Optimal Mutual Location of Compact Sets in Spaces Endowed with Euclidean Invariant Gromov–Hausdorif Metric

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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CALCULATION OF OPTIMAL INJECTION RATE FOR DISPERSED WATERFLOODING SYSTEM

Oil and Gas Studies ◽

10.31660/0445-0108-2017-6-63-67 ◽

2017 ◽

pp. 63-67

Author(s):

L. A. Vaganov ◽

A. Yu. Sencov ◽

A. A. Ankudinov ◽

N. S. Polyakova

Keyword(s):

Injection Rate ◽

Oil Field ◽

Injection Well ◽

Water Migration ◽

Mutual Location ◽

Optimal Injection ◽

Technical Measures ◽

Injection Rates

The article presents a description of the settlement method of necessary injection rates calculation, which is depended on the injected water migration into the surrounding wells and their mutual location. On the basis of the settlement method the targeted program of geological and technical measures for regulating the work of the injection well stock was created and implemented by the example of the BV7 formation of the Uzhno-Vyintoiskoe oil field.

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ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

Real Analysis Exchange ◽

10.2307/44153417 ◽

1982 ◽

Vol 8 (2) ◽

pp. 455

Author(s):

Akemann ◽

Bruckner

Keyword(s):

Continuous Functions ◽

Compact Sets

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Relatively compact sets of Heisenberg manifolds

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2021.101739 ◽

2021 ◽

Vol 76 ◽

pp. 101739

Author(s):

Sebastian Boldt

Keyword(s):

Compact Sets ◽

Heisenberg Manifolds

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Deep Learning Insights into Lanthanides Complexation Chemistry

Molecules ◽

10.3390/molecules26113237 ◽

2021 ◽

Vol 26 (11) ◽

pp. 3237

Author(s):

Artem A. Mitrofanov ◽

Petr I. Matveev ◽

Kristina V. Yakubova ◽

Alexandru Korotcov ◽

Boris Sattarov ◽

...

Keyword(s):

Deep Learning ◽

Stability Constants ◽

Black Box ◽

Lanthanide Ions ◽

Structure Property ◽

Target Property ◽

Mutual Location ◽

Molecule Structure ◽

Complexation Chemistry ◽

Main Influence

Modern structure–property models are widely used in chemistry; however, in many cases, they are still a kind of a “black box” where there is no clear path from molecule structure to target property. Here we present an example of deep learning usage not only to build a model but also to determine key structural fragments of ligands influencing metal complexation. We have a series of chemically similar lanthanide ions, and we have collected data on complexes’ stability, built models, predicting stability constants and decoded the models to obtain key fragments responsible for complexation efficiency. The results are in good correlation with the experimental ones, as well as modern theories of complexation. It was shown that the main influence on the constants had a mutual location of the binding centers.

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A Weak Hadamard Smooth Renorming of L1(Ω, μ)

Canadian Mathematical Bulletin ◽

10.4153/cmb-1993-055-5 ◽

1993 ◽

Vol 36 (4) ◽

pp. 407-413 ◽

Cited By ~ 17

Author(s):

Jonathan M. Borwein ◽

Simon Fitzpatrick

Keyword(s):

Compact Sets ◽

Weakly Compact ◽

Weakly Compact Sets

AbstractWe show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.

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