding. Conflicts*of*Interest: The authors declare no conflict*of*interest. ...##
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An application of the partial r-Bell polynomials on some family of bivariate polynomials
[article]

2018
*
arXiv
*
pre-print

The aim

arXiv:1801.01915v3
fatcat:f2vzuslwunaw3km3rx7rhucbzm
*of*this paper is to give some combinatorial relations linked*polynomials*generalizing those*of*Appell type to the partial r-*Bell**polynomials*. ... We give an inverse relation, recurrence relations involving some family*of**polynomials*and their exact expressions at rational values in terms*of*the partial r-*Bell**polynomials*. ... These*polynomials*present a naturel*extension**of*the partial*Bell**polynomials*[1] and generalize the r-Whitney numbers*of*both kinds, the r-Lah numbers and the r-Whitney-Lah numbers. ...##
###
A Family of the r-Associated Stirling Numbers of the Second Kind and Generalized Bernoulli Polynomials

2021
*
Axioms
*

Herein, we use the Blissard umbral approach and the familiar

doi:10.3390/axioms10030219
fatcat:lmgyobs6ongpho2g4ccv2bfm5a
*Bell**polynomials*. Links with available literature on this subject are also pointed out. The*extension*to the*bivariate*case is discussed. ... In this article, we derive representation formulas for a class*of*r-associated Stirling numbers*of*the second kind and examine their connections with a class*of*generalized Bernoulli*polynomials*. ... When j = 2*bivariate**extensions**of*the Bernoulli and Euler*polynomials*were introduced [39] , the case*of*higher dimensions was also considered in [32] . ...##
###
Page 7917 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

for the Hermite weight is

*bell*-shaped. ... Summary: “The aim*of*the present paper is to show that many Phelps type duality results, relating the*extension*properties*of*var- ious classes*of*functions (continuous, linear continuous, bounded bilinear ...##
###
Bell-based Genocchi polynomials

2021
*
New Trends in Mathematical Sciences
*

In this study, we introduce

doi:10.20852/ntmsci.2021.428
fatcat:expkccihgjcx7lg4ay3oaancne
*Bell*-based Genocchi*polynomials**of*order α and then derive multifarious correlations and formulas including some implicit summation formulas and derivative properties. ... The*bivariate**Bell**polynomials*are defined as follows (cf. [5] , [8] , [9] ): ∞ ∑ n=0 Bel n (x; y) t n n! ... In the special case x = 0 in (10), we acquire*Bell*-Genocchi*polynomials*Bel G(α) n (y)*of*order α, which are also new*extensions**of*the Genocchi numbers*of*order α in (2), as follows: (e t −1) . ...##
###
Page 2093 of Mathematical Reviews Vol. , Issue 85e
[page]

1985
*
Mathematical Reviews
*

The resulting expressions involve

*Bell**polynomials*and can be inter- preted in terms*of*convolved random variables with one*of*the convolutes having the form*of*the marginal distribution. ... From the foreword: “It is the purpose*of*this paper to exhibit models*of**bivariate*distributions. We use the*polynomial*generat- ing functions*of*the collection*of*random variables introduced by J. ...##
###
Complex Gaussian noise moments

1971
*
IEEE Transactions on Information Theory
*

The

doi:10.1109/tit.1971.1054613
fatcat:iqjknfy2mvdyjksxqroyp5kwmy
*bivariate*complex Hermite*polynomials*may be extended to nonpositive-integer values*of*n, etc. in the same way as the*extension*is made for the univariate complex Hermite functions. ... INTR~DLJCTJ~N T HE computation*of*means*of*Gaussian random processes is very common and has an*extensive*history. ... The author is with*Bell*Telephone Laboratories, Inc., Murray Hill, N.J. 07974. I. INTRODUCTION A. ...##
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Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion

2013
*
Entropy
*

Such results demonstrated the merits

doi:10.3390/e15041375
fatcat:kfd2k4544jh5nowqmhte7sqwuq
*of*the*bivariate*feature distribution estimation and the superiority*of*the maximal posterior probability decision criterion for analysis*of*knee joint VAG signals. ... The estimated densities*of*the VAG signals showed explicit distributions*of*the normal and abnormal signal groups, along with the corresponding contours in the*bivariate*feature space. ...*Bell*, for the work*of*data acquisition. This work was supported in part by the National Natural Science ...##
###
Page 293 of Mathematical Reviews Vol. 23, Issue 3B
[page]

1962
*
Mathematical Reviews
*

Formulas

*of*this type are exact em f (=) is a*polynomial**of*degree <2n—1 and the 2; (j=1, ---,) are the zeros*of*the nth-degree*polynomial*which is orthogonal on [a,b] with respect to w(x) to all*polynomials*...*of*lower The z; and A; have been*extensively*tabulated for several different functions w(x), so that they may now be investi- gated by inspection. ...##
###
The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states

2014
*
Journal of Physics A: Mathematical and Theoretical
*

The contraction

doi:10.1088/1751-8113/47/21/215204
fatcat:kjzzfssorjhljhrtak5bhiunwe
*of*SO(3) to E(2) is used to show that the*bivariate*Charlier*polynomials*correspond to a limit*of*the*bivariate*Krawtchouk*polynomials*. ... A family*of*multivariate orthogonal*polynomials*generalizing the standard (univariate) Charlier*polynomials*is shown to arise in the matrix elements*of*the unitary representation*of*the Euclidean group ... Acknowledgments V.X.G. holds an Alexander-Graham-*Bell*fellowship from the Natural Sciences and Engineering Research Council*of*Canada (NSERC). The research*of*L.V. is supported in part by NSERC. ...##
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Polynomial Optimization Methods for Matrix Factorization

2017
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

direction) by solving a

doi:10.1609/aaai.v31i1.10941
fatcat:soyn7gtzunhwnmzmmrhuyxlpta
*bivariate*quartic*polynomial*optimization problem. ... In this paper we present an approach based upon*polynomial*optimization techniques that both improves the convergence time*of*matrix factorization algorithms and helps them escape from local optima. ... This result is important theoretically, because it provides a basis for the global solvability*of*the such*polynomial*(*bivariate*quartic) optimization problems. ...##
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Page 4438 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

In addition, the conditional probability generating functions

*of*both the P-B and the P-P model are derived using properties*of**Bell**polynomials*. M. G. ... The planning, execution and ways*of*evaluating the results*of*the study are*extensively*discussed. H. T. ...##
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Multivariate Stable Eulerian Polynomials on Segmented Permutations
[article]

2019
*
arXiv
*
pre-print

To prove Nunge's conjecture, we also develop a general approach to obtain generalized Sturm sequences from

arXiv:1807.00984v2
fatcat:3vkrqdlaufa2lfr2jlkht2zsxy
*bivariate*stable*polynomials*. ... By acting on Brändén's*polynomials*with a stability-preserving linear operator, we get a multivariate refinement*of*the generalized Eulerian*polynomials*. ... This work was supported by the National Science Foundation*of*China (Nos. 11626172, 11701424) , the PHD Program*of*TJNU (No. XB1616), and MECF*of*Tianjin (No. JW1713). ...
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