Search results for "continuity"
showing 10 items of 378 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…
Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments
2020
In the field of hydrology, stage&ndash
Persistence of orographic mixed‐phase clouds
2016
Mixed-phase clouds (MPCs) consist of ice crystals and supercooled water droplets at temperatures between 0 and approximately −38°C. They are thermodynamically unstable because the saturation vapor pressure over ice is lower than that over supercooled liquid water. Nevertheless, long-lived MPCs are ubiquitous in the Arctic. Here we show that persistent MPCs are also frequently found in orographic terrain, especially in the Swiss Alps, when the updraft velocities are high enough to exceed saturation with respect to liquid water allowing simultaneous growth of supercooled liquid droplets and ice crystals. Their existence is characterized by holographic measurements of cloud particles obtained …
Effects of a mobile disturbance pattern on dynamic patch networks and metapopulation persistence
2021
Abstract Motivation Certain early-succession habitats may emerge only at restricted locations following disturbance. Therefore, whether disturbances tend to occur at certain sites or not can significantly affect habitat availability and metapopulation persistence of early-successional habitat specialists. Available models that combine metapopulation and landscape processes do not address how to model mobile, spatially shifting disturbance intensities independent of factors of site suitability. We present a model that allows the study on how a mobile disturbance pattern, of either natural or anthropogenic origin, affects patch network and metapopulation dynamics in realistic, heterogeneous l…
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…
A risk assessment proposal for underground cavities in Hard Soils-Soft Rocks
2018
Abstract Underground calcarenite quarries in Marsala (Sicily) have been involved in a number of collapses that have, seriously damaged numerous buildings. The stability conditions were therefore examined in order to assess risk conditions within the historical centre of the town and the surrounding areas, which are subject to urban expansion. Starting with an extensive collection of historical information, the research was carried out through surveys of the cavities, systematic sampling of material, petrographic analysis and geotechnical testing. The results of laboratory tests and in situ investigations provided a geotechnical characterization of both the intact material and the rock mass.…