scholarly journals Bach-flat asymptotically locally Euclidean metrics

2004 ◽  
Vol 160 (2) ◽  
pp. 357-415 ◽  
Author(s):  
Gang Tian ◽  
Jeff Viaclovsky
2012 ◽  
Vol 22 (4) ◽  
pp. 832-877 ◽  
Author(s):  
Antonio G. Ache ◽  
Jeff A. Viaclovsky

2013 ◽  
Vol 43 (2) ◽  
pp. 237-248
Author(s):  
Steven B. Caudill ◽  
Franklin G. Mixon ◽  
C. Paul Mixon
Keyword(s):  

AIAA Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Zhoufang Xiao ◽  
Carl Ollivier-Gooch

2021 ◽  
Author(s):  
I.V. Stepanyan ◽  
S.S. Grokhovsky ◽  
O.V. Kubryak

Stabilometry is a modern method for assessing the functional state of a person by the ability to maintain a stable balance of an upright posture. Technically, the implementation of the stabilometry method consists in measuring, with the help of specialized devices, the values that make up the support reaction, with the subsequent determination, according to these measurements, of the coordinates of the center of body pressure on the support. The nature of the migrations of the center of pressure during the stabilometric study is a source of information about the features of the processes of postural regulation. At the same time, up to the present time, there is a problem of the correct interpretation of the results of stabilometry. The adequacy of the conclusions is largely determined by the human factor, i.e. qualification of a specialist analyzing stabilometry data. Thus, in our opinion, the task of objectifying the assessment of stabilometry results is urgent. The aim of this work is to study the possibility of applying the neurocluster method using self-organizing neural networks to objectify the analysis of stabilometry data. The authors proposed a technique for analyzing the structure of individual and group stabilometric data by clustering them using selforganizing Kohonen neural maps with Euclidean metrics. Neuroclusterization of stabilometric data allows in automatic mode (without human intervention) to identify the type of group of subjects corresponding to the norm or pathology, various types of pathologies, as well as individual biometric characteristics of the subjects. The subsequent analysis of the individual characteristics of the data of the subjects, grouped in this way, makes it possible to detect deviations indicating the presence of abnormalities or the formation of various pathological conditions, which can be useful for the early diagnosis of diseases.


2018 ◽  
Vol 51 (32) ◽  
pp. 850-854 ◽  
Author(s):  
Lempert Anna ◽  
Le Quang Mung

Author(s):  
Martin de Borbon ◽  
Cristiano Spotti

Abstract We construct Asymptotically Locally Euclidean (ALE) and, more generally, asymptotically conical Calabi–Yau metrics with cone singularities along a compact simple normal crossing divisor. In particular, this includes the case of the minimal resolution of 2D quotient singularities for any finite subgroup $\Gamma \subset U(2)$ acting freely on the three-sphere, hence generalizing Kronheimer’s construction of smooth ALE gravitational instantons.


Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 79 ◽  
Author(s):  
Constantin Udriste ◽  
Ionel Tevy

The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m-distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.


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