On the Real Group Actions Preserving a Pencil of Straight Lines in the Lobachevskii Space

2019 ◽  
Vol 63 (3) ◽  
pp. 25-30
Author(s):  
E. N. Sosov
Keyword(s):  
Group Actions ◽  
The Real ◽  
Lobachevskii Space ◽  
Real Group ◽  
Straight Lines

scholarly journals Effect of Neurofeedback Facilitation on Post-stroke Gait and Balance Recovery: A Randomized Controlled Trial

Neurology ◽  
2021 ◽  
pp. 10.1212/WNL.0000000000011989
Author(s):  
Masahito Mihara ◽  
Hiroaki Fujimoto ◽  
Noriaki Hattori ◽  
Hironori Otomune ◽  
Yuta Kajiyama ◽  
...  
Keyword(s):  
Randomized Controlled Trial ◽  
Motor Imagery ◽  
Controlled Trial ◽  
Cortical Activation ◽  
Gait Disturbance ◽  
Balance Recovery ◽  
The Real ◽  
Post Stroke ◽  
Randomized Controlled ◽  
Real Group

Objective:To test the hypothesis that supplementary motor area (SMA) facilitation with functional near-infrared spectroscopy mediated neurofeedback (fNIRS-NFB) augments post-stroke gait and balance recovery. Using the 3-meter-Timed Up-and-Go (TUG) test, we conducted this two-center, double-blind, randomized controlled trial involving 54 Japanese patients.Methods:Patients with subcortical stroke-induced mild-to-moderate gait disturbance more than 12 weeks from onset, underwent 6 sessions of SMA neurofeedback facilitation during gait- and balance-related motor imagery using fNIRS-NFB. Participants were randomly allocated to intervention (REAL: 28 patients) or placebo (SHAM: 26 patients) group. In the REAL group, the fNIRS signal contained participants’ cortical activation information. Primary outcome was TUG improvement, 4 weeks post intervention.Results:The REAL group showed greater improvement in the TUG test (12.84 ± 15.07 s, 95% CI: 7.00-18.68) than the SHAM group (5.51± 7.64 s, 95% CI: 2.43 – 8.60; group difference 7.33 s, 95% CI: 0.83 – 13.83; p = 0.028), even after adjusting for covariates (group × time interaction; F1.23,61.69 = 4.50, p = 0.030, partial η2 = 0.083). Only the REAL group showed significantly increased imagery-related SMA activation and enhancement of resting-state connectivity between SMA and ventrolateral premotor area. Adverse effects associated with fNIRS-mediated neurofeedback intervention were absent.Conclusion:SMA facilitation during motor imagery using fNIRS neurofeedback may augment post-stroke gait and balance recovery by modulating the SMA and its related network.Classification of Evidence:This study provides Class III evidence that for patients with gait disturbance from subcortical stroke, SMA neurofeedback facilitation improves TUG time.

An Easy Proof for Some Classical Theorems in Plane Geometry

1992 ◽  
Vol 35 (4) ◽  
pp. 560-568 ◽  
Author(s):  
C. Thas
Keyword(s):  
Projective Plane ◽  
Projective Geometry ◽  
The Other ◽  
Plane Geometry ◽  
The Real ◽  
Easy Proof ◽  
Special Cases ◽  
Euclidean Planes ◽  
Straight Lines ◽  
Short Method

AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).

Exact Transient Response of an Elastic Half Space Loaded Over a Rectangular Region of Its Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 516-522 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Real Axis ◽  
Transient Response ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Impulsive Loading ◽  
Rectangular Region ◽  
The Real ◽  
Algebraic Expressions ◽  
Straight Lines

The response of an elastic half space to a normal impulsive loading over one half and also over one quarter of its bounding surface is considered. By a simple superposition the solution is obtained for a half space loaded on a finite rectangular region. In each case the solution was found to be a superposition of plane waves directly under the load, plus waves emanating from bounding straight lines and the corners of the loaded region. The solution was found by Cagniard’s technique and by extending the real transformation of de Hoop to double Fourier integrals with singularities on the real axis of the transform variables. Velocities in the interior of the half space are given for arbitrary values of Poisson’s ratio in terms of single integrals and algebraic expressions.

scholarly journals Increased Accuracy of Emotion Recognition in Individuals with Autism-Like Traits after Five Days of Magnetic Stimulations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Pingping Liu ◽  
Guixian Xiao ◽  
Kongliang He ◽  
Long Zhang ◽  
Xinqi Wu ◽  
...  
Keyword(s):  
Emotion Recognition ◽  
Sham Group ◽  
Recognition Accuracy ◽  
Autism Spectrum ◽  
Social Deficits ◽  
Resting State Functional Connectivity ◽  
The Real ◽  
Neural Modulation ◽  
Real Group ◽  
The Right

Individuals with autism-like traits (ALT) belong to a subclinical group with similar social deficits as autism spectrum disorders (ASD). Their main social deficits include atypical eye contact and difficulty in understanding facial expressions, both of which are associated with an abnormality of the right posterior superior temporal sulcus (rpSTS). It is still undetermined whether it is possible to improve the social function of ALT individuals through noninvasive neural modulation. To this end, we randomly assigned ALT individuals into the real (n=16) and sham (n=16) stimulation groups. All subjects received five consecutive days of intermittent theta burst stimulation (iTBS) on the rpSTS. Eye tracking data and functional magnetic resonance imaging (fMRI) data were acquired on the first and sixth days. The real group showed significant improvement in emotion recognition accuracy after iTBS, but the change was not significantly larger than that in the sham group. Resting-state functional connectivity (rsFC) between the rpSTS and the left cerebellum significantly decreased in the real group than the sham group after iTBS. At baseline, rsFC in the left cerebellum was negatively correlated with emotion recognition accuracy. Our findings indicated that iTBS of the rpSTS could improve emotion perception of ALT individuals by modulating associated neural networks. This stimulation protocol could be a vital therapeutic strategy for the treatment of ASD.

