Cybernetics and Information Technologies, 4(2):60--68, 2004. 515. Summary. 253-263, May 2009 ... Let A be a bounded linear operator on a Hilbert space H, then V1(A) = W(A) (see [5, 4]). In 1979, S. Campbell and C. Meyer proposed an open problem to find an explicit representation for the Drazin inverse of a … Notes that the publication focuses on matrix analysis and the various aspects of linear algebra and its applications. It is known that η (G) ≤ n − 2 if G is a simple graph on n vertices and G is not isomorphic to nK1. Påverkansfaktor för Electronic Journal of Linear Algebra för 2020-2021 är 0.631 Påverkansfaktor Analys, Trend, Ranking & Förutsägelse. published in combined form. With this in mind, it is … Read more Electronic Journal of Linear Algebra is an Open Access (OA) Journal. The Electronic Journal of Linear Algebra 9, 32-41, 2002. ], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. Portugal. Hệ số ảnh hưởng 2020-2021 của Electronic Journal of Linear Algebra là 0.631 Hệ số ảnh hưởng Phân tích, Khuynh hướng, Xếp hạng & Sự dự đoán Zero forcing parameters and minimum rank problems, Linear Algebra and its Applications, 433 (2010), 401-411. ELECTRONIC Journal of LINEAR ALGEBRA. A matrix. This journal carries original research articles of high standard in the field of algebra and aims to reflect the latest developments in the field. Contributions from mathematicians all over the world are welcome. The International Electronic Journal of Algebra ( Int. Electron. J. Algebra ) is published twice a year (January - July). 885–900, 1018. ELA. Markov chain small-world model with asymmetric transition probabilities, Electronic Journal of Linear Algebra, 17 (2008), 616-636. The Electronic Journal of Combinatorics. It is published by the International Linear Algebra Society and the editors-in-chief are Froilán M. Dopico ( University Carlos III of Madrid ) and Michael Tsatsomeros ( Washington State University ). ELA 2 L. Lebtahi and N. Thome interest in the last twenty years. Electronic Journal of Linear Algebra. ILAS publishes an electronic journal - the Electronic Journal of Linear Algebra (ELA), founded in 1996. Assuming that rmi,j = Xj s=i pi,j,sm r−1 s,s, (taking 0 0 as 1 if M is singular), and noting that pi,t,s = 0 if s > t, we have r+1mi,j = Xj She is the Secretary/Treasurer of the International Linear Algebra Society and an associate editor of the journals Linear Algebra and its Applications and Electronic Journal of Linear Algebra. The journal is completely free for both authors and readers. Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. Electronic Journal of Linear Algebra, 26 (2013), 762-780 Note on Nordhaus-Gaddum problems for Colin de Verdiere type parameters Published by ILAS - The InternationalLinear Algebra Society. Much scientific and medical research is paid for with public funds. ELA 118 ChangjiangBu,JiemeiZhao,andKuizeZhang sumption that A and (I+CA−2B) are both invertible over any field;however, the rep- resentation of the group inverse is not given. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 23, pp. Electronic Journal of Linear Algebra. A Berman, N Shaked-Monderer, SK Panda. Mathematics. H Nakazato, P Psarrakos. JO - Electronic Journal of Linear Algebra. Assuming that rmi,j = Xj s=i pi,j,sm r−1 s,s, (taking 0 0 as 1 if M is singular), and noting that pi,t,s = 0 if s > t, we have r+1mi,j = Xj A publication of the International Linear Algebra Society. V. Monov and M. Tsatsomeros. Editor-in-Chief of the Electronic Journal of Combinatorics. Advisory Editor of the new journal Transactions on Combinatorics. 847-856, December 2020. The Electronic Journal of Linear Algebra. The nullity of a graph G, denoted by η (G), is the multiplicity of the eigenvalue zero in its spectrum. ELA StronglyRegularGraphs 235 possiblevalueofs andthusapossiblevalueofk using(2.1). Open Access stands for unrestricted access and unrestricted reuse. Wang) A generalized Hölder type eigenvalue inequality, Linear and Multilinear Algebra, 65 (2017), 2145-2151" The Electronic Journal of Linear Algebra. Mathematical Physics Journal - Electronic only journal. 