scholarly journals Generic properties of operator-dependent normal mappings

2021 ◽  
Vol 3 (2) ◽  
Keyword(s):  
Generic Properties

scholarly journals Some Generic Properties of Non Degeneracy for Critical Points of Functionals and Applications

2011 ◽  
Vol 79 (1) ◽  
pp. 285-291
Author(s):  
Marco Ghimenti ◽  
Anna Maria Micheletti
Keyword(s):  
Critical Points ◽  
Generic Properties

Generic properties of nonlinear functional equations

1983 ◽  
Vol 26 (1) ◽  
pp. 120-121
Author(s):  
Witold Jarczyk
Keyword(s):  
Functional Equations ◽  
Generic Properties ◽  
Nonlinear Functional

scholarly journals Generic Dynamical Properties of Connections on Vector Bundles

2021 ◽  
Author(s):  
Mihajlo Cekić ◽  
Thibault Lefeuvre
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Differential Operators ◽  
Parallel Transport ◽  
Conformal Killing ◽  
Generic Properties ◽  
Geometric Problems ◽  
Pseudo Differential Operators ◽  
Divergence Type ◽  
Open Question

Abstract Given a smooth Hermitian vector bundle $\mathcal{E}$ over a closed Riemannian manifold $(M,g)$, we study generic properties of unitary connections $\nabla ^{\mathcal{E}}$ on the vector bundle $\mathcal{E}$. First of all, we show that twisted conformal Killing tensors (CKTs) are generically trivial when $\dim (M) \geq 3$, answering an open question of Guillarmou–Paternain–Salo–Uhlmann [ 14]. In negative curvature, it is known that the existence of twisted CKTs is the only obstruction to solving exactly the twisted cohomological equations, which may appear in various geometric problems such as the study of transparent connections. The main result of this paper says that these equations can be generically solved. As a by-product, we also obtain that the induced connection $\nabla ^{\textrm{End}({\operatorname{{\mathcal{E}}}})}$ on the endomorphism bundle $\textrm{End}({\operatorname{{\mathcal{E}}}})$ has generically trivial CKTs as long as $(M,g)$ has no nontrivial CKTs on its trivial line bundle. Eventually, we show that, under the additional assumption that $(M,g)$ is Anosov (i.e., the geodesic flow is Anosov on the unit tangent bundle), the connections are generically opaque, namely that generically there are no non-trivial subbundles of $\mathcal{E}$ that are preserved by parallel transport along geodesics. The proofs rely on the introduction of a new microlocal property for (pseudo)differential operators called operators of uniform divergence type, and on perturbative arguments from spectral theory (especially on the theory of Pollicott–Ruelle resonances in the Anosov case).

scholarly journals Measures with maximum total exponent and generic properties of $C^{1}$ expanding maps

2013 ◽  
Vol 43 (3) ◽  
pp. 351-370 ◽  
Author(s):  
Takehiko Morita ◽  
Yusuke Tokunaga
Keyword(s):  
Generic Properties ◽  
Expanding Maps

Some generic properties of stochastic differential equations

1996 ◽  
Vol 57 (3-4) ◽  
pp. 235-245 ◽  
Author(s):  
K. Bahlali ◽  
B. Mezerdi ◽  
Y. Ouknine
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Generic Properties

scholarly journals Formal analysis of design process dynamics

2010 ◽  
Vol 24 (3) ◽  
pp. 397-423 ◽  
Author(s):  
Tibor Bosse ◽  
Catholijn M. Jonker ◽  
Jan Treur
Keyword(s):  
Design Process ◽  
Formal Analysis ◽  
Formal Theory ◽  
Generic Properties ◽  
Design Processes ◽  
Process Dynamics ◽  
To Come ◽  
Automated Support ◽  
Trace Language ◽  
Different Levels

AbstractThis paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design properties at different levels of aggregation. This approach is specifically suitable for component-based design processes. A complicating factor for supporting the design process is that not only the generic properties of design must be specified, but also the language chosen should be rich enough to allow specification of complex properties of the system under design. This requires a language rich enough to operate at these different levels. The Temporal Trace Language used in this paper is suitable for that. The paper shows that the analysis at the level of a design process as a whole and at subprocesses thereof is precise enough to allow for automatic simulation. Simulation allows the modeler to manipulate the specifications of the system under design to better understand the interlevel relationships in his design. The approach is illustrated by an example.

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