Search results for "MATHEMATICS"

A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

2020

The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.

Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

2022

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz-Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.

Reverse Catmull-Clark Subdivision

2006

Reverse subdivision consists in constructing a coarse mesh of a model from a finer mesh of this same model. In this paper, we give formulas for reverse Catmull-Clark subdivision. These formulas allow the constructing of a coarse mesh for almost all meshes. The condition for being able to apply these formulas is that the mesh to be reversed must be generated by the subdivision of a coarse mesh. Except for this condition, the mesh can be arbitrary. Vertices can be regular or extraordinary and the mesh itself can be arbitrary (triangular, quadrilateral…).

The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

2020

In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expressio…

Discussing Mathematical Learning and Mathematical Praxeologies from a Subject Scientific Perspective

2018

International audience; This programmatic contribution discusses the link between concepts from Anthropological Theory of Didactics (ATD) and the “subject-scientific point of view” according to Holzkamp (1985, 1993). The main common concern of ATD and the subject-scientific approach is to conceptualize and analyse “objects” like “institutionalized mathematical knowledge” and “university” not as conditions that cause reactions but essentially as meanings in the sense of generalized societal reified action possibilities. The link of both approaches is illustrated by the issue of “real numbers” in the transition from school to university: Hypotheses are derived for further actual-empirical res…

Location of solutions for quasi-linear elliptic equations with general gradient dependence

2017

Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.

Attacking TrustZone on devices lacking memory protection

2021

AbstractARM TrustZone offers a Trusted Execution Environment (TEE) embedded into the processor cores. Some vendors offer ARM modules that do not fully comply with TrustZone specifications, which may lead to vulnerabilities in the system. In this paper, we present a DMA attack tutorial from the insecure world onto the secure world, and the design and implementation of this attack in a real insecure hardware.

On arithmetic sums of Ahlfors-regular sets

2021

Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$ for all $\theta \in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.

Rozpoznawanie indywidualnych potrzeb edukacyjnych i wspieranie rozwoju uczniów w wieku wczesnoszkolnym z trudnościami w uczeniu się matematyki

2018

Finite-frequency spin susceptibility and spin pumping in superconductors with spin-orbit relaxation

2020

Static spin susceptibility of superconductors with spin-orbit relaxation has been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov. Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the ordinary and spin-orbit scattering. Using the developed formalism we study the linear spin pumping…