scholarly journals Nash multiplicities and isolated points of maximum multiplicity

2019 ◽  
Vol 223 (6) ◽  
pp. 2598-2614 ◽  
Author(s):  
Beatriz Pascual-Escudero
2019 ◽  
Vol 194 ◽  
pp. 390-408 ◽  
Author(s):  
Carlos Matheus ◽  
Carlos Gustavo Moreira

2014 ◽  
Vol 30 (2) ◽  
pp. 348-352 ◽  
Author(s):  
André G. P. Andrade ◽  
Janaine C. Polese ◽  
Leopoldo A. Paolucci ◽  
Hans-Joachim K. Menzel ◽  
Luci F. Teixeira-Salmela

Lower extremity kinetic data during walking of 12 people with chronic poststroke were reanalyzed, using functional analysis of variance (FANOVA). To perform the FANOVA, the whole curve is represented by a mathematical function, which spans the whole gait cycle and avoids the need to identify isolated points, as required for traditional parametric analyses of variance (ANOVA). The power variables at the ankle, knee, and hip joints, in the sagittal plane, were compared between two conditions: With and without walking sticks at comfortable and fast speeds. For the ankle joint, FANOVA demonstrated increases in plantar flexion power generation during 60–80% of the gait cycle between fast and comfortable speeds with the use of walking sticks. For the knee joint, the use of walking sticks resulted in increases in the knee extension power generation during 10–30% of the gait cycle. During both speeds, the use of walking sticks resulted in increased power generation by the hip extensors and flexors during 10–30% and 40–70% of the gait cycle, respectively. These findings demonstrated the benefits of applying the FANOVA approach to improve the knowledge regarding the effects of walking sticks on gait biomechanics and encourage its use within other clinical contexts.


1983 ◽  
Vol 29 (101) ◽  
pp. 70-77 ◽  
Author(s):  
J. F. Nye

AbstractIsotropic points are structurally stable features of any complicated field of stress or strain-rate, and therefore will almost always be present on the surface of a glacier. A given isotropic point for strain-rate will belong to one of six different classes, depending on the pattern (lemon, star, or monstar) of principal directions and the contours (ellipses or hyperbolas) of constant principal strain-rate values in its neighbourhood. The central isotropic point on a glacier should theoretically have a monstar pattern, but the contours around it may sometimes be elliptic and sometimes hyperbolic. Nearby, but not coincident with it there will be an isotropic point for stress. This will also have a monstar pattern but, in contrast to the strain-rate point, the contours around it must be hyperbolic. Published examples are consistent with these conclusions. In addition to isotropic points for strain-rate a glacier surface will contain isolated points of pure shear; these also can be classified into six different types. Stable features of this kind give information about the essential structure of a tensor field and form useful points of comparison between observation and numerical simulation.


1977 ◽  
Vol 20 (4) ◽  
pp. 513-514 ◽  
Author(s):  
John Ginsburg

AbstractIt is shown that the diagonal of X has a countable neighborhood base in X × X if and only if X is a metrizable space whose set of non-isolated points is compact.


2009 ◽  
Vol 205 (2) ◽  
pp. 179-189 ◽  
Author(s):  
Chris Good ◽  
Brian E. Raines ◽  
Rolf Suabedissen
Keyword(s):  

1971 ◽  
Vol 23 (2) ◽  
pp. 315-324 ◽  
Author(s):  
A. McD. Mercer

1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity1.1in which D2 = d2/du2. Furthermore, when g is a solution of y″ + λ2y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to1.2In this note we generalize these results to the real Euclidean space EN, our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of1.3to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.


1972 ◽  
Vol 24 (4) ◽  
pp. 622-630 ◽  
Author(s):  
Jack R. Porter ◽  
R. Grant Woods

Let X be a metric space. Assume either that X is locally compact or that X has no more than countably many isolated points. It is proved that if F is a nowhere dense subset of X, then it is regularly nowhere dense (in the sense of Katětov) and hence is contained in the topological boundary of some regular-closed subset of X. This result is used to obtain new properties of the remote points of the Stone-Čech compactification of a metric space without isolated points.Let βX denote the Stone-Čech compactification of the completely regular Hausdorff space X. Fine and Gillman [3] define a point p of βX to be remote if p is not in the βX-closure of a discrete subset of X.


2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Hanbiao Yang ◽  
Katsuro Sakai ◽  
Katsuhisa Koshino

Abstract Let X be an infinite compact metrizable space having only a finite number of isolated points and Y be a non-degenerate dendrite with a distinguished end point v. For each continuous map ƒ : X → Y , we define the hypo-graph ↓vƒ = ∪ x∈X {x} × [v, ƒ (x)], where [v, ƒ (x)] is the unique arc from v to ƒ (x) in Y . Then we can regard ↓v C(X, Y ) = {↓vƒ | ƒ : X → Y is continuous} as the subspace of the hyperspace Cld(X × Y ) of nonempty closed sets in X × Y endowed with the Vietoris topology. Let be the closure of ↓v C(X, Y ) in Cld(X ×Y ). In this paper, we shall prove that the pair , ↓v C(X, Y )) is homeomorphic to (Q, c0), where Q = Iℕ is the Hilbert cube and c0 = {(xi )i∈ℕ ∈ Q | limi→∞xi = 0}.


2019 ◽  
Vol 26 (2) ◽  
pp. 221-243
Author(s):  
Samir Elloumi

AbstractTextual Feature Selection (TFS) aims to extract relevant parts or segments from text as being the most relevant ones w.r.t. the information it expresses. The selected features are useful for automatic indexing, summarization, document categorization, knowledge discovery, so on. Regarding the huge amount of electronic textual data daily published, many challenges related to the semantic aspect as well as the processing efficiency are addressed. In this paper, we propose a new approach for TFS based on Formal Concept Analysis background. Mainly, we propose to extract textual features by exploring the regularities in a formal context where isolated points exist. We introduce the notion ofN-composite isolated points as a set ofNwords to be considered as a unique textual feature. We show that a reduced value ofN(between 1 and 3) allows extracting significant textual features compared with existing approaches even for non-completely covering an initial formal context.


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