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Frequency and phenotype of GAA-FGF14 disease in bilateral vestibulopathy syndromes: insights from repeat expansion carriers, including a case of co-occurrence with RFC1-related CANVAS. [PDF]

open access: yesJ Neurol
Pellerin D   +11 more
europepmc   +1 more source
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On Series Expansions and Stochastic Matrices

SIAM Journal on Matrix Analysis and Applications, 1993
Summary: Let \(P(0)\in R^{n\times n}\) be a stochastic matrix representing transition probabilities in a Markov chain, which is completely decomposable into \(m\) independent chains plus a number of transient states. Also, suppose that for all \(\varepsilon>0\) small enough \(P(\varepsilon)\equiv P(0)+\varepsilon C\) is a stochastic matrix representing
Moshe Haviv, Yaacov Ritov
openaire   +2 more sources

Power series expansion and structural analysis for life cycle assessment

open access: yesInternational Journal of Life Cycle Assessment, 2007
Goal, Scope and Background. The usefulness of power series expansion for an LCA system has often been doubted, as those systems may not possess the unique properties that enable power series expansion and analyses based on the power series.
Sangwon Suh   +2 more
exaly   +2 more sources

Beta-expansion and continued fraction expansion over formal Laurent series

open access: yesFinite Fields and Their Applications, 2008
Let x∈I be an irrational element and n⩾1, where I is the unit disc in the field of formal Laurent series F((X−1)), we denote by kn(x) the number of exact partial quotients in continued fraction expansion of x, given by the first n digits in the β ...
Jun Wu
exaly   +2 more sources

Interpretation of functional series expansions

Annals of Biomedical Engineering, 1991
While much research has been devoted to the implementation and application of Volterra and Wiener functional series expansions in the identification and characterization of biological systems, little effort has been focused on the fundamental problem of interpreting the resulting kernels.
W, Krenz, L, Stark
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On Series Expansions for the Renewal Moments

Biometrika, 1963
SUMMARY Given a renewal situation specified by a 'lifetime' distribution function F(t), let H(t) be the renewal function and qS.(t) the nth 95-moment. Then two (integral) recurrence equations are developed for OSn. The first expresses 0. in terms of On-, and H, and the second is an integral equation involving On, On-, and F.
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Expansions in series of Legendre functions

Proceedings of the London Mathematical Society, 1992
The Legendre functions\(P_\nu ^\mu (x)\)occurring in this paper are sometimes called modlfied Legendre functions, or Legendre functions on the cut. They are defined in [2, p.143, eq. (6)] as $$P_{v}^{x}(x) = \frac{1}{{\Gamma (1 - \mu )}}{{\left( {\frac{{1 + x}}{{1 - x}}} \right)}^{{\frac{1}{2}\mu }}}F\left( { - v;1 + v;1 - \mu ;\frac{{1 - x}}{2 ...
E. R. Love, M. N. Hunter
openaire   +1 more source

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