Search results for " continuity."
showing 10 items of 229 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Effects of local forest continuity on the diversity of fungi on standing dead pines
2018
Human-induced fragmentation affects forest continuity, i.e. availability of a suitable habitat for the target species over a time period. The dependence of wood-inhabiting fungi on landscape level continuity has been well demonstrated, but the importance of local continuity has remained controversial. In this study, we explored the effects of local forest continuity (microhabitat and stand level) on the diversity of wood-inhabiting fungi on standing dead trunks of Scots pine (Pinus sylvestris L.). We studied species richness and community composition of decomposers and Micarea lichens on 70 trunks in 14 forests in central Finland that differed in their state of continuity. We used dendrochr…
Adaptive control of uncertain nonlinear systems with quantized input signal
2018
Abstract This paper proposes new adaptive controllers for uncertain nonlinear systems in the presence of input quantization. The control signal is quantized by a class of sector-bounded quantizers including the uniform quantizer, the logarithmic quantizer and the hysteresis quantizer. To clearly illustrate our approaches, we will start with a class of single-loop nonlinear systems and then extend the results to multi-loop interconnected nonlinear systems. By using backstepping technique, a new adaptive control algorithm is developed by constructing a new compensation method for the effects of the input quantization. A hyperbolic tangent function is introduced in the controller with a new tr…
Adaptive Control of Quantized Uncertain Nonlinear Systems
2017
Abstract This paper proposes a new adaptive controller for uncertain nonlinear systems in presence of quantized input signal and unknown external disturbance. A hysteresis quantizer is incorporated to reduce chattering phenomenon. By proposing a new transformation of the final control signal, using the sector-bound property of the quantizer and introducing a hyperbolic tangent function, the effects from input quantization and external disturbance are effectively compensated and the Lipschitz condition required for the nonlinear functions in the systems is removed. Besides showing global stability, tracking error performance is also established and can be adjusted by tuning certain design pa…
Adaptive consensus of uncertain nonlinear systems with event triggered communication and intermittent actuator faults
2019
This paper investigates distributed consensus tracking problem for uncertain nonlinear systems with event-triggered communication. The common desired trajectory information and each subsystem's state will be broadcast to their linked subsystems only when predefined triggering conditions are satisfied. Compared with the existing related literature, the main features of the results presented in this paper include four folds. (i) A totally distributed adaptive control scheme is developed for multiple nonlinear systems without Lipschitz condition, while with parametric uncertainties. (ii) The derivative of desired trajectory function is allowed unknown by all subsystems and directed communicati…
In nomine patris: Discursive strategies and ideology in the Cosa Nostra family discourse
2017
Abstract The article investigates how Cosa Nostra family discourse is characterized by a series of discursive strategies that give shape to specific ideological structures. By analysing a TV interview to the son of Bernardo Provenzano, boss of Cosa Nostra, it is possible to understand how the criminal values and practices are maintained and reproduced within the father–son relationship. Specifically, we show how the son justifies, legitimises or denies the criminal actions of his father. The ideology of Cosa Nostra seems to be based on the inter-generational cultural continuity of its members, on the family as main locus of adherence, reductionism of its mediatic image, amoralism as father–…
Estimates for the differences of positive linear operators and their derivatives
2019
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
2015
We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…