We propose a new class of SBVPs which deals with exothermic reactions. We also propose four computationally stable methods to solve singular nonlinear BVPs by using Hermite wavelet collocation which are coupled with Newton's quasilinearization and Newton-Raphson method. We compare the results which are obtained by using Hermite wavelets with the results obtained by using Haar wavelets. The efficiency of these methods are verified by applying these four methods on Lane-Emden equations. Convergence analysis is also presented.
{"title":"On some computational aspects of Hermite & Haar wavelets on a class of nonlinear singular BVPs","authors":"Amit Verma, D. Tiwari","doi":"10.2298/AADM191123020V","DOIUrl":"https://doi.org/10.2298/AADM191123020V","url":null,"abstract":"We propose a new class of SBVPs which deals with exothermic reactions. We also propose four computationally stable methods to solve singular nonlinear BVPs by using Hermite wavelet collocation which are coupled with Newton's quasilinearization and Newton-Raphson method. We compare the results which are obtained by using Hermite wavelets with the results obtained by using Haar wavelets. The efficiency of these methods are verified by applying these four methods on Lane-Emden equations. Convergence analysis is also presented.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By means of the generating function approach, we derive several summation formulae involving multiple harmonic numbers Hn,? (?), as well as other combinatorial numbers named after Bernoulli, Euler, Bell, Genocchi and Stirling.
{"title":"Summation formulae involving multiple harmonic numbers","authors":"Dongwei Guo, W. Chu","doi":"10.2298/aadm190712026g","DOIUrl":"https://doi.org/10.2298/aadm190712026g","url":null,"abstract":"By means of the generating function approach, we derive several summation formulae involving multiple harmonic numbers Hn,? (?), as well as other combinatorial numbers named after Bernoulli, Euler, Bell, Genocchi and Stirling.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68352956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To an extended generalized permutohedron we associate the weighted integer points enumerator, whose principal specialization is the f-polynomial. In the case of poset cones it refines Gessel's P-partitions enumerator. We show that this enumerator is a quasisymmetric function obtained by universal morphism from the Hopf algebra of posets.
{"title":"Weighted P-partitions enumerator","authors":"M. Pešović, Tanja Stojadinovic","doi":"10.2298/AADM200525013P","DOIUrl":"https://doi.org/10.2298/AADM200525013P","url":null,"abstract":"To an extended generalized permutohedron we associate the weighted integer points enumerator, whose principal specialization is the f-polynomial. In the case of poset cones it refines Gessel's P-partitions enumerator. We show that this enumerator is a quasisymmetric function obtained by universal morphism from the Hopf algebra of posets.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":"13-13"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Ayyappan, G. Chatzarakis, T. Gopal, E. Thandapani
In this paper, we present some new oscillation criteria for nonlinear neutral difference equations of the form ?(b(n)?(a(n)?z(n))) + q(n)x?(?(n)) = 0 where z(n) = x(n) + p(n)x(?(n)),? > 0, b(n) > 0, a(n) > 0, q(n) ? 0 and p(n) > 1. By summation averaging technique, we establish new criteria for the oscillation of all solutions of the studied difference equation above. We present four examples to show the strength of the new obtained results.
{"title":"Oscillation criteria of third-order nonlinear neutral delay difference equations with noncanonical operators","authors":"G. Ayyappan, G. Chatzarakis, T. Gopal, E. Thandapani","doi":"10.2298/AADM200913011A","DOIUrl":"https://doi.org/10.2298/AADM200913011A","url":null,"abstract":"In this paper, we present some new oscillation criteria for nonlinear neutral difference equations of the form ?(b(n)?(a(n)?z(n))) + q(n)x?(?(n)) = 0 where z(n) = x(n) + p(n)x(?(n)),? > 0, b(n) > 0, a(n) > 0, q(n) ? 0 and p(n) > 1. By summation averaging technique, we establish new criteria for the oscillation of all solutions of the studied difference equation above. We present four examples to show the strength of the new obtained results.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this work is to establish the monotonicity of a Darboux, 2-injective function
本文的目的是建立一个2-单射函数的单调性
{"title":"The monotonicity of Darboux and 2-injective functions","authors":"C. Mortici","doi":"10.2298/aadm200616024m","DOIUrl":"https://doi.org/10.2298/aadm200616024m","url":null,"abstract":"The aim of this work is to establish the monotonicity of a Darboux, 2-injective function","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present several potentially useful properties of the Barnes G-function. The properties considered here include, for example, its integral representation, complete monotonicity, and continued-fraction approximation. We also derive continued-fraction approximations of the Glaisher-Kinkelin constant and the Choi-Srivastava constants.
