Search results for "Counterexample"
showing 10 items of 48 documents
Finite Alphabet Control of Logistic Networks with Discrete Uncertainty
2014
We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative exampl…
Hidden oscillations in nonlinear control systems
2011
Abstract The method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden oscillations of control systems. In the present paper new analytical-numerical algorithm for hidden oscillation localization is discussed. Counterexamples construction to Aizerman's conjecture and Kalman's conjecture on absolute stability of control systems are considered.
Hairy black-holes in shift-symmetric theories
2020
Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current $J^2$ diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since $J^2$ is not a scalar quantity, since $J^\mu$ is not a diff-invariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function $G_5 \s…
A Note on added information in the RAS Procedure: reexamination of some evidence
2006
International audience; An example in Miernyk (1977) presented a rather counterintuitive result, namely that introducing accurate exogenous information into an RAS matrix estimating procedure could lead to an estimate that was worse than one generated by RAS using no exogenous information at all. This became an oft-cited black mark against RAS. Miller and Blair (1985) included a different (and small) illustration of the same possibility. It was recently pointed out by one of us that the Miller/Blair numerical results are wrong. For that reason, we decided to reexamine all the empirical evidence we could find on the subject. While figures in both Miernyk and Miller/Blair appear to be wrong, …
Isometries of nilpotent metric groups
2016
We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups, distinguished examples are sub-Riemannian Lie groups and, in particular, Carnot groups equipped with Carnot-Carath\'eodory distances. We study the regularity of isometries, i.e., distance-preserving homeomorphisms. Our first result is the analyticity of such maps between metric Lie groups. The second result is that if two metric Lie groups are connected and nilpotent then every isometry between the groups is the composition of a left translation and an isomorphism.…
A reflection approach to the broken ray transform
2013
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres $S^n$. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray t…
On minima of discrimination functions
2008
Abstract A discrimination function ψ ( x , y ) assigns a measure of discriminability to stimulus pairs x , y (e.g., the probability with which they are judged to be different in a same-different judgment scheme). If for every x there is a single y least discriminable from x , then this y is called the point of subjective equality (PSE) for x , and the dependence h ( x ) of the PSE for x on x is called a PSE function. The PSE function g ( y ) is defined in a symmetrically opposite way. If the graphs of the two PSE functions coincide (i.e., g ≡ h − 1 ), the function is said to satisfy the Regular Minimality law. The minimum level functions are restrictions of ψ to the graphs of the PSE funct…
Abnormal escape rates from nonuniformly hyperbolic sets
1999
Consider a $C^{1+\epsilon}$ diffeomorphism $f$ having a uniformly hyperbolic compact invariant set $\Omega$, maximal invariant in some small neighbourhood of itself. The asymptotic exponential rate of escape from any small enough neighbourhood of $\Omega$ is given by the topological pressure of $-\log |J^u f|$ on $\Omega$ (Bowen–Ruelle in 1975). It has been conjectured (Eckmann–Ruelle in 1985) that this property, formulated in terms of escape from the support $\Omega$ of a (generalized Sinai–Ruelle–Bowen (SRB)) measure, using its entropy and positive Lyapunov exponents, holds more generally. We present a simple $C^\infty$ two-dimensional counterexample, constructed by a surgery using a Bowe…
The forgotten mathematical legacy of Peano
2019
International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.
WHEN DEDUCTION LEADS TO BELIEF
1995
The paper questions the common assumption that rational individuals believe all propositions which they know to be logical consequences of their other beliefs: although we must acknowledge the truth of a proposition which is a deductive consequence of our beliefs, we may not genuinely believe it. This conclusion is defended by arguing that some familiar counterexamples to the claim that knowledge is justified true belief fail because they involve propositions which are not really believed. Beliefs guide conduct or issue in assertion by answering questions which arise in the course of deliberation and conversation, but the troublesome cases present propositions which do not present the agent…