scholarly journals A Metric Space Approach on the Molecular vs. Chemical Similarity of Some Analgesic and Euphoric Compounds

2019 ◽  
Author(s):  
Demetrios Xenides ◽  
Dionisia Fostiropoulou ◽  
Dimitrios S Vlachos
Keyword(s):  
Metric Space ◽  
Clinical Findings ◽  
Space Theory ◽  
Chemical Similarity ◽  
Analgesic Drugs ◽  
Structural Indices ◽  
Space Approach

<p>There is a relentless effort on gaining information on the reason why some compounds could cause similar effects though they are or not structural similar. That is the chemical similarity that plays an equally important role and we approach it via metric space theory on a set of analgesic drugs and euphoric compounds. The findings of the present study are in agreement to these obtained via traditional structural indices moreover are in accord with clinical findings.</p>

scholarly journals A Metric Space Approach on the Molecular vs. Chemical Similarity of Some Analgesic and Euphoric Compounds

2019 ◽  
Author(s):  
Demetrios Xenides ◽  
Dionisia Fostiropoulou ◽  
Dimitrios S Vlachos
Keyword(s):  
Metric Space ◽  
Clinical Findings ◽  
Space Theory ◽  
Chemical Similarity ◽  
Analgesic Drugs ◽  
Structural Indices ◽  
Space Approach

<p>There is a relentless effort on gaining information on the reason why some compounds could cause similar effects though they are or not structural similar. That is the chemical similarity that plays an equally important role and we approach it via metric space theory on a set of analgesic drugs and euphoric compounds. The findings of the present study are in agreement to these obtained via traditional structural indices moreover are in accord with clinical findings.</p>

Decomposition Space Theory and the Bing Shrinking Criterion

2021 ◽  
pp. 62-76
Author(s):  
Christopher W. Davis ◽  
Boldizsár Kalmár ◽  
Min Hoon Kim ◽  
Henrik Rüping
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Embedding Theorem ◽  
Space Theory ◽  
Compact Metric Space ◽  
Decomposition Spaces ◽  
Compact Metric Spaces ◽  
Space Decomposition ◽  
Decomposition Space ◽  
Continuous Decomposition

‘Decomposition Space Theory and the Bing Shrinking Criterion’ gives a proof of the central Bing shrinking criterion and then provides an introduction to the key notions of the field of decomposition space theory. The chapter begins by proving the Bing shrinking criterion, which characterizes when a given map between compact metric spaces is approximable by homeomorphisms. Next, it develops the elements of the theory of decomposition spaces. A key fact is that a decomposition space associated with an upper semi-continuous decomposition of a compact metric space is again a compact metric space. Decomposition spaces are key in the proof of the disc embedding theorem.

Segmentation of statistical texture images using the metric space theory

1996 ◽  
Vol 53 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Sang Y. Doh ◽  
Rae-Hong Park
Keyword(s):  
Metric Space ◽  
Space Theory

Synthesis and Singularity Analysis of N-UU Parallel Wrists: A Symmetric Space Approach

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Yuanqing Wu ◽  
Marco Carricato
Keyword(s):  
Symmetric Space ◽  
Mirror Symmetry ◽  
Singularity Analysis ◽  
Space Theory ◽  
Euclidean Group ◽  
Half Angle ◽  
Symmetric Submanifold ◽  
Spherical Mechanism ◽  
Space Approach ◽  
Angle Property

We report some recent advances in kinematics and singularity analysis of the mirror-symmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace.

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