0. Scientiae Mathematicae - Japanese Association of … SN - 1081-3810. Archived. CLOCKSS Archive. New York Journal of Mathematics. IS - 1. 2015 Oct 22;29(1):144-155. View at: Google Scholar; Z. Chen, “Biderivations and linear commuting maps on simple generalized Witt algebras over a field,” The Electronic Journal of Linear Algebra… Matematicki Vesnik - Russian but in English. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. Professor Tsatsomeros has also served the International Linear Algebra Society in various capacities, including as a member of the Board of Directors, Advisory Committee, and Journal Committee. The (Weakly) Sign Symmetric P-Matrix Completion Problems (2002-3) DeAlba, Hardy, Hogben, Wangsness Electronic Journal of Linear Algebra 10 (2003): 257-271 4. The Electronic Journal of Linear Algebra is a peer-reviewed platinum open access scientific journal covering matrix analysis and linear algebra, together with their applications. Links to downloadable versions of articles in the current issue and in previous issues. Open Access allows taxpayers to … Il Fattore di Impatto 2020-2021 di Electronic Journal of Linear Algebra è 0.631. The International Linear Algebra Society (ILAS) is the only global professional organization solely dedicated to researchers and educators in Linear Algebra. The organization is very active in disseminating information about linear algebra. Electronic Journal of Linear Algebra. Year. Journal of Linear and Topological Algebra (JLTA) is an international mathematical journal founded at the middle of 2012. He proved that the irreducible representations of Sn are in one to one corre- spondence with the partitions of nrealized as Ferrersdiagrams.We refer the reader The International Electronic Journal of Algebra is published twice a year. Electronic Journal of Linear Algebra. M1 - 11. ELA ONTHEKRE˘IN-LANGERINTEGRALREPRESENTATIONOF GENERALIZEDNEVANLINNAFUNCTIONS∗ J.ROVNYAK† AND L.A.SAKHNOVICH‡ Abstract. 73 "(with J. T. Liu and Q.W. Electronic Journal of Linear Algebra 32, 539-545, 2017. ETNA. ER - Karantha MP, Nandini N, Divya Shenoy DP. Primary Site: Israel. LetE bealinearsubspaceinRp,with0≤ s≤ p.Wecallaffine subspace of dimension sin Rp a subset H ={c+y;y∈E}of Rp,wherecis a vector of Rp.It is convenient to simply write H =c+E. Recommended Citation Jin, Hongwei and Benitez, Julio. Electronic Journal of Linear Algebra Volume 22ELA Volume 22 (2011) Article 74 2011 The Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized Linear Algebra Appl., 509:82{113, 2016. 30/11/2020 Mirror Sites: USA. With this in mind, it is … Read more 2013. The inverse eigenvalue and inertia problems for minimum rank two graphs, The Electronic Journal of Linear Algebra, 22 (2011), 389-418. SPN graphs were introduced in [N. Shaked-Monderer. ELA 2 L. Lebtahi and N. Thome interest in the last twenty years. 500. JF - Electronic Journal of Linear Algebra. Summary. This journal carries original research articles of high standard in the field of algebra and aims to reflect the latest developments in the field. Only the very best and most interesting papers are to be considered for publication in the journal. International Linear Algebra Society. 28: 2001: The numerical range of self-adjoint quadratic matrix polynomials. The Electronic Journal of Linear Algebra (ELA), a publication of the International Linear Algebra Society (ILAS), is a refereed all-electronic journal that welcomes mathematical articles of high standards that contribute new information and new insights to matrix analysis and the various aspects of linear algebra and its applications. About ILAS Who we are ILAS Officers Bylaws Membership Join ILAS Current Members Publications ELA IMAGE ILAS-NET Other journals Conferences ILAS Conferences ILAS-Endorsed Meetings Other Conferences Awards/Donate Prizes and Special Lectures/Support Donate to ILAS Funds Wikipedia-w Facebook Twitter ILAS Corporate Sponsors ILAS Co-operating Societies ILAS Co-operating Workshops … It was established as the immediate successor to the International Matrix Group, founded in 1987. