Boundary singularities of N -harmonic functions

We construct N-harmonic functions in a domain with one isolated singularity on the boundary of the domain. By using solutions of the spherical p-harmonic spectral problem, we give an inductive method to produce a large variety of separable p-harmonic functions.Comment: 14 pages. To appear in Communications in Partial Differential equation

Boundary Harnack inequality and a priori estimates of singular solutions of quasilinear elliptic equations

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a domain.Comment: 17 page

A Lightweight Security Protocol for NFC-based Mobile Payments

© 2016 Published by Elsevier B.V. In this work, we describe a security solution that can be used to securely establish mobile payment transactions over the Near-Field Communication (NFC) radio interface. The proposed solution is very lightweight one; it uses symmetric cryptographic primitives on devices having memory and CPU resources limitations. We show that our approach maintains the security of NFC communications and we further demonstrate that our solution is simple, scalable, cost-effective, and incurs minimal computational processing overheads

DocCert: Nostrification, Document Verification and Authenticity Blockchain Solution

Many institutions and organizations require nostrification and verification of qualification as a prerequisite for hiring. The idea is to recognize the authenticity of a copy or digital document issued by an institution in a foreign country and detect forgeries. Certificates, financial records, health records, official papers and others are often required to be attested from multiple entities in distinct locations. However, in this digital era where most applications happen online, and document copies are uploaded, the traditional signature and seal methods are obsolete. In a matter of minutes and with a simple photo editor, a certificate or document copy may be plagiarized or forged. Blockchain technology offers a decentralized approach to record and verify transactions without the need for huge infrastructure investment. In this paper, we propose a blockchain based nostrification system, where awarding institutions generate a digital certificate, store in a public but permissioned blockchain, where students and other stakeholders may verify. We present a thorough discussion and formal evaluation of the proposed system.Comment: The Fifth International Conference on Blockchain Computing and Applications (BCCA 2023), held in Conjunction with Kuwait Fintech and Blockchain Summit 2023, 24,26 Oct 2023, Kuwait City, Kuwai

Boundary singularities of solutions of N-harmonic equations with absorption

We study the boundary behaviour of solutions u of $− \Delta_Nu + |u|^{q−1}u = 0$ in a bounded smooth domain $\Omega ⊂ R^N$ subject to the boundary condition u = 0 except at one point, in the range $q >N−1$.We prove that if $q \geq 2N −1$ such an u is identically zero, while, if $N −

Privacy-Preserving and Efficient Aggregation for Smart Grid based on Blockchain

In this paper, we address the problem of privacy-preserving of the consumer’s energy measurements in the context of the SG. To this end, we present a blockchain-based approach to preserve the privacy for smart grid users and to detect data forgery, replay attacks, and data injection attacks

Long-term integrity and non-repudiation protocol for multiple entities

© 2017 Smart cities aim at developing new applica-tions and architectures to improve the quality of urban services. However, privacy and security are still two of the technical issues that remain unsolved. The reason is that traditional solutions such as Public Key Infrastructures (PKI) were created to ensure some security services such as non-repudiation and data integrity. PKI enable the use of digital certificates and public key cryptosystems and require the cooperation among multiple entities to verify the certificates validity and to maintain a certificate revocation list. Due to the latest development in quantum computing, PKI-based solutions will not be able to provide continuous data integrity and non-repudiation. In fact, the techniques used by today PKI-based solutions to sign docu-ments are not future-proof. To address these drawbacks, we propose an efficient, lightweight non-repudiation protocol for multiples entities that makes use of Merkle tree and of a Hash function that is future-proof. In contrast to PKI-based solutions, we demonstrate the efficiency of our proposed approach in terms of its low transmission and message overheads, and ability to maintain continuous data integrity and non-repudiation for smart cities’ applications and services

Singularités au bord de solutions d'équations quasilinéaires

This thesis divided into five chapters, is devoted to the study of two types of equations: p-harmonic equation and p-harmonic equation with absorption. The first chapter is devoted to the study of the boundary singularities of p-harmonic functions into a half-space. In order to characterize the boundary singularities in any smooth domain, we derive a series of boundary Harnack inequalities for positive solutions of some quasilinear equations, this is imposed into the second chapter. In the third chapter, we study the existence and the classification of positive singular solutions of p-harmonic equation with absorption in a spherical cone. In some cases we prove that the isolated singularities are removable, and in another case we show the existence of two distinct types of singularities. In the last two chapters, we extend these results to a general domain, but in the case p = N. We also give a device to construct by induction separable p-harmonic functions.Les travaux présentés dans cette thèse sont regroupés en cinq chapitres. Ils traitent de deux types d'équations: L'équation p-harmonique et l'équation p-harmonique avec absorption. Le premier chapitre est consacré à l'étude de la singularité au bord dans le demi-espace. Dans le deuxième chapitre nous montrons les inégalités de Harnack au bord pour certaines types d'équations quasilinéaires. Dans le troisième chapitre, nous étudions les singularités possibles des solutions p-harmoniques avec absorption dans un cone. Nous montrons l'éliminabilité des singularités dans certains cas et l'existence des solutions singulières de deux types dans d'autres cas. Dans les deux derniers chapitres, nous généralisons les résultats du chapitre précédent dans un domaine régulier pour le cas p=N. Nous donnons aussi une méthode de construction des fonctions p-harmoniques séparables par récurrence.TOURS-BU Sciences Pharmacie (372612104) / SudocSudocFranceF

DocCert: Nostrification, Document Verification and Authenticity Blockchain Solution

Many institutions and organizations require nostrification and verification of qualification as a prerequisite for hiring. The idea is to recognize the authenticity of a copy or digital document issued by an institution in a foreign country and detect forgeries. Certificates, financial records, health records, official papers and others are often required to be attested from multiple entities in distinct locations. However, in this digital era where most applications happen online, and document copies are uploaded, the traditional signature and seal methods are obsolete. In a matter of minutes and with a simple photo editor, a certificate or document copy may be plagiarized or forged. Blockchain technology offers a decentralized approach to record and verify transactions without the need for huge infrastructure investment. In this paper, we propose a blockchain based nostrification system, where awarding institutions generate a digital certificate, store in a public but permissioned blockchain, where students and other stakeholders may verify. We present a thorough discussion and formal evaluation of the proposed system