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

Mahid M. Mangontarum
2020 arXiv   pre-print
In this paper, we extend the r-Dowling 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).  ... 
arXiv:2005.08730v2 fatcat:leti7mhv2nbwtglcw66nlz2wsq

Lah-Bell numbers and polynomials [article]

Dae San Kim, Taekyun Kim
2020 arXiv   pre-print
In this paper, we introduce the Lah-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) ).  ... 
arXiv:2007.13291v1 fatcat:h27fggwzhrhfvanzz22mx4apwy

On Degenerate Truncated Special Polynomials

Ugur Duran, Mehmet Acikgoz
2020 Mathematics  
Also, the degenerate truncated forms 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.  ... 
doi:10.3390/math8010144 fatcat:yibr7hi5mvhodplrwqylaz65um

An application of the partial r-Bell polynomials on some family of bivariate polynomials [article]

Miloud Mihoubi, Yamina Saidi
2018 arXiv   pre-print
The aim 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.  ... 
arXiv:1801.01915v3 fatcat:f2vzuslwunaw3km3rx7rhucbzm

A Family of the r-Associated Stirling Numbers of the Second Kind and Generalized Bernoulli Polynomials

Paolo Emilio Ricci, Rekha Srivastava, Pierpaolo Natalini
2021 Axioms  
Herein, we use the Blissard umbral approach and the familiar 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] .  ... 
doi:10.3390/axioms10030219 fatcat:lmgyobs6ongpho2g4ccv2bfm5a

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

Ugur Duran, Mehmet Acikgoz
2021 New Trends in Mathematical Sciences  
In this study, we introduce 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) .  ... 
doi:10.20852/ntmsci.2021.428 fatcat:expkccihgjcx7lg4ay3oaancne

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

W. McGee
1971 IEEE Transactions on Information Theory  
The 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.  ... 
doi:10.1109/tit.1971.1054613 fatcat:iqjknfy2mvdyjksxqroyp5kwmy

Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion

Yunfeng Wu, Suxian Cai, Shanshan Yang, Fang Zheng, Ning Xiang
2013 Entropy  
Such results demonstrated the merits 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  ... 
doi:10.3390/e15041375 fatcat:kfd2k4544jh5nowqmhte7sqwuq

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

Vincent X Genest, Hiroshi Miki, Luc Vinet, Alexei Zhedanov
2014 Journal of Physics A: Mathematical and Theoretical  
The contraction 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.  ... 
doi:10.1088/1751-8113/47/21/215204 fatcat:kjzzfssorjhljhrtak5bhiunwe

Polynomial Optimization Methods for Matrix Factorization

Po-Wei Wang, Chun-Liang Li, J. Kolter
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
direction) by solving a 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.  ... 
doi:10.1609/aaai.v31i1.10941 fatcat:soyn7gtzunhwnmzmmrhuyxlpta

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.  ... 

Multivariate Stable Eulerian Polynomials on Segmented Permutations [article]

Philip B. Zhang, Xutong Zhang
2019 arXiv   pre-print
To prove Nunge's conjecture, we also develop a general approach to obtain generalized Sturm sequences from 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).  ... 
arXiv:1807.00984v2 fatcat:3vkrqdlaufa2lfr2jlkht2zsxy
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