The rational homotopy groups of Diff (M) and Homeo (Mn) in the stability range

1979 ◽  
pp. 604-626 ◽  
Author(s):  
D. Burghelea
Keyword(s):  
Homotopy Groups ◽  
Rational Homotopy ◽  
Stability Range ◽  
The Stability

scholarly journals Influence of the Al content on the phase transformations in Cu-Al-Ag alloys

2003 ◽  
Vol 28 (1) ◽  
pp. 33-38 ◽  
Author(s):  
A. T. Adorno ◽  
A. V. Benedetti ◽  
R. A. G. da Silva ◽  
M. Blanco
Keyword(s):  
Thermal Analysis ◽  
Differential Thermal Analysis ◽  
Transition Temperature ◽  
Phase Transformations ◽  
Decomposition Reaction ◽  
Phase Decomposition ◽  
Stability Range ◽  
X Ray ◽  
Al Content ◽  
The Stability

The influence of the Al content on the phase transformations in Cu-Al-Ag alloys was studied by classical differential thermal analysis (DTA), optical microscopy (OM) and X-ray diffractometry (XRD). The results indicated that the increase in the Al content and the presence of Ag decrease the rate of the <FONT FACE=Symbol>b</font>1 phase decomposition reaction and contribute for the raise of this transition temperature, thus decreasing the stability range of the perlitic phase resulted from the b1 decomposition reaction.

An arithmetic characterization of the rational homotopy groups of certain spaces

1979 ◽  
Vol 53 (2) ◽  
pp. 117-133 ◽  
Author(s):  
John B. Friedlander ◽  
Stephen Halperin
Keyword(s):  
Homotopy Groups ◽  
Rational Homotopy

scholarly journals Coformality and rational homotopy groups of spaces of long knots

2008 ◽  
Vol 15 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Greg Arone ◽  
Pascal Lambrechts ◽  
Victor Turchin ◽  
Ismar Volić
Keyword(s):  
Homotopy Groups ◽  
Rational Homotopy

scholarly journals Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor

1998 ◽  
Vol 120 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. D. Manring ◽  
G. R. Luecke
Keyword(s):  
Order System ◽  
Axial Piston Pump ◽  
Third Order ◽  
Stability Range ◽  
Hydrostatic Transmission ◽  
Control Gain ◽  
Variable Displacement ◽  
Linearized System ◽  
The Stability ◽  
Axial Piston

This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.

Rational Equivalence of Fibrations with Fibre G/K

1982 ◽  
Vol 34 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Stephen Halperin ◽  
Jean Claude Thomas
Keyword(s):  
Finite Type ◽  
Homotopy Type ◽  
Lie Group ◽  
The Other ◽  
Homotopy Groups ◽  
Homotopy Equivalence ◽  
Rational Homotopy ◽  
Algebraic Invariants ◽  
Associated Bundles ◽  
Connected Lie Group

Let be two Serre fibrations with same base and fibre in which all the spaces have the homotopy type of simple CW complexes of finite type. We say they are rationally homotopically equivalent if there is a homotopy equivalence between the localizations at Q which covers the identity map of BQ.Such an equivalence implies, of course, an isomorphism of cohomology algebras (over Q) and of rational homotopy groups; on the other hand isomorphisms of these classical algebraic invariants are usually (by far) insufficient to establish the existence of a rational homotopy equivalence.Nonetheless, as we shall show in this note, for certain fibrations rational homotopy equivalence is in fact implied by the existence of an isomorphism of cohomology algebras. While these fibrations are rare inside the class of all fibrations, they do include principal bundles with structure groups a connected Lie group G as well as many associated bundles with fibre G/K.

Aqueous nonelectrolyte solutions — Part XX: Formula of structure I methane hydrate, congruent dissociation melting point, and formula of the metastable hydrate

2003 ◽  
Vol 81 (12) ◽  
pp. 1443-1450 ◽  
Author(s):  
David N Glew
Keyword(s):  
Melting Point ◽  
Equilibrium Constant ◽  
Methane Hydrate ◽  
Equilibrium Constants ◽  
Stability Range ◽  
Congruent Melting Point ◽  
Quadruple Point ◽  
Dissociation Equilibrium ◽  
Metastable Structure ◽  
The Stability

Sixteen new measurements of high precision for structure I methane hydrate with water between 31.93 and 47.39 °C are shown to be metastable and exhibit higher methane pressures than found by earlier workers. Comparison of earlier measurements between 26.7 and 47.2 °C permit positive identification of the structure II and the structure I hydrates. Forty-nine equilibrium constants Kp(h1[Formula: see text]l1g) for dissociation of structure I methane hydrate into water and methane, 32 between –0.29 and 26.7 °C for the stable hydrate and 17 between 31.93 and 47.39 °C for the metastable hydrate, are best represented by a three-parameter thermodynamic equation, which indicates a standard error (SE) of 0.63% on a single Kp(h1[Formula: see text]l1g) determination. The congruent dissociation melting point C(h1l1gxm) of metastable structure I methane hydrate is at 47.41 °C with SE 0.02 °C and at pressure 505 MPa. The congruent equilibrium constant Kp(h1[Formula: see text]l1g) is 102.3 MPa with SE 0.2 MPa. ΔH°t(h1[Formula: see text]l1g) is 62 281 J mol–1 with SE 184 J mol–1, and the congruent formula is CH4·5.750H2O with SE 0.059H2O. At the congruent point, ΔV(h1[Formula: see text]l1g) is zero within experimental precision, and its estimate is 1.3 with SE 1.6 cm3 mol–1. The stability range of structure I methane hydrate with water extends from quadruple point Q(s1h1l1g) at –0.29 °C up to quadruple point Q(h1h2l1g) at 26.7 °C, and its metastability range with water extends from 26.7 °C up to the congruent dissociation melting point C(h1l1gxm) at 47.41 °C. Key words: methane hydrate, clathrate structure I, metastability range, dissociation equilibrium constant, formula, congruent melting point, metastability of structure I hydrate.

Observation of Less Heat Generation and Investigation of Its Effect on the Stability Range of a Nd:YAG Laser

2000 ◽  
Vol 39 (Part 1, No. 6A) ◽  
pp. 3419-3421 ◽  
Author(s):  
Chao-Chia Cheng ◽  
Tong-Long Huang ◽  
Sheng-Hsiung Chang ◽  
Hung-Sheng Tsai ◽  
Hai-Pei Liu
Keyword(s):  
Heat Generation ◽  
Nd:Yag Laser ◽  
Stability Range ◽  
The Stability

scholarly journals Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Aming Hao ◽  
Xiaolong Li ◽  
Longhua She
Keyword(s):  
Adaptive Control ◽  
Hopf Bifurcation ◽  
Large Scale ◽  
Stability Range ◽  
Hopf Bifurcation Point ◽  
Maglev System ◽  
Large Scale Disturbance ◽  
Excited Vibration ◽  
Parameter Variance ◽  
The Stability

EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.

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