scholarly journals Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number

2012 ◽  
Vol 36 ◽  
pp. 26-31 ◽  
Author(s):  
Paweł Solarz
Keyword(s):  
Rotation Number ◽  
General Theorem ◽  
Iterative Roots

scholarly journals Singular values and bounded Siegel disks

2017 ◽  
Vol 165 (2) ◽  
pp. 249-265
Author(s):  
ANNA MIRIAM BENINI ◽  
NÚRIA FAGELLA
Keyword(s):  
Critical Point ◽  
Finite Order ◽  
Rotation Number ◽  
General Theorem ◽  
Singular Values ◽  
Transcendental Function ◽  
Siegel Disk ◽  
Entire Transcendental Function

AbstractLet f be an entire transcendental function of finite order and Δ be a forward invariant bounded Siegel disk for f with rotation number in Herman's class $\mathcal{H}$. We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.

scholarly journals Hodge decomposition of string topology

2021 ◽  
Vol 9 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C. Ramadoss ◽  
Yining Zhang
Keyword(s):  
Lie Algebras ◽  
General Theorem ◽  
Hodge Decomposition ◽  
String Topology ◽  
Free Loop Space ◽  
Oriented Manifold ◽  
Universal Enveloping Algebras ◽  
Finite Dimensional ◽  
Equivariant Homology ◽  
Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

The Generating Functions of Certain Special Determinants

1904 ◽  
Vol 24 ◽  
pp. 387-392 ◽  
Author(s):  
Thomas Muir
Keyword(s):  
Generating Functions ◽  
General Theorem ◽  
Image Position

(1) From a general theorem, known since 1855, and perhaps earlier, regarding the reciprocal of the seriesit follows thatwhere β0 = 1 and

scholarly journals Sets of Semi-Commutative Matrices

1933 ◽  
Vol 3 (3) ◽  
pp. 179-188
Author(s):  
J. Williamson
Keyword(s):  
General Theorem ◽  
Unit Matrix ◽  
Maximum Value ◽  
Image Position

In a paper entitled “Sets of anticommuting matrices” Eddington proved that if El, E2, …., Eqform a set of q four-rowed square matrices satisfying the relations,,where E is the unit matrix, then the maximum value of q is five. Later Newman showed that this result is a particular case of the general theorem that ifE1, E2, …., Eqform a set of q t-rowed square matrices satisfying (1), where t = 2Pτ and τ is odd, then the maximum value of q is 2p + 1.

Effects of Rotation on Heat Transfer for a Single Row Jet Impingement Array With Crossflow

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Justin A. Lamont ◽  
Srinath V. Ekkad ◽  
Mary Anne Alvin
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Rotation Number ◽  
Coriolis Force ◽  
Room Temperature ◽  
Turbine Blades ◽  
Target Surface ◽  
Channel Height ◽  
Potential Core ◽  
Single Row

The effects of the Coriolis force are investigated in rotating internal serpentine coolant channels in turbine blades. For complex flow in rotating channels, detailed measurements of the heat transfer over the channel surface will greatly enhance the blade designers’ ability to predict hot spots so coolant may be distributed more effectively. The present study uses a novel transient liquid crystal technique to measure heat transfer in a rotating, radially outward channel with impingement jets. A simple case with a single row of constant pitch impinging jets with the crossflow effect is presented to demonstrate the novel liquid crystal technique and document the baseline effects for this type of geometry. The present study examines the differences in heat transfer distributions due to variations in jet Rotation number, Roj, and jet orifice-to-target surface distance (H/dj = 1,2, and 3). Colder air, below room temperature, is passed through a room temperature test section to cause a color change in the liquid crystals. This ensures that buoyancy is acting in a similar direction as in actual turbine blades where walls are hotter than the coolant fluid. Three parameters were controlled in the testing: jet coolant-to-wall temperature ratio, average jet Reynolds number, Rej, and average jet Rotation number, Roj. Results show, such as serpentine channels, the trailing side experiences an increase in heat transfer and the leading side experiences a decrease for all jet channel height-to-jet diameter ratios (H/dj). At a jet channel height-to-jet diameter ratio of 1, the crossflow from upstream spent jets greatly affects impingement heat transfer behavior in the channel. For H/dj = 2 and 3, the effects of the crossflow are not as prevalent as H/dj = 1: however, it still plays a detrimental role. The stationary case shows that heat transfer increases with higher H/dj values, so that H/dj = 3 has the highest results of the three examined. However, during rotation the H/dj = 2 case shows the highest heat transfer values for both the leading and trailing sides. The Coriolis force may have a considerable effect on the developing length of the potential core, affecting the resulting heat transfer on the target surface.

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