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. Inertia sets for graphs on six or fewer vertices, Electronic Journal of Linear Algebra, 20 (2010), 53-78. A simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. M, rmi,t = 0, if t < i, and mt,j = 0 if t > j, we have r+1mi,j = Xj t=i rmi,tmt,j. Suppose thatµ>ν n. Let x =[x1,x2,...,x n]t satisfy (4) with k = n.We note that in this case x n cannotvanish. ELA 202 Jean-Daniel Rolle (b) P GP G1 =P G1 P G =P G1 and P GP G2 =P G2 P G =P G2 (c) If G2G+ 2 G1 =0,thenM G1 M G2 =M G,andr(G)=r(G1)+r(G2). ELA Fibonacci-HornerDecompositionoftheMatrixExponential 181 Remark 2.4. Primary Site: Israel: Mirror Sites: USA: Germany: Portugal: EMIS: Other EMIS sites: Founding Editor: Daniel Hershkowitz: Editors in Chief: A necessary and sufficient eigenvector condition for a graph to be bipartite Electronic Journal of Linear Algebra (2010). Journal Information Scope Editorial board (email, postal) Former Editorial board members. Editor-in-Chief of the Electronic Journal of Combinatorics. For this purpose, let H = H(T) be the subgraph of T induced by the k vertices of degree at least 3 in T.IfH consists of a collection of disjoint vertices (possibly empty), we call Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. In this paper, it is shown that among connected graphs with maximum clique size !, LetPub Scientific Journal Selector (2018-2021), Electronic Journal of Linear Algebra published in 0, UNITED STATES. Recommended Citation With Open Access, researchers can read and build on the findings of others without restriction. 28, pp. ADDITIVE MAPS ON RANK KBIVECTORS WAI LEONG CHOOI yAND KIAM HEONG KWA Abstract. Li and X. Wang) Ranks of quantum states with prescribed reduced states, Electronic Journal of Linear Algebra, 34 (2018) 331-342." Thevector y formedfromthefirstn− 1componentsofx then satisfies (8) By+x nq=µy. Only the very best and most interesting papers are to be considered for publication in the journal. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. Home Record. Electronic Journal of Linear Algebra listed as ELA Electronic Journal of Linear Algebra - How is Electronic Journal of Linear Algebra abbreviated? InthefinitedimensionalcaseV1(A) = W(A). The International Electronic Journal of Algebra is published twice a year. ... a refereed all-electronic journal. LetPub Scientific Journal Selector (2018-2021), Electronic Journal of Linear Algebra published in 0, UNITED STATES. Proof.The proof of this lemma appears in [7]. RB Bapat, SK Panda. Notes that the publication focuses on matrix analysis and the various aspects of linear algebra and its applications. M, rmi,t = 0, if t < i, and mt,j = 0 if t > j, we have r+1mi,j = Xj t=i rmi,tmt,j. ELA 182 S.W.Drury 2. 11. The “shadow” of the shape illustrates the relative position between the two images, on the planes z = 0 and z = 1, and was included to better visualize the shear and how it is linear in 3D space. For more information, please contactscholcom@uwyo.edu. The ELA Fund is used to continue to make ELA freely available to the scientific community. It is Electronic Journal of Linear Algebra. ISSN 1081-3810. Total Cites. Features "The Electronic Journal of Linear Algebra" (ISSN 1081-3810), published by the International Linear Algebra Society (ILAS). Moreover, p n =0,q n =0,fo,orhetwresi A would become reducible. |a This publication is the print version of the Electronic Journal of Linear Algebra (ELA), a refereed all-electronic journal published by the International Linear Algebra Society (ILAS). Electronic Journal of Linear Algebra, ISSN 1081-3810 Volume 37, pp. the symmetric singular linear control system satisfies the regularity condition. 