{"title":"Some new properties of the Barnes G-function and related results","authors":"Chao Chen, H. Srivastava","doi":"10.2298/aadm200424056c","DOIUrl":"https://doi.org/10.2298/aadm200424056c","url":null,"abstract":"In this paper, we present several potentially useful properties of the Barnes G-function. The properties considered here include, for example, its integral representation, complete monotonicity, and continued-fraction approximation. We also derive continued-fraction approximations of the Glaisher-Kinkelin constant and the Choi-Srivastava constants.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+). The results will be proved by employing the self-improving property of the discrete Ap-Muckenhoupt weights and the Marcinkiewicz Interpolation Theorem.
本文证明了离散Ap-Muckenhoupt权理论中离散Hardy-Littlewood极大算子在lpw (Z+)上有界的一个离散Rubio De Francia外推定理。利用离散Ap-Muckenhoupt权值的自改进性质和Marcinkiewicz插值定理对结果进行了证明。
{"title":"Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems","authors":"S. Saker, R. Agarwal","doi":"10.2298/aadm210120017s","DOIUrl":"https://doi.org/10.2298/aadm210120017s","url":null,"abstract":"In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+). The results will be proved by employing the self-improving property of the discrete Ap-Muckenhoupt weights and the Marcinkiewicz Interpolation Theorem.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Feng Qi (祁锋), Da-Wei Niu, D. Lim, Bai-Ni Guo (郭白妮)
In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, find logarithmically complete monotonicity of these extended functions, and, in light of logarithmically complete monotonicity of these extended functions, derive some inequalities for multinomial coefficients and multivariate beta functions. These results recover, extend, and generalize some known conclusions.
{"title":"Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions","authors":"Feng Qi (祁锋), Da-Wei Niu, D. Lim, Bai-Ni Guo (郭白妮)","doi":"10.2298/AADM191111033Q","DOIUrl":"https://doi.org/10.2298/AADM191111033Q","url":null,"abstract":"In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, find logarithmically complete monotonicity of these extended functions, and, in light of logarithmically complete monotonicity of these extended functions, derive some inequalities for multinomial coefficients and multivariate beta functions. These results recover, extend, and generalize some known conclusions.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45227572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two subfamilies of Motzkin paths, with the same numbers of up, down, horizontal steps were known to be equinumerous with ternary trees and related objects. We construct a bijection between these two families that does not use any auxiliary objects, like ternary trees.
{"title":"A bijection between two subfamilies of Motzkin paths","authors":"Nancy S. S. Gu, H. Prodinger","doi":"10.2298/aadm200707026g","DOIUrl":"https://doi.org/10.2298/aadm200707026g","url":null,"abstract":"Two subfamilies of Motzkin paths, with the same numbers of up, down,\u0000 horizontal steps were known to be equinumerous with ternary trees and\u0000 related objects. We construct a bijection between these two families that\u0000 does not use any auxiliary objects, like ternary trees.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48967775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1944, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the properties hypothesized for it by Dyson was discovered in 1988 by G.E. Andrews and F.G. Garvan. In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new infinite families of linear inequalities for the partition function p(n). The number of Garden of Eden partitions are also considered in this context in order to provide other infinite families of linear inequalities for p(n).
{"title":"Rank partition functions and truncated theta identities","authors":"M. Merca","doi":"10.2298/AADM190401023M","DOIUrl":"https://doi.org/10.2298/AADM190401023M","url":null,"abstract":"In 1944, Freeman Dyson defined the concept of rank of an integer partition\u0000 and introduced without definition the term of crank of an integer partition.\u0000 A definition for the crank satisfying the properties hypothesized for it by\u0000 Dyson was discovered in 1988 by G.E. Andrews and F.G. Garvan. In this\u0000 paper, we introduce truncated forms for two theta identities involving the\u0000 generating functions for partitions with non-negative rank and non-negative\u0000 crank. As corollaries we derive new infinite families of linear inequalities\u0000 for the partition function p(n). The number of Garden of Eden partitions are\u0000 also considered in this context in order to provide other infinite families\u0000 of linear inequalities for p(n).","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48269199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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