Search results for "Polygon"
showing 10 items of 282 documents
Broken ray transform on a Riemann surface with a convex obstacle
2014
We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of the obstacle. Our proof is based on a Pestov identity with boundary terms, and it involves Jacobi fields on broken rays. We also discuss applications of the broken ray transform.
Measure differential inclusions: existence results and minimum problems
2020
AbstractWe focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to…
Dynamics of the Selkov oscillator.
2018
A classical example of a mathematical model for oscillations in a biological system is the Selkov oscillator, which is a simple description of glycolysis. It is a system of two ordinary differential equations which, when expressed in dimensionless variables, depends on two parameters. Surprisingly it appears that no complete rigorous analysis of the dynamics of this model has ever been given. In this paper several properties of the dynamics of solutions of the model are established. With a view to studying unbounded solutions a thorough analysis of the Poincar\'e compactification of the system is given. It is proved that for any values of the parameters there are solutions which tend to inf…
Locally convex quasi $C^*$-normed algebras
2012
Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Size and shape effects on the thermodynamic properties of nanoscale volumes of water
2017
Small systems are known to deviate from the classical thermodynamic description, among other things due to their large surface area to volume ratio compared to corresponding big systems. As a consequence, extensive thermodynamic properties are no longer proportional to the volume, but are instead higher order functions of size and shape. We investigate such functions for second moments of probability distributions of fluctuating properties in the grand-canonical ensemble, focusing specifically on the volume and surface terms of Hadwiger's theorem, explained in Klain, Mathematika, 1995, 42, 329–339. We resolve the shape dependence of the surface term and show, using Hill's nanothermodynamics…
Inflection points and topology of surfaces in 4-space
2000
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
Semi-Regular Triangle Remeshing: A Comprehensive Study
2014
Semi-regular triangle remeshing algorithms convert irregular surface meshes into semi-regular ones. Especially in the field of computer graphics, semi-regularity is an interesting property because it makes meshes highly suitable for multi-resolution analysis. In this paper, we survey the numerous remeshing algorithms that have been developed over the past two decades. We propose different classifications to give new and comprehensible insights into both existing methods and issues. We describe how considerable obstacles have already been overcome, and discuss promising perspectives.
MULTIRESOLUTION ANALYSIS FOR IRREGULAR MESHES WITH APPEARANCE ATTRIBUTES
2004
We present a new multiresolution analysis framework based on the lifting scheme for irregular meshes with attributes. We introduce a surface prediction opera- tor to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geomet- rical analysis of the model.We present an application to adaptive visualization and some experimental results to show the efficiency of our framework.
Multiresolution Analysis for Meshes with Appearance Attributes
2005
International audience; We present a new multiresolution analysis framework for irregular meshes with attributes based on the lifting scheme. We introduce a surface prediction operator to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geometrical analysis of the model. A set of experimental results are given to show the efficiency of our framework. We present two applications to adaptive visual-ization and denoising.