Search results for "Invariant"
showing 10 items of 783 documents
Maximal regularity for Kolmogorov operators in L2 spaces with respect to invariant measures
2006
Abstract We prove an optimal embedding result for the domains of Kolmogorov (or degenerate hypoelliptic Ornstein–Uhlenbeck) operators in L 2 spaces with respect to invariant measures. We use an interpolation method together with optimal L 2 estimates for the space derivatives of T ( t ) f near t = 0 , where T ( t ) is the Ornstein–Uhlenbeck semigroup and f is any function in L 2 .
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
Geometric Properties of Planar BV -Extension Domains
2009
We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.
Locality of order-invariant first-order formulas
1998
A query is local if the decision of whether a tuple in a structure satisfies this query only depends on a small neighborhood of the tuple. We prove that all queries expressible by order-invariant first-order formulas are local.
Cores for parabolic operators with unbounded coefficients
2009
Abstract Let A = ∑ i , j = 1 N q i j ( s , x ) D i j + ∑ i = 1 N b i ( s , x ) D i be a family of elliptic differential operators with unbounded coefficients defined in R N + 1 . In [M. Kunze, L. Lorenzi, A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients, Trans. Amer. Math. Soc., in press], under suitable assumptions, it has been proved that the operator G : = A − D s generates a semigroup of positive contractions ( T p ( t ) ) in L p ( R N + 1 , ν ) for every 1 ⩽ p + ∞ , where ν is an infinitesimally invariant measure of ( T p ( t ) ) . Here, under some additional conditions on the growth of the coefficients of A , which cover also some growths with an ex…
Conjugate unstable manifolds and their underlying geometrized Markov partitions
2000
Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.
Discrete Derivatives for Atom-Pairs as a Novel Graph-Theoretical Invariant for Generating New Molecular Descriptors: Orthogonality, Interpretation an…
2013
This report presents a new mathematical method based on the concept of the derivative of a molecular graph (G) with respect to a given event (S) to codify chemical structure information. The derivate over each pair of atoms in the molecule is defined as ∂G/∂S(vi , vj )=(fi -2fij +fj )/fij , where fi (or fj ) and fij are the individual frequency of atom i (or j) and the reciprocal frequency of the atoms i and j, respectively. These frequencies characterize the participation intensity of atom pairs in S. Here, the event space is composed of molecular sub-graphs which participate in the formation of the G skeleton that could be complete (representing all possible connected sub-graphs) or comp…
Periodic and quasi-periodic orbits of the dissipative standard map
2011
We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…
Control of Production-Distribution Systems under Discrete Disturbances and Control Actions
2011
This paper deals with the robust control and optimization of production-distribution systems. The model used in our problem formulation is a general network flow model that describes production, logistics, and transportation applications. The novelty in our formulation is in the discrete nature of the control and disturbance inputs. We highlight three main contributions: First, we derive a necessary and sufficient condition for the existence of robustly control invariant hyperboxes. Second, we show that a stricter version of the same condition is sufficient for global convergence to an invariant set. Third, for the scalar case, we show that these results parallel existing results in the set…
Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points
2018
In mathematical modeling it is often required the analysis of the vector field topology in order to predict the evolution of the variables involved. When a dynamical system is multi-stable the trajectories approach different stable states, depending on the initialmconditions. The aim of this work is the detection of the invariant manifolds of thesaddle points to analyze the boundaries of the basins of attraction. Once that a sufficient number of separatrix points is found a Moving Least Squares meshfree method is involved to reconstruct the separatrix manifolds. Numerical results are presented to assess the method referring to tri-stable models with complex attractors such as limit cycles o…