Results 231 to 240 of about 84,298 (262)

A unified framework for detecting point and collective anomalies in operating system logs via collaborative transformers. [PDF]

Sci Rep
Nasirzadeh M, Tahmoresnezhad J, Rashidi-Khazaee P.   +2 more
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Oral Cancer Detection By Using Tabular Data Synthesis and Classification. [PDF]

IEEE Int Conf Data Min Workshops
Xue Z, Rajaraman S, Liang Z, Marini N, Antani S.   +4 more
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The <i>R</i> = 1 threshold can misclassify epidemic stability. [PDF]

Commun Phys
Parag KV, Santillana M, Cori A, Obolski U.   +3 more
europepmc   +1 more source

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Balancing Numbers as Sum of Same Power of Consecutive Balancing Numbers

Vietnam Journal of Mathematics, 2022
The sequence of balancing numbers \( \{B_n\}_{n\ge 0} \) is defined by the binary recurrence \( B_0=0 \), \( B_1=1 \), and \( B_{n+!}=6B_n-B_{n-1} \) for all \( n\ge 1 \). In the paper under review, the authors study the Diophantine equation \[ B_n^{x}+B_{n+1}^{x}+\cdots +B_{n+k-1}^{x}=B_m,\tag{1} \] in positive integers \( (m,n,k,x) \).
Souleymane Nansoko, Euloge Tchammou, Alain Togbé   +2 more
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On $(a,b)$-balancing numbers

Publicationes Mathematicae Debrecen, 2010
A positive integer \(n\) is a balancing number if \(1 +\dots + (n - 1) = (n + 1) + \dots + (n + r)\) holds with some positive integer \(r\). The problem of finding balancing numbers goes back to the work of \textit{R. Finkelstein} [Am.\ Math.\ Mon.\ 72, 1082--1088 (1965; Zbl 0151.03305)].
Kovács, Tünde, Liptai, Kálmán, Olajos, Péter   +2 more
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Periodicity of Balancing Numbers

Acta Mathematica Hungarica, 2014
The balancing numbers originally introduced by \textit{A. Behera} and \textit{G. K. Panda} [Fibonacci Q. 37, No. 2, 98--105 (1999; Zbl 0962.11014)] as solutions of a Diophantine equation on triangular numbers possess many interesting properties. Many of these properties are comparable to certain properties of Fibonacci numbers, while some others are ...
Panda, G. K., Rout, S. S.
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$$k$$ k -Gap balancing numbers

Periodica Mathematica Hungarica, 2015
A natural number \(n\) is called a balancing number with balancer \(r\) if \[ 1 + 2 + \ldots + (n - 1) = (n + 1) + (n + 2) + \ldots + (n + r). \] On other hand \(n\) is called a cobalancing number with cobalancer \(r\) if \[ 1 + 2 + \ldots + n = (n + 1) + (n + 2) + \ldots + (n + r). \] Several papers in this area are presently available.
Sudhansu Sekhar Rout, Gopal Krishna Panda   +1 more
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On the number of balanced signed graphs

The Bulletin of Mathematical Biophysics, 1967
The classical enumeration theorem of Polya (Acta Math.,68, 145–254, 1937) is applied to a modified version of Harary’s (Pacific J. Math.,8, 743–755, 1958) generating functions for counting bicolored graphs to derive a counting function for the number of balanced signed graphs. Methods for computing these counting polynomial functions are discussed.
Harary, Frank, Palmer, Edgar M.
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Factoriangular numbers in balancing and Lucas-balancing sequence

Boletín de la Sociedad Matemática Mexicana, 2020
The balancing numbers \(\{B_n\}_{n\ge 0}\) have initial terms \(B_0=0,~B_1=1\) and satisfy the recurrence \(B_{n+2}=6B_{n+1}-B_n\) for all \(n\ge 0\). The Lucas-balancing numbers \(\{C_n\}_{n\ge 0}\) have initial terms \(C_0=1,~C_1=3\) and satisfy the same recurrence relation as the balancing numbers.
Sai Gopal Rayaguru, Japhet Odjoumani, Gopal Krishna Panda   +2 more
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