Search results for "mathematics"

Comments on “Overflow characteristics of streamlined weirs based on model experimentation” by Bagheri S. and Kabiri-Samani A

2021

Abstract In this paper the stage-discharge equation of a streamlined weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationship are estimated using the experimental results by Bagheri and Kabiri-Samani.

Flow measurement using circular portable flume

2018

Abstract The circular portable flume is a simple device to measure discharge in circular drainage networks. Since the unit can be easily installed and removed, it is helpful in water distribution measurement and management. First in this paper the available studies are reviewed for highlighting the effect of both the contraction ratio and the flume slope on the stage-discharge relationship. Then the Buckingham's Theorem of the dimensional analysis and the self-similarity theory are used to deduce the stage-discharge curve of the circular flume. The new theoretical stage-discharge equation is calibrated by the literature available experimental data and those obtained in this experimental inv…

Closure to “Extraction of the Flow Rate Equation under Free and Submerged Flow Conditions in Pivot Weirs with Different Side Contractions” by N. Shei…

2018

Analytical approach extending the Granier method to radial sap flow patterns

2020

Abstract The Granier thermal dissipation (TD) method is probably the most applied method to compute the transpiration flux of trees, due to its simplicity and effective compromise between theory and data availability. Starting from the heat transfer equations at the basis of Granier’s method, the objective of this paper is to derive an analytical solution for the transpiration flux to extend the sap flow equations to the radial domain. We adopted a flexible approach to cope with the differences in radial sapflow density (SFD) profile shapes that are known to occur in relation to wood anatomy (diffuse porous vs. ring- or non-porous xylem). With this purpose, we investigated the robustness of…

Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold

2017

This technical note addresses the structure preserving stabilization by output feedback of conservative input-output contact systems, a class of input-output Hamiltonian systems defined on contact manifolds. In the first instance, achievable contact forms in closed-loop and the associated Legendre submanifolds are analysed. In the second instance the stability properties of a hyperbolic equilibrium point of a strict contact vector field are analysed and it is shown that the stable and unstable manifolds are Legendre submanifolds. In the third instance the consequences for the design of stable structure preserving output feedback are derived: in closed-loop one may achieve stability only rel…

Adaptive-Gain Observers and Applications

2007

We distinguish two kinds of observers for nonlinear systems which are used by scientists and engineers: empirical observers and converging observers.

Субфинслерова задача на группе Картана

2019

Изучается задача субфинслеровой геометрии на свободной нильпотентной группе ранга $2$ глубины $3$. Такая группа также называется группой Картана, она имеет естественную структуру группы Карно, на которой вводится метрика с помощью $\ell _\infty $-нормы на ее первом слое. Используются методы теории оптимального управления. С помощью принципа максимума Понтрягина охарактеризованы экстремальные кривые. Описаны анормальные и особые дуги, построен релейный поток.

Modified F-transform Based on B-splines

2018

The aim of this paper is to improve the F-transform technique based on B-splines. A modification of the F-transform of higher degree with respect to fuzzy partitions based on B-splines is done to extend the good approximation properties from the interval where the Ruspini condition is fulfilled to the whole interval under consideration. The effect of the proposed modification is characterized theoretically and illustrated numerically.

Metric Rectifiability of ℍ-regular Surfaces with Hölder Continuous Horizontal Normal

2021

Abstract Two definitions for the rectifiability of hypersurfaces in Heisenberg groups $\mathbb{H}^n$ have been proposed: one based on ${\mathbb{H}}$-regular surfaces and the other on Lipschitz images of subsets of codimension-$1$ vertical subgroups. The equivalence between these notions remains an open problem. Recent partial results are due to Cole–Pauls, Bigolin–Vittone, and Antonelli–Le Donne. This paper makes progress in one direction: the metric Lipschitz rectifiability of ${\mathbb{H}}$-regular surfaces. We prove that ${\mathbb{H}}$-regular surfaces in $\mathbb{H}^{n}$ with $\alpha $-Hölder continuous horizontal normal, $\alpha> 0$, are metric bilipschitz rectifiable. This impr…

A Novel Intelligent Technique of Invariant Statistical Embedding and Averaging via Pivotal Quantities for Optimization or Improvement of Statistical …

2020

In the present paper, for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a decision criterion and averaging this criterion over pivots’ probability distributions is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging via pivotal quantities (ISE&APQ) is independent of the choice of priors and represents a novelty i…