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Strengthening emergency care capacity to increase inpatient admissions: a single-centre quality improvement project in Tokyo. [PDF]

BMJ Open Qual
Yanagawa T, Tamura M, Inui M, Fukumoto K, Sato M, Azuma K, Kurihara N.   +6 more
europepmc   +1 more source

Prognostic Modeling of 1-Year Survival in Hepatocellular Carcinoma: A Comparative Evaluation of Machine Learning Methods with Class Balancing. [PDF]

Diseases
Wang J, Li H, Ju C, Liu H.
europepmc   +1 more source

Regulation of Schistosoma infections in snail populations: a modelling framework with inheritable resistance in snails

van Dijk NJ, de Vlas SJ, Emery AM, Webster BL, Knopp S, Ali SM, Pennance T, Coffeng LE.   +7 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
openaire   +1 more source

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.
openaire   +1 more source

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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$$k$$ 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.
openaire   +3 more sources