STRATIFIED TRANSVERSALITY OF HOLOMORPHIC MAPS

2013 ◽  
Vol 24 (13) ◽  
pp. 1350106 ◽  
Author(s):  
SAURABH TRIVEDI
Keyword(s):  
Weak Topology ◽  
Stein Manifold ◽  
Real Case ◽  
Holomorphic Maps ◽  
Countable Collection ◽  
Stein Manifolds ◽  
The Real ◽  
Oka Manifold ◽  
The Stability ◽  
Necessary And Sufficient

We discuss genericity and stability of transversality of holomorphic maps to complex analytic stratifications. We prove that the set of maps between Stein manifolds and Oka manifolds transverse to a countable collection of submanifolds in the target is dense in the space of holomorphic maps with the weak topology. This greatly generalizes earlier results on the genericity of transverse maps by Forstnerič and by Kaliman and Zaidenberg. As an application we show that the Whitney (a)-regularity of a complex analytic stratification is necessary and sufficient for the stability of transverse holomorphic maps between a Stein manifold and an Oka manifold. This gives an analogue of a theorem in the real case due to Trotman.

COMPLEXIFICATIONS OF HOLOMORPHIC ACTIONS AND THE BERGMAN METRIC

2004 ◽  
Vol 15 (08) ◽  
pp. 735-747 ◽  
Author(s):  
ANDREA IANNUZZI ◽  
ANDREA SPIRO ◽  
STEFANO TRAPANI
Keyword(s):  
Lie Groups ◽  
Complex Manifold ◽  
Analogous Result ◽  
Stein Manifold ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bergman Metric ◽  
Stein Manifolds ◽  
Invariant Domain ◽  
Necessary And Sufficient

Let G=(ℝ,+) act by biholomorphisms on a Stein manifold X which admits the Bergman metric. We show that X can be regarded as a G-invariant domain in a "universal" complex manifold X* on which the complexification [Formula: see text] of G acts. The analogous result holds for actions of a larger class of real Lie groups containing, e.g. abelian and certain nilpotent ones. For holomorphic actions of such groups on Stein manifolds, necessary and sufficient conditions for the existence of X* are given.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

Some Structural Properties of Systolic Tree Automata

1989 ◽  
Vol 12 (4) ◽  
pp. 571-585
Author(s):  
E. Fachini ◽  
A. Maggiolo Schettini ◽  
G. Resta ◽  
D. Sangiorgi
Keyword(s):  
Structural Properties ◽  
Stability Problem ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

scholarly journals All adapted topologies are equal

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder
Keyword(s):  
Stochastic Processes ◽  
Weak Topology ◽  
Equilibrium Problems ◽  
Diffusion Processes ◽  
Temporal Structure ◽  
Wasserstein Distance ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Nested Distance ◽  
The Stability

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.

Predictive Value of Assessing Vehicle Interior Design Ergonomics in a Virtual Environment

2004 ◽  
Vol 4 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Thomas Reuding ◽  
Pamela Meil
Keyword(s):  
Virtual Environments ◽  
Interior Design ◽  
Real World ◽  
Predictive Value ◽  
Work Processes ◽  
Complex Activity ◽  
Vehicle Interior ◽  
Design Work ◽  
The Real ◽  
The Stability

The predictive value and the reliability of evaluations made in immersive projection environments are limited when compared to the real world. As in other applications of numerical simulations, the acceptance of such techniques does not only depend on the stability of the methods, but also on the quality and credibility of the results obtained. In this paper, we investigate the predictive value of virtual reality and virtual environments when used for engineering assessment tasks. We examine the ergonomics evaluation of a vehicle interior, which is a complex activity relying heavily on know-how gained from personal experience, and compare performance in a VE with performance in the real world. If one assumes that within complex engineering processes certain types of work will be performed by more or less the same personnel, one can infer that a fairly consistent base of experience-based knowledge exists. Under such premises and if evaluations are conducted as comparisons within the VE, we believe that the reliability of the assessments is suitable for conceptual design work. Despite a number of unanswered questions at this time we believe this study leads to a better understanding of what determines the reliability of results obtained in virtual environments, thus making it useful for optimizing virtual prototyping processes and better utilization of the potential of VR and VEs in company work processes.

A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

2015 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Robust Stability ◽  
Convex Combination ◽  
Convexity Property ◽  
Ecological Principles ◽  
Sign Structure ◽  
Previous Solution ◽  
Peer Community ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Complete Dependence

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

A successful example of citizen science within the PRISMA network applied to the 15th March 2021 bolide over Italy

2021 ◽  
Author(s):  
Daniele Gardiol ◽  
Tiberio Cuppone ◽  
Giovanni Ascione ◽  
Dario Barghini ◽  
Albino Carbognani ◽  
...  
Keyword(s):  
Citizen Science ◽  
Video Recording ◽  
Real Case ◽  
The Real ◽  
The City

<p>PRISMA is the italian fireball network dedicated to observation of bright meteors and recovery of freshly fallen meteorites. Since the very beginning of the project, we experienced an increasing enthusiastic participation of non-professionals, starting from amateur astronomers and reaching an ever wider audience among citizens. Nowadays PRISMA has become an established italian stakeholder in the field of meteors and meteorites, being the reference for visual warnings, video recording of fireballs and report of suspect meteorite finds.</p> <p>In this contribution we will describe our experience on this topic and the methodologies we have developed to capitalize such potential, by actively training and involving citizens in activities focused on meteorite/meteorwrong identification and organized on-field search campaigns. We will show an application to the real case of the 15<sup>th</sup> march 2021 meteorite-dropping bolide in sourthern Italy, near the city of Isernia.</p>

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