A Logarithmic Minimization Property of the Unitary Polar Factor in the Spectral and Frobenius Norms

2014 ◽  
Vol 35 (3) ◽  
pp. 1132-1154 ◽  
Author(s):  
Patrizio Neff ◽  
Yuji Nakatsukasa ◽  
Andreas Fischle
Keyword(s):  
Polar Factor ◽  
Minimization Property

scholarly journals The minimization of matrix logarithms: On a fundamental property of the unitary polar factor

2014 ◽  
Vol 449 ◽  
pp. 28-42 ◽  
Author(s):  
Johannes Lankeit ◽  
Patrizio Neff ◽  
Yuji Nakatsukasa
Keyword(s):  
Fundamental Property ◽  
Polar Factor

scholarly journals On the free time minimizers of the NewtonianN-body problem

2013 ◽  
Vol 156 (2) ◽  
pp. 209-227 ◽  
Author(s):  
ADRIANA DA LUZ ◽  
EZEQUIEL MADERNA
Keyword(s):  
Special Class ◽  
Body Problem ◽  
Free Time ◽  
Global Minimization ◽  
Kam Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
Homothetic Motion ◽  
The Least Action Principle ◽  
Minimization Property

AbstractIn this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. An example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice ofx0, there should be at least one free time minimizerx(t)defined for allt≥ 0 and satisfyingx(0)=x0. We prove that such motions are completely parabolic. Using Marchal's theorem we deduce as a corollary that there are no entire free time minimizers, i.e. defined on$\mathbb{R}$. This means that the Mañé set of the NewtonianN-body problem is empty.

Conservation and Evolution of Marine and Coastal Ecosystems: Polar Factor

2021 ◽  
pp. 209-228
Author(s):  
Svetlana A. LIPINA ◽  
◽  
Pavel Yu. LAMOV ◽  
Keyword(s):  
Staff Training ◽  
Coastal Ecosystems ◽  
The Arctic ◽  
Polar Regions ◽  
Case Scenario ◽  
Ecological Problems ◽  
Polar Factor ◽  
The Antarctic ◽  
Local Levels

The paper presents an analysis of polar ecological policy actors. From this perspective, authors discuss in detail a role of state in conservation and development of marine and coastal ecosystems. Furthermore, they describe a green agenda for polar regions. At last, some ways for creating of ecological policies in the Arctic and the Antarctic regions, most especially on behalf of sea and marginal ecosystems conservation and evolution, are proposed. One of the most vital parts of such policies is staff training. The authors have attempted a comprehensive analysis of the Green Agenda at the global, national and local levels in terms of the effectiveness of its proposed mechanisms for the protection of biodiversity in polar areas. Researchers have also reviewed plans of Russia according to the new set of strategies for Arctic and Antarctic regions, which were adopted in 2020. The ideas proposed by the authors can be used in a real-case scenario both for strategies implementation and for public discussion on the global ecological problems.

Steric Crowding and the Reactivity of Substituted tert-Butyl Perbenzoates

1975 ◽  
Vol 53 (7) ◽  
pp. 979-985 ◽  
Author(s):  
Siddick Icli ◽  
Kandil A. Kandil ◽  
C. Thankachan ◽  
Thomas T. Tidwell
Keyword(s):  
Ground State ◽  
Hydrogen Abstraction ◽  
Activation Parameters ◽  
Carboxyl Group ◽  
Enhancing Effect ◽  
Tert Butyl ◽  
Rate Acceleration ◽  
Steric Crowding ◽  
Polar Factor

The relative rates of decomposition of peroxyesters in cumene at 100° and their activation parameters ΔH≠ (kcal/mol) and ΔS≠ (cal deg−1 mol−1) were tert-butyl perbenzoate (1) 1.0, 34.0, 9.3; tert-butyl pertoluate (7) 1.3, 32.2, 4.8; tert-butyl permesitoate (8) 11, 31.9, 8.4; and tert-butyl 2,4,6-tri-tert-butylperbenzoate (9) 29, 32.9, 13.0. Each peroxyester yielded the corresponding acid as one of the products. The reactions are all interpreted as proceeding through a rate-determining scission of the O—O bond to yield a benzoyloxy radical, which then undergoes competitive decarboxylation and hydrogen abstraction from the solvent. The small rate acceleration due to a para substituent is interpreted as due to a polar factor and the larger rate enhancing effect of the ortho substituents is interpreted as due to destabilization of the ground state due to twisting of the carboxyl group out of conjugation with the ring.

New perturbation bounds in unitarily invariant norms for subunitary polar factors

2018 ◽  
Vol 34 ◽  
pp. 231-239
Author(s):  
Lei Zhu ◽  
Wei-wei Xu ◽  
Hao Liu ◽  
Li-juan Ma
Keyword(s):  
Polar Decomposition ◽  
Positive Semidefinite ◽  
Perturbation Bounds ◽  
Unitarily Invariant Norms ◽  
Polar Factor ◽  
New Perturbation

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

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