Search results for "Polygon"

Locally Convex Quasi *-Algebras

2020

This chapter is devoted to locally convex quasi *-algebras and locally convex quasi C*-algebras. Both these notions generalize what we have discussed in Chaps. 3 and 5. The advantage is, of course, that the range of applications becomes larger and larger; the drawback is that the theory becomes more involved.

Creating “mathematically” sustainable world: from the spirograph, a reverse path

2014

The approach to the subject of mathematic learning, represents, in the pedagogical-educational field, a problematic situation. Nowadays we attend to an heated discussion on the character of the basic mathematical concepts, on the analytical-critical succession between processes and objects. The purpose of these notes is to recover and to value the contribution of the autopoiesis theory in the characterization of the mathematical domain going beyond the mere reiteration, inspecting and testing new and generative paths of ideas. In this mechanism we would insert the use of the spirograph as a disturbing, uncertain element able to nourish the “mind-system”.

Nonlinear multivalued Duffing systems

2018

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).

Existence and Relaxation Results for Second Order Multivalued Systems

2021

AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$ A ( x ) and of a multivalued perturbation $F(t,x,y)$ F ( t , x , y ) which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$ D ( A ) ≠ R N and $D(A)= \mathbb{R}^{N}$ D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

The stability problem and noisy projections in discrete tomography

2004

Abstract The new field of research of discrete tomography will be described in this paper. It differs from standard computerized tomography in the reduced number of projections. It needs ad hoc algorithms which usually are based on the definition of the model of the object to reconstruct. The main problems will be introduced and an experimental simulation will prove the robustness of a slightly modified version of a well known method for the reconstruction of binary planar convex sets, even in case of projections affected by error. To the best of our knowledge this is one of the first experimental study of the stability problem with a statistical approach. Prospective applications include c…

Advanced SVG Triangulation/Polygonalization of Digital Images

2005

Registration of arbitrary multi-view 3D acquisitions

2013

International audience; To register 3D meshes representing smooth surfaces we track the 3D digitization system using photogrammetric techniques and calibrations. We present an example by digitizing a 800 mm x 600 mm portion of a car door. To increase the tracking accuracy the 3D scanner is placed in a cubic frame of side 0.5 m covered with 78 targets. The target frame moves in a volume that is approximately 1100 mm x 850 mm x 900 mm, to digitize the area of interest. Using four cameras this target frame is tracked with of an accuracy of 0.03 mm spatially and 0.180 mrad angularly. A registration accuracy between 0.1 mm and 2 mm is reached. This method can be used for the registration of mesh…

Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws

2007

We review a conservative finite difference shock capturing scheme that has been used by our research team over the last years for the numerical simulations of complex flows [3, 6]. This scheme is based on Shu and Osher’s technique [9] for the design of highly accurate finite difference schemes obtained by flux reconstruction procedures (ENO, WENO) on Cartesian meshes and Donat-Marquina’s flux splitting [4]. We then motivate the need for mesh adaptivity to tackle realistic hydrodynamic simulations on two and three dimensions and describe some details of our Adaptive Mesh Refinement (AMR) ([2, 7]) implementation of the former finite difference scheme [1]. We finish the work with some numerica…

Steady-state radiation heat transfer problem

1996

In Section 8.2, we shall see that the steady-state radiative heat transfer problem can be transformed to minimization of a smooth nonquadratic functional J over a convex and closed subset of a Banach space V. To this end we firstly shortly recall some basic definitions concerning differentiability of J, because these sometimes differ in the literature.

On Γ-convergence of pairs of dual functionals

2011

Abstract The paper considers a slightly modified notion of the Γ-convergence of convex functionals in uniformly convex Banach spaces and establishes that under standard coercitivity and growth conditions the Γ-convergence of a sequence of functionals { F j } to F ˜ implies that the corresponding sequence of dual functionals { F j ⁎ } converges in an analogous sense to the dual to F ˜ functional F ˜ ⁎ .