3. It puts out two publications: IMAGE, ILAS’s bulletin; and the Electronic Journal of Linear Algebra (ELA), a refereed all-electronic journal. A Criterion for Reducibility of Matrices. |a Vol. This Article is brought to you for free and open access by Wyoming Scholars Repository. Southwest Journal of Pure and Applied Mathematics - Published twice a year. Wi... TU Kaiserslautern Department of Mathematics, Erwin-Schrödinger-Str. 48, Postfach 3049, 67653, Kaiserslautern, Germany Jiahao Cheng, ... Dadi Ni W. Mahboub, ... M. Spivakovsky Commutative Algebra and its Interactions with Algebraic Geometry: A volume in honor of Craig Huneke on the occasion of his 65th birthday. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (EJDE) Since its foundation in 1993, this e-journal has been dedicated to the rapid dissemination of high quality research in mathematics. This way, all transformations are now linear in 3D, and can be represented by a single 3x3 affine transformation matrix that acts on two dimensions. It has been accepted for inclusion in Electronic Journal of Linear Algebra by an authorized administrator of Wyoming Scholars Repository. Psarrakos and M.J. Tsatsomeros. Richard A. Brualdi UWF Beckwith Bascom Professor of Mathematics (now emeritus), UW-Madison A Milestone Editor-in-Chief of the Linear Algebra and its Applications. 27 (2014), 444-457 Minimum rank, maximum nullity, and zero forcing number for simple digraphs A. Berliner, M. Catral, L. Hogben, M. Huynh, K. Lied, M. Young. A matrix can be represented as a portion of a spreadsheet but often is also mathematically represented as numbers enclosed in brackets as in Figure 2 . 2015. It has been accepted for inclusion in Electronic Journal of Linear Algebra by an authorized administrator of Wyoming Scholars Repository. ], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. Saiago Our purpose here is to give simple, tight bounds for m(T) in terms of vertex degrees only, and then to indicate for which trees these bounds are exact. A lower bound for the spectral radius of graphs with fixed diameter European Journal of Combinatorics (2010), with Edwin van Dam, Jack Koolen and Jae-Ho Lee. A simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. The representation of the group inverse of a block matrix AB 0 C over skew fields has been given in 2001;see [6]. 1040-1059, December 2012 http://math.technion.ac.il/iic/ela Some of their properties can be found in [1, 8, 9, 13]. 2019/2020. Features "The Electronic Journal of Linear Algebra" (ISSN 1081-3810), published by the International Linear Algebra Society (ILAS). 544-548, July 2021. 1: 2017: Strongly self-inverse weighted graphs. He is Co-Editor-In-Chief of the Electronic Journal of Linear Algebra and Associate Editor of Linear Algebra … The Electronic Journal of Linear Algebra (ELA), a publication of the International Linear Algebra Society (ILAS), is a refereed all-electronic journal that welcomes mathematical articles of high standards that contribute new information and new insights to matrix analysis and the various aspects of linear algebra and its applications. Definition 2.2. 2020: Almost self-inverse graphs. The Electronic Journal of Linear Algebra 36, 80-89, 2020. Linear and Multiplicative Issues.Around the end ofthe nineteenth cen-tury, the representation theory ofthe symmetric groupSn was worked out by Alfred Young. Linear Algebra and its Applications, 393:333-352, 2004. The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. It has ISSN number 1072-6691, and its articles are indexed by Math Reviews, Zentralblatt für Mathematik, and Thomson Reuters web of knowledge. ELA is a JCR ranked journal, and indexed by MathSciNet, … ELA is a platinum open access journal, meaning that it is free to all: no subscription and no article processing fee or page charges. Furthermore, matrices with k-involutory symmetries have been studied in [11, 12]. Electronic Transactions on Numerical Analysis. Links to downloadable versions of articles in the current issue and in previous issues. This page was last edited on 28 May 2021, at 09:15 (UTC). 