scholarly journals DIFFERENTIAL-ALGEBRAIC JET SPACES PRESERVE INTERNALITY TO THE CONSTANTS

2015 ◽  
Vol 80 (3) ◽  
pp. 1022-1034
Author(s):  
ZOE CHATZIDAKIS ◽  
MATTHEW HARRISON-TRAINOR ◽  
RAHIM MOOSA
Keyword(s):  
Algebraic Variety ◽  
Tangent Bundle ◽  
Jet Space ◽  
Analytic Geometry ◽  
Jet Spaces ◽  
Generic Point ◽  
Generic Type ◽  
Finite Dimensional ◽  
Generic Behaviour

AbstractSuppose p is the generic type of a differential-algebraic jet space to a finite dimensional differential-algebraic variety at a generic point. It is shown that p satisfies a certain strengthening of almost internality to the constants. This strengthening, which was originally called “being Moishezon to the constants” in [9] but is here renamed preserving internality to the constants, is a model-theoretic abstraction of the generic behaviour of jet spaces in complex-analytic geometry. An example is given showing that only a generic analogue holds in the differential-algebraic case: there is a finite dimensional differential-algebraic variety X with a subvariety Z that is internal to the constants, such that the restriction of the differential-algebraic tangent bundle of X to Z is not almost internal to the constants.

scholarly journals Jet and prolongation spaces

2010 ◽  
Vol 9 (2) ◽  
pp. 391-430 ◽  
Author(s):  
Rahim Moosa ◽  
Thomas Scanlon
Keyword(s):  
Algebraic Variety ◽  
Jet Spaces ◽  
Abstract Setting ◽  
The Difference

AbstractThe notion of a prolongation of an algebraic variety is developed in an abstract setting that generalizes the difference and (Hasse) differential contexts. An interpolating map that compares these prolongation spaces with algebraic jet spaces is introduced and studied.

scholarly journals Ideals on the Quantum Plane’s Jet Space

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 352
Author(s):  
Andrey Glubokov
Keyword(s):  
Prime Ideals ◽  
Jet Space ◽  
Quantum Plane ◽  
Prime Spectrum ◽  
Jet Spaces

The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (Theorems 1–4) about the prime spectrum of these rings.

Two kinds of finite-dimensional integrable reduction to the Harry–Dym hierarchy

2016 ◽  
Vol 30 (32n33) ◽  
pp. 1650396
Author(s):  
Jinbing Chen
Keyword(s):  
Hamiltonian Systems ◽  
Tangent Bundle ◽  
Type Systems ◽  
Lax Pair ◽  
Symplectic Space ◽  
Spatial Variables ◽  
Parametric Solutions ◽  
Finite Dimensional ◽  
Neumann Type ◽  
Temporal And Spatial

In this paper, two kinds of finite-dimensional integrable reduction are studied for the Harry–Dym (HD) hierarchy. From the nonlinearization of Lax pair, the HD hierarchy is reduced to a class of finite-dimensional Hamiltonian systems (FDHSs) in view of a Bargmann map and a set of Neumann type systems by a Neumann map, which separate temporal and spatial variables on the symplectic space [Formula: see text] and the tangent bundle of ellipsoid [Formula: see text], respectively. It turns out that involutive solutions of the resulted finite-dimensional integrable systems (FDISs) directly give rise to finite parametric solutions of HD hierarchy through the Bargmann and Neumann maps. The finite-gap potential to the high-order stationary HD equation is obtained that cuts out a finite-dimensional invariant subspace for the HD flows. Finally, some comparisons of two kinds of integrable reductions are then discussed.

scholarly journals INTEGRABLE SYSTEMS ON TANGENT BUNDLE OF MULTI-DIMENSIONAL SPHERE

2017 ◽  
Vol 20 (7) ◽  
pp. 60-69
Author(s):  
N.V. Pokhodnya ◽  
M.V. Shamolin
Keyword(s):  
Force Field ◽  
Integrable Systems ◽  
Tangent Bundle ◽  
First Integrals ◽  
Dimensional Sphere ◽  
Elementary Functions ◽  
Finite Dimensional ◽  
Transcendental Functions

The systems which have finite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tan- gent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimen- sional sphere under increase of its dimension and absence of force field is ana- lyzed. At that, nonconservative fields of forces are presented with the presence of which the systems possess the complete choice of first integrals expressing in terms of finite combination of elementary functions and are, in general, the transcendental functions of its variables.

Numerical Solution of Constrained Systems Using Jet Spaces

2007 ◽  
Author(s):  
Jukka Tuomela ◽  
Teijo Arponen ◽  
Villesamuli Normi
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Constrained Systems ◽  
Lagrangian Formalism ◽  
Jet Space ◽  
Jet Spaces ◽  
Conservation Of Energy ◽  
Holonomic Constraints ◽  
Motion Constraints ◽  
Spurious Oscillations

The major difficulty in simulations of constrained systems is how to avoid drift off and spurious oscillations. We describe results obtained by our method which addresses these issues. Our computational model considers differential equations in jet spaces. In case of multibody systems we use Lagrangian formalism to derive the equations of motion. Constraints and possible invariants (like conservation of energy) are taken into account by restricting the dynamics to an appropriate submanifold of a jet space. We will consider only holonomic constraints in this paper. However, nonholonomic problems can also be formulated and solved with our method.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Tire Treadwear — A Comprehensive Evaluation of the Factors: Generic Type, Aspect Ratio, Tread Pattern, and Tread Composition Part III: Results of Supplementary and UTQG Treadwear Test Series

1986 ◽  
Vol 14 (4) ◽  
pp. 235-263
Author(s):  
A. G. Veith
Keyword(s):  
Carbon Black ◽  
Comprehensive Evaluation ◽  
Work Intensity ◽  
Generic Type ◽  
Aspect Ratios ◽  
Index Variation ◽  
Primary Determinant ◽  
Severity Levels ◽  
High Test ◽  
Better Than

Abstract The effect of tread compound variation on tire treadwear was studied using bias and radial tires of two aspect ratios. Compound variations included types of rubber and carbon black as well as the levels of carbon black, process oil, and curatives. At low to moderate test severity, SBR and an SBR/BR blend performed better than NR while at high test severity NR and SBR were better than the SBR/BR blend. The SBR/BR blend was the best at low severity testing. Higher structure and higher surface area carbon black gave improved treadwear at all severity levels. The concept of a “frictional work intensity” as the primary determinant of treadwear index variation with test severity is proposed. Some factors which influence frictional work intensity are discussed.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

Sign in / Sign up

Export Citation Format

Share Document