Search results for "differential geometry"
showing 10 items of 462 documents
Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces
2011
We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.
Fixed Points for Pseudocontractive Mappings on Unbounded Domains
2010
We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integral equations is given.
Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces
2012
Abstract We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples. MSC:47H10, 54H25.
Development of an earth observation processing chain for crop bio-physical parameters at local scale
2015
This paper proposes a full Earth observation processing chaing for biophysical parameter estimation at local scales. In particular, we focus on the Leaf Area Index (LAI) as an essential climate variable required for the monitoring and modeling of land surfaces at local scale. The main goal of this study is tied to the use of optical satellite images to retrieve Earth Observation (EO) biophysical parameters able to describe the spatio-temporal changes in agro-ecosystems at local scale. The objective of this work is two-fold: (i) to set up and update the EO products processing chain at high resolution (local) scale; and (ii) derive multitemporal LAI maps at 30 m resolution to be fed into a cr…
The Identification of Convex Function on Riemannian Manifold
2014
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://10.1155/2014/273514 The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds. © 2014 Li Zou e…
Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution
2015
We construct the time-optimal synthesis for 3 problems that are linear in the control and with polytopic constraints in the controls. Namely, the Brockett integrator, the Grushin plane, and the Martinet distribution. The main purpose is to illustrate the steps in solving an optimal control problem and in particular the use of second order conditions. The Grushin and the Martinet case are particularly important: the first is the prototype of a rank-varying distribution, the second of a non-equiregular structure.
Corrections to “Multipactor Susceptibility Charts for Ridge and Multi-Ridge Waveguides” [Dec 12 3601-3607]
2014
The authors have detected an error in Section IV-A in the above paper (ibid., vol. 59, no. 12, pp. 3601-3607, Dec. 2012). The analyzed rectangular waveguide in the actual version of the article is the WR137, instead of the WR90. As a consequence, the corrections presented here have to be implemented.
Development and validation of a nonlinear dynamic impact model for a notch impact
2015
Finite element simulations are being more and more applied when studying the crash-worthiness of vehicles during impact. This paper deals with setting up such a simulation and discusses several ways to simplify and verify a simulated crash. For this purpose, a notch impact-testing machine will be released from a certain angle and crash into a model constructed with three different wall thicknesses. The plastic and elastic deformation is measured in the front of the model and is then used for validation of the simulation. In the end, the simulation was found to be in good agreement with the real crash data.
G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel
1981
Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].
Symbolic integration of hyperexponential 1-forms
2019
Let $H$ be a hyperexponential function in $n$ variables $x=(x_1,\dots,x_n)$ with coefficients in a field $\mathbb{K}$, $[\mathbb{K}:\mathbb{Q}] <\infty$, and $\omega$ a rational differential $1$-form. Assume that $H\omega$ is closed and $H$ transcendental. We prove using Schanuel conjecture that there exist a univariate function $f$ and multivariate rational functions $F,R$ such that $\int H\omega= f(F(x))+H(x)R(x)$. We present an algorithm to compute this decomposition. This allows us to present an algorithm to construct a basis of the cohomology of differential $1$-forms with coefficients in $H\mathbb{K}[x,1/(SD)]$ for a given $H$, $D$ being the denominator of $dH/H$ and $S\in\mathbb{K}[x…