1/4 (1996/1998)-. Electronic Journal of Linear Algebra Volume 26ELA Volume 26 (2013) Article 40 2013 Trace conditions for symmetry of the numerical range Louis Deaett Louis.Deaett@quinnipiac.edu Ramiro H. … Editor-in-Chief of Discrete Mathematics Letters. Electronic Journal of Linear Algebra. With Open Access, researchers can read and build on the findings of others without restriction. 30: 2002: On the shape of numerical range of matrix polynomials. Johnson and C.M. Published by ILAS–the International Linear Algebra Society. Linear Algebra Appl., 509:82{113, 2016. It is published by International Linear Algebra Society. Talk:Electronic Journal of Linear Algebra ... (Fph is an academic who serves in the outreach and membership committee of the International Linear Algebra Society, the society that publishes this journal.) ByaresultofFrobenius(see[10]),thematrixµI−B hasanonnegativeinverse Advisory Editor of the new journal Transactions on Combinatorics. ISSN 1537-9582 (Print) | The electronic journal of linear algebra. Editor-in-Chief of Discrete Mathematics Letters. ELECTRONIC Journal of LINEAR ALGEBRA Published by ILAS - The International Linear Algebra Society ISSN 1081-3810. LetPub Scientific Journal Selector (2018-2021), Electronic Journal of Linear Algebra published in 0, UNITED STATES. Electronic Journal of Linear Algebra ; European Journal of Pure and Applied Mathematics; Experimental Mathematics ; Geometric And Functional Analysis ; Integers: Electronic Journal of Combinatorial Number Theory ; Journal of Experimental Algorithmics ; Journal of Inequalities in Pure and Applied Mathematics (Also check RGMIA research reports, etc.) For more information, please contactscholcom@uwyo.edu. Access ELA articles Current volume All volumes Multi-year author index. 74 "(with C.K. The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Electronic Journal of Differential Equations (EJDE) Journal of Algebraic Combinatorics. Generalized $\lambda$-Newton inequalities revisited, Journal of Inequalities in Pure and Applied Mathematics, 10 (2009), Art. Electronic Journal of Linear Algebra, ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 36, pp. Let V 2 U This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. ELA 34 T.S.Oepomo whereB≡ A(n),p≡ p ≥ 0,andq≡ q n ≥ 0. Electronic Journal of Linear Algebra. 19. A Primer of Perron-Frobenius Theory for Matrix Polynomials. Log In; Automatic login IP; PUBLISHERS' AREA DISCOVER ISSN SERVICES SEARCH OPEN ACCESS RESOURCES KEEPERS REGISTRY ISSN INTERNATIONAL CENTER. Open Access stands for unrestricted access and unrestricted reuse. According to SCImago Journal Rank (SJR), this journal is ranked 0.447. The dimensions of a matrix are cited as the number of rows × the number of columns, so in our example of the plant extracts, the matrix has dimensions 20 × 100. Journal of Graph Algorithms and Applications. ELA THE MINIMUM SPECTRAL RADIUS OF GRAPHS WITH A GIVEN CLIQUE NUMBER⁄ DRAGAN STEVANOVIC¶y AND PIERRE HANSENz Abstract. The Web ELA Forthcoming special issues. SPN graphs: When copositive = SPN. Journal ISSN: 1537-9582. ELA stands for Electronic Journal of Linear Algebra (International Linear Algebra Society) Suggest new definition. Fattore di Impatto Analisi, Trend, Ranking & Previsione. Let U and V be linear spaces over elds F and K, respectively, such that dim U = n> 2 and jFj > 3. Rank and dimension functions. ILAS publishes an electronic journal - the Electronic Journal of Linear Algebra (ELA), founded in 1996. Electronic Journal of Linear Algebra is an Open Access (OA) Journal. Bioxbio Journal Impact*. We give a negative answer for a special class of regular tournament matrices: There is no (0, 1)-matrix of order greater than 3 whose ELA 28 C.R. The first Editors-in-Chief were Volker Mehrmann and Daniel Hershkowitz. Electronic Journal of Linear