Real Moment Map and Hyperkähler Geometry Techniques: The Cotangent Bundle to the 2-Sphere and SL(2, ℂ)-Adjoint Orbits

2012 ◽  
Vol 19 (02) ◽  
pp. 181-218
Author(s):  
Ralph J. Bremigan
Keyword(s):  
Complex Manifold ◽  
Cotangent Bundle ◽  
Adjoint Action ◽  
Moment Map ◽  
Semisimple Element ◽  
Reductive Groups ◽  
The Real ◽  
Real Group ◽  
Adjoint Orbits ◽  
Hyperkähler Geometry

Going back to Kirwan and others, there is an established theory that uses moment map techniques to study actions by complex reductive groups on Kähler manifolds. Work of P. Heinzner, G. Schwarz, and H. Stötzel has extended this theory to actions by real reductive groups. In this paper, we apply these techniques to actions of the real group SU(1,1) ⊂ SL(2, ℂ) on a certain complex manifold of dimension two. More precisely, because of the SU(2)-invariant hyperkähler structure on this manifold, we are able to study a family of actions which includes and “interpolates” two well-known actions of SL(2, ℂ): the adjoint action on the orbit of a semisimple element of 𝔰𝔩(2, ℂ), and the action of SL(2, ℂ) on the cotangent bundle of the flag variety of SL(2, ℂ).

Will the Real Group Worker Please Stand Up!

1988 ◽  
Vol 11 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ruth Middleman ◽  
Beulah Rothman
Keyword(s):  
The Real ◽  
Real Group

scholarly journals The comparison of different teaching approaches related to the achievements of students’ knowledge and skills

2015 ◽  
Vol 34 (2) ◽  
pp. 389
Author(s):  
Shemsedin Abduli ◽  
Slobotka Aleksovska ◽  
Bujar Durmishi
Keyword(s):  
Control Group ◽  
Traditional Teaching ◽  
Teaching Approaches ◽  
Control Groups ◽  
Simulation Experiments ◽  
Knowledge And Skills ◽  
The Real ◽  
Real Group ◽  
Second Year ◽  
Test Of Knowledge

<p>This paper presents the comparative aspects of the efficiency of three different teaching approaches on the acquisition of students’ knowledge and skills. The research was carried out with students (245 in total) of the second year of secondary schools from three different cities in Macedonia in relation to the topic <em>pH and Indicators</em>. In one of the groups (so-called Control group), the traditional teaching approach was used; in the second, simulation experiments were carried out (Sim group); and in the third group, real experiments were performed (Real group). After the accomplishment of the topic a test of knowledge was implemented. The statistical analysis of the results showed that the Real and Sim groups showed better results than Control groups. Some of the questions concerning the understanding of the processes on molecular level were better answered in Sim groups, however, in general, it was concluded that the real experiments approach was the most efficient.</p>

Sylvester's Problem for Spreads of Curves

1980 ◽  
Vol 32 (1) ◽  
pp. 219-239 ◽  
Author(s):  
Kym S. Watson
Keyword(s):  
Continuous Family ◽  
Real Plane ◽  
Line Segments ◽  
The Real ◽  
Continuous Analogue ◽  
Sylvester’S Problem ◽  
Straight Lines

Spreads of curves were introduced by Grunbaum in [1]. A spread of curves is a continuous family of simple arcs in the real plane, every two of which intersect in exactly one point. A spread is the continuous analogue of a finite arrangement of pseudolines in the plane. Sylvester's problem for finite arrangements of pseudolines asks if every non-trivial arrangement has a simple vertex, that is a point contained in exactly two pseudolines of the arrangement. This question was answered in the affirmative by Kelly and Rottenberg [5]. One interesting feature of this result is that it does not depend on the pseudolines being straight lines.Here we settle Sylvester's problem for spreads. We show that every nontrivial spread of line segments has uncountably many simple vertices. But we also give examples of non-trivial spreads with no simple vertices.

scholarly journals Geometrical Notes

1884 ◽  
Vol 3 ◽  
pp. 38-42 ◽  
Author(s):  
J. S. Mackay
Keyword(s):  
Middle Point ◽  
The Real ◽  
Straight Line ◽  
Straight Lines

A straight line KK′ meets the circumference of a circle at two real or two imaginary points K, K′, and H is the middle point of the real or imaginary chord KK′. If A, B, C, D be any four points on the circumference, and the pairs of straight lines AB, DC, AC, BD, AD, CB meet KK′ at the pairs of points E,E′, F,F′, G,G′; then if any one pair of points be equidistant from H, the two other pairs will also be equidistant.

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