Results 11 to 20 of about 157 (137)
Conical limit sets and continued fractions [PDF]
, 2007 Inspired by questions of convergence in continued fraction theory, Erdős, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Möbius maps acting on the Riemann sphere, S2.
Crane, Dr. Edward +5 more
core +4 more sources
The hyperbolic geometry of continued fractions K(1|bn) [PDF]
, 2006 The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fraction K(1|bn) diverges. H. S. Wall asks whether just convergence, rather than absolute convergence of ∑bn is sufficient for the divergence of K(1|bn).
Short, Ian
core +5 more sources
Convergence of Vectorial Continued Fractions Related to the Spectral Seminorm [PDF]
, 2008 We show that the spectral seminorm is useful to study convergence or divergence of vectorial continued fractions in Banach algebras because such convergence or divergence is related to a spectral ...
Amzil M +3 more
core +1 more source
On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture
, 2004 8 pagesWe consider the limit periodic continued fractions of Stieltjes $$ \frac{1}{1-} \frac{g_1 z}{1-} \frac{g_2(1-g_1) z}{1-} \frac{g_3(1-g_2)z}{1-...,}, z\in \mathbb C, g_i\in(0,1), \lim\limits_{i\to \infty} g_i=1/2, \quad (1) $$ appearing as Shur ...
Tsygvintsev, Alexei
core +3 more sources
A Theorem on Divergence in the General Sense for Continued Fractions [PDF]
, 2004 If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued ...
Bowman, Douglas, McLaughlin, James
core +3 more sources
Modelling stem cell differentiation related processes—A practical overview for biologists
FEBS Letters, EarlyView.Stem cell differentiation is complex and difficult to control experimentally. This review introduces suitable computational modelling approaches that can support stem cell research, from mechanistic ODE and abstract models to multiscale and deep learning methods.
Ricco Zeegelaar +4 more
wiley +1 more source
On The Divergence in the General Sense of q-Continued Fractions on the Unit Circle [PDF]
, 2003 We show, for each q-continued fraction G(q) in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which G(q) diverges in the general sense.
Bowman, Douglas, McLaughlin, James
core +1 more source
Design and analysis strategies for robust microbiome ageing research
FEBS Letters, EarlyView.The gut microbiome changes with age and associates with age‐related morbidity and mortality, establishing it as a potential biomarker and intervention target for ageing. Realising this potential requires methodological rigour, yet distinguishing biological signals from methodological artefacts remains challenging across cohorts. This review provides an
Mark Olenik +5 more
wiley +1 more source
Liver organoids: modelling complexity in homeostasis and disease
FEBS Letters, EarlyView.Studying liver in vitro has been challenging because simple 2D cell cultures fail to capture liver's cellular and architectural complexity. To bridge this gap, scientists increasingly use organoids, 3D liver models which better mimic liver composition and function. This review examines recent advances in liver organoid complexity and realism, discusses
Anna M. Dowbaj, Meritxell Huch
wiley +1 more source
FEBS Letters, EarlyView.This review focuses on the role of autophagy and mitophagy in maintaining pancreatic β‐cell function and homeostasis. We discuss how genetic defects affecting these pathways contribute to the development of type 1, type 2, monogenic, and gestational diabetes. We further explore their potential as therapeutic targets. Created in BioRender.
Yunkyeong Lee +2 more
wiley +1 more source