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24-hour NIHSS may be a reliable surrogate for 90-day mRS after mechanical thrombectomy-a prospective study in anterior and posterior circulation infarctions. [PDF]

Front Neurol
Liu Q, He Q, Luo J, Yang J, Zhu G.
europepmc   +1 more source

Enabling health and maintaining independence for older people at home: the 'HomeHealth' Randomised Controlled Trial.

Health Technol Assess
Walters K, Frost R, Barrado-Martín Y, Kalwarowsky S, Marston L, Pan S, Avgerinou C, Goodman C, Clegg A, Gardner B, Hopkins J, Mahmood F, Gould RL, Elaswarapou R, Jowett C, Skelton DA, Drennan VM, Cooper C, Kharicha K, Logan P, Prescot M, Thornton G, Rookes T, Catchpole J, Hunter R.   +24 more
europepmc   +1 more source

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Linear independence in bottleneck algebras

Fuzzy Sets and Systems, 1996
The paper presents ten diverse generalizations of the definition of vector independence over a field to that over a lattice used in recent literature [cf. e.g. \textit{M. Gondran} and \textit{M. Minoux}, L'indépendance linéaire dans les dioides, Bull. Dir. Etudes Rech., Sér. C Math. Inform. 38-48 (1978); \textit{K. H. Kim} and \textit{F. W.
Jan Plavka, Katarina Cechlárová
exaly   +3 more sources

On Linear Independence of Theta Values

Monatshefte Fur Mathematik, 2004
In this paper, the linear independence (over \(\mathbb{Q}\)) of the Tschakaloff function \[ T_q(z):=\sum_{n=0}^\infty z^n q^{-n(n-1)/2} \] is not only studied at distinct (arithmetically characterized) points \(z\), but also for different (a.c.) values of the parameter \(q\). More precisely, the main result can be described as follows.
Keijo Väänänen, Väänänen Keijo, Masaaki Amou   +2 more
exaly   +2 more sources

On the Independence of Linear Functionals of Linear Processes

SIAM Journal on Applied Mathematics, 1969
A class of continuous parameter random processes is defined whose members, $x(t)$, are integrals of a nonstationary random “filter” function, $h(t,\lambda )$, with respect to an independent increments process $Z(\lambda )$. Linear functionals l of $x(t)$ expressible as integrals of a random function $\phi (\lambda )$ with respect to $Z(\lambda )$ are ...
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Units and linear independence

Journal of Algebra and Its Applications, 2023
An algebra [Formula: see text] will be called fluid if for any linearly independent set [Formula: see text] consisting of units, the set [Formula: see text] of inverses of the elements of [Formula: see text] is also linearly independent. We consider various examples of fluid algebras and study fluid algebras in some specific settings including direct ...
Sergio R. López-Permouth, Jeremy Moore, Nick Pilewski, Steve Szabo   +3 more
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Linear Independence and Dependence

1978
A set of vectors E is said to be linearly dependent if there exist distinct vectors A1,..., A k in E and numbers a1,...,a k , not all zero, such that $$ {a_1}{{\rm{A}}_1}{\rm{ }} + {\rm{ }}{a_2}{{\rm{A}}_2}{\rm{ }} + {\rm{ }}...{\rm{ }} + {\rm{ }}{a_k}{{\rm{A}}_k} = 0. $$ (*) Equation (*) is called a linear relation between A1,...,A k .
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Linear Independence and Dimension

1995
The notions of linear independence and bases are defined and studied for arbitrary vector spaces. The notion of dimension is defined. To study bases for arbitrary vector spaces, the Hausdorff Maximum Principle is introduced and used. The properties of finite-dimensional vector spaces are considered.
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