Results 21 to 30 of about 125,919 (262)
Formulas for the Number of Spanning Trees in a Chain of Cycles
Sultan Qaboos University Journal for Science, 2010 We give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. The formula uses basic properties of continued fractions.
Thomas Bier
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Approximation by continued fractions [PDF]
Proceedings of the American Mathematical Society, 1974 Let x x be a real irrational number whose continued fraction has infinitely many partial quotients not less than
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The Generating Functions for Special Pringsheim Continued Fractions
Communications in Advanced Mathematical Sciences, 2020 In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated.
Ali Hikmet Değer, Ümmügülsün Akbaba
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Tasoev's continued fractions and Rogers–Ramanujan continued fractions
Journal of Number Theory, 2004 The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
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On the metrical theory of a non-regular continued fraction expansion
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the ...
Lascu Dan, Cîrlig George
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Continued fractions related to a group of linear fractional transformations
Open Mathematics, 2023 There are strong relations between the theory of continued fractions and groups of linear fractional transformations. We consider the group G3,3{G}_{3,3} generated by the linear fractional transformations a=1−1∕za=1-1/z and b=z+2b=z+2.
Demir Bilal
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Continued Fractions and Linear Fractional Transformations
Integers, 2014 Rational approximations to a square root $\sqrt{k}$ can be produced by iterating the transformation $f(x) = (dx+k)/(x+d)$ starting from $\infty$ for any positive integer $d$. We show that these approximations coincide infinitely often with continued fraction convergents if and only if $4d^2/(k-d^2)$ is an integer, in which case the continued fraction ...
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A Note on Continued Fractions [PDF]
Canadian Journal of Mathematics, 1960 Any real number y leads to a continued fraction of the type(1)where ai, bi are integers which satisfy the inequalities(2)by means of the algorithm(3)the a's being assigned positive integers. The process terminates for rational y; the last denominator bk satisfying bk ≥ ak + 1. For irrational y, the process does not terminate.
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Children with sickle cell disease (SCD) face multiple acute and chronic medical complications that may impact their quality of life as reported by patients themselves. Health‐related social needs (HRSNs), such as food and housing insecurity, are common in people with SCD, but the association between HRSNs and patient‐reported ...
Sarah J. Marks +5 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Fertility preservation (FP) is increasingly integrated into the care of pediatric patients exposed to gonadotoxic therapy or conditioning for hematopoietic stem cell transplantation (HSCT), yet perioperative data in infants and toddlers remain scarce.
Kerstin Saalabian +13 more
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