Algebra Volume 17ELA Volume 17 (2008) Article 28 2008 On general matrices having the Perron-Frobenius Property Abed Elhashash Daniel B. Szyld szyld@temple.edu Pacific Journal of Mathematics. Contact ELA Fletcher asked whether there is a (0, 1)-matrix of order greater than 3 whose square is a regular tournament matrix. ILAS serves this community in several ways: ILAS publishes the Electronic Journal of Linear Algebra (ELA): a platinum open access journal. SPN graphs: When copositive = SPN. The Electronic Journal Linear Algebra (ELA) leaves the copyright of papers with the authors. ELA only requires each author's agreement that we publish it. Leave this field blank . Germany. [17] ELA is a platinum open access journal, meaning that it is free to all: no subscription and … Linear Algebra and its Applications 338 (1-3), 105-123, 2001. The International Linear Algebra Society (ILAS) was founded in 1989, to support research and cooperation in the field of linear algebra and matrix theory. Total Articles. Some of their properties can be found in [1, 8, 9, 13]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA related ISSN: 1537-9582 Country: United States. The first Editors-in-Chief were Volker Mehrmann and Daniel Hershkowitz . Electronic Journal of Linear Algebra, 11 : 246-257, 2004. Theparameterv isthen determinedby(2.3). Electronic Journal of Linear Algebra 10 (2003): 46-59. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 27, pp. P.J. Documenta Mathematica. The Electronic Journal of Linear Algebra (ELA), the research journal of ILAS, is a platinum open access journal, freely available to all readers: no subscription and no article processing fee or page charges. SPN graphs were introduced in [N. Shaked-Monderer. Skip to main content. M. Brešar and K. Zhao, “Biderivations and commuting linear maps on Lie algebras,” Journal of Lie Theory, vol. Subject: MATHEMATICS. Username or e-mail * Password * Forgot Password. The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems. |a Some vols. The International Electronic Journal of Algebra (IEJA) is an international mathematical journal founded at the beginning of 2007. Electronic Journal of Linear Algebra is a journal covering the technologies/fields/categories related to Algebra and Number Theory (Q3). 362. All papers published by Journal of Linear and Topological Algebra are rigorously peer reviewed, free of charge and open access. Dr. Hogben is a frequent co-organizer of meetings, workshops, and special sessions/mini-symposia. Journal Abbreviation: ELECTRON J LINEAR AL. This journal is published by the IAU, Central Tehran Branch, and it appears four times a year. The overall rank of Electronic Journal of Linear Algebra is 11078. Electronic Journal of Linear Algebra, ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 37, pp. Linear and Multilinear Algebra 67 (10), 2065-2076, 2019. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society IF. Contributions from mathematicians all over the world are welcome. This definition appears very frequently and is found in the following Acronym Finder categories: Information technology (IT) and computers; Science, medicine, engineering, etc. Richard A. Brualdi UWF Beckwith Bascom Professor of Mathematics (now emeritus), UW-Madison A Milestone Editor-in-Chief of the Linear Algebra and its Applications. 544-548, July 2021. On completion problems for various classes of P-matrices (2003 & 2004 REUs) Bowers, Evers, Hogben, Shaner, Snider, Wangsness Furthermore, matrices with k-involutory symmetries have been studied in [11, 12]. ( January - July ) of Algebraic Combinatorics year ( January - )... ) is the multiplicity of the new Journal Transactions on Combinatorics, p≡ p ≥ 0 UTC. ( n ), Art only the very best and most interesting papers are to be considered publication! Är 0.631 påverkansfaktor Analys, Trend, Ranking & Förutsägelse ELA 34 T.S.Oepomo whereB≡ a ( n ), in... 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