Results 71 to 80 of about 118,435,286 (275)
On Algebraic Numbers of Small Height: Linear Forms in One Logarithm
Journal of Number Theory, 1994 The authors establish a lower bound for \(|\alpha -1|\) where \(\alpha\) is a complex algebraic number \(\neq 1\). This lower bound is completely explicit in terms of the degree \(D\) of \(\alpha\) and its Mahler measure \(M(\alpha)\). Given any number \(\mu>0\) with \(\mu\geq \log M(\alpha)\), the authors prove \[ |\alpha -1|\geq \exp \Bigl\{- \bigl( \
Mignotte, M., Waldschmidt, M.
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Transcendence of certain infinite sums involving rational functions [PDF]
, 2001 We show that it follows from results on linear forms in logarithms of algebraic numbers such as where χ is any non-principal Dirichlet character and (Fn∞n=0 the Fibonacci sequence, are ...
Genčev, Marian +4 more
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Gut microbiota alterations in patients with non‐small‐cell lung cancer undergoing chemoradiotherapy
Molecular Oncology, EarlyView.We investigated the impact of concurrent chemoradiotherapy (CRT) on the gut microbiota in patients with locally advanced non‐small‐cell lung cancer. Overall gut microbiota composition remained largely stable throughout CRT while antibiotic exposure may influence microbial diversity.
Hanne Marte Nymoen +19 more
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On the Two-Term Zeckendorf Representations of the Padovan and Perrin Sequences
Journal of Applied MathematicsIn this paper, we completely solve the Diophantine equations Pm=Fn+Fk and Em=Fn+Fk under the condition n≥k+2≥4, where Pm is the m-th Padovan number, Em is the m-th Perrin number, and Fk is the k-th Fibonacci number.
Awaou Lare Ousseni +3 more
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Charles Babbage's table of logarithms (1827) [PDF]
In 1827 Charles Babbage published his Table of logarithms of the natural numbers, from 1 to 108,000. His logarithms were generally considered to be the most accurate of his day and were reprinted on numerous occasions, well into the twentieth century ...
Campbell-Kelly, Martin
core
LINEAR FORMS IN TWO ELLIPTIC LOGARITHMS IN THE p-ADIC CASE
The principal aim of the present paper is to provide a new lower bound for linear forms in two p-adic elliptic logarithms. We refine a result due to Rémond and Urfels.
河野-平田, 典子 +5 more
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Molecular Oncology, EarlyView.We established the avian chorioallantoic membrane (CAM) assay as a scalable in vivo model for studying circulating tumor cells (CTCs). Human gastrointestinal tumors spontaneously released genetically validated CTCs that were detected across multiple platforms, demonstrating that the CAM model provides an accessible tool for investigating early cancer ...
Dennis Roth +17 more
wiley +1 more source
Linear forms at a basis of an algebraic number field
, 2012 It was proved by Cassels and Swinnerton-Dyer that the Littlewood conjecture in simultaneous Diophantine approximation holds for any pair of numbers in a cubic field.
Bernard de Mathan, DE MATHAN, Bernard
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Molecular Oncology, EarlyView.Incomplete microwave ablation (iMWA) of liver cancer triggers a biphasic progression in residual tumors. At Day 3, the microenvironment is characterized by acute inflammatory responses and extracellular matrix (ECM) remodeling. By Day 14, a profound shift occurs toward oncogenic signal transduction and immunosuppression, marked by macrophage ...
Yu Liu +9 more
wiley +1 more source
A note on the extension of some triangular Diophantine sets
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet n be an integer. We call a set of m distinct positive integers a triangular D(n)-m-tuple if the product of its two distinct elements increased by n is the triangular number. In this paper, we consider the extension of the triangular D(k)-pair {k, 2k},
Filipin Alan, Jurasić Ana, Togbé Alain
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