Zeraoulia Rafik

Counterexamples and corrections concerning a 2025 paper on Ulam stability of a fractional boundary-value problem

This independent mathematical comment examines the published formulations in I. Nasrallah, R. Aouafi and S. Kouachi, Mathematics 13 (2025), 157, DOI: 10.3390/math13010157. An explicit example satisfies the printed hypotheses of the uniqueness theorem while admitting infinitely ma...

A finite counterexample to two best proximity point theorems in non-Archimedean generalized Menger spaces

This independent correction-note preprint examines Theorems 1 and 2 of Oumertou et al., Mathematics 14 (2026), 1443 (doi:10.3390/math14091443). A complete six-point non-Archimedean generalized Menger space and a cyclic mapping satisfy the printed hypotheses, including proximal ad...

A two-point counterexample to a common fixed point theorem in elliptic-valued suprametric spaces

This independent correction-note preprint examines Theorem 2 of B. Alamri, Fixed Point Theorems in Elliptic-Valued Suprametric Spaces and Their Applications, Mathematics 14 (2026), 413 (doi:10.3390/math14030413). A complete two-point metric space, viewed as an elliptic-valued sup...

Two Corrections to the Heisenberg Example and Sobolev Formulation in The Work of Hong Wang

This correction note identifies two local formulation errors in Christopher D. Sogge’s survey The Work of Hong Wang, arXiv:2609.40161v1 (30 September 2026). The displayed four-real-parameter Heisenberg family has only three real parameters of complex directions, so it cannot prov...

Two Corrections to the Heisenberg Example and Sobolev Formulation in The Work of Hong Wang

This correction note identifies two local formulation errors in Christopher D. Sogge’s survey The Work of Hong Wang, arXiv:2609.40161v1 (30 September 2026). The displayed four-real-parameter Heisenberg family has only three real parameters of complex directions, so it cannot prov...

Counterexamples and controller corrections for full-state hybrid projective synchronization of discrete systems

This independent mathematical correction note examines the printed controllers and global synchronization claims in Adel Ouannas, “On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems,” Journal of Nonlinear Dynamics (2014), Article ID 983293, DOI: 1...

A correction note on normalization and auxiliary estimates in Sharp volume bounds for BRK-type sets of surfaces of revolution

This independent correction note examines auxiliary assertions in Xianghong Chen and Tongou Yang, “Sharp volume bounds for BRK-type sets of surfaces of revolution,” arXiv:2609.39059v1 (30 September 2026). A family of shrinking spheres satisfies a common neighborhood-intersection...

A counterexample and a controller correction for global synchronization of the fractional Newton–Leipnik reaction–diffusion system

This independent technical note examines the controller printed in equation (26) and the global synchronization assertion of Theorem 5.3 in Mansouri, Bendoukha, Abdelmalek and Youkana, Applicable Analysis 100 (2021), 675–694, DOI: 10.1080/00036811.2019.1616694. An incorrect produ...

Structural Obstructions and Corrections to "Existence, Uniqueness and Stability Analysis for Delay Fractional Evolution Equations with Maxima"

We examine several assertions in F. Abdeldjebbar, N. Rezoug, A. Salim and M. Benchohra, Analysis 46 (2026), 21–38, concerning delay fractional evolution equations with maxima. Several independent structural, analytic and logical obstructions are identified. First, the quantity[\m...

Structural Obstructions and Corrections to "Existence, Uniqueness and Stability Analysis for Delay Fractional Evolution Equations with Maxima"

We examine several assertions in F. Abdeldjebbar, N. Rezoug, A. Salim and M. Benchohra, Analysis 46 (2026), 21–38, concerning delay fractional evolution equations with maxima. Several independent structural, analytic and logical obstructions are identified. First, the quantity[\m...

A Correction Note on Sobolev Propagation and Polynomial Truncation for a Dirichlet-to-Neumann Approximation in Thin Dielectric Multilayers

This correction note discusses two technical points in the derivation of the Dirichlet-to-Neumann operator in B. Alliti, T. Laadj and K. M'hamed-Messaoud, Mathematical Methods in the Applied Sciences 46 (2023), 6843–6856. First, the proof of the exact transfer formula is based on...

A Correction Note on Sobolev Propagation and Polynomial Truncation for a Dirichlet-to-Neumann Approximation in Thin Dielectric Multilayers

This correction note discusses two technical points in the derivation of the Dirichlet-to-Neumann operator in B. Alliti, T. Laadj and K. M'hamed-Messaoud, Mathematical Methods in the Applied Sciences 46 (2023), 6843–6856. First, the proof of the exact transfer formula is based on...

Step-size restrictions and recentering bounds in the semidefinite linear complementarity problem: counterexamples and a corrected local analysis

This technical note examines the step-size estimates and recentering analysis in M. Achache and N. Boudiaf, “Complexity analysis of primal-dual algorithms for the semidefinite linear complementarity problem,” Rev. Anal. Numer. Theor. Approx. 40 (2011), no. 2, 95–106, DOI: 10.3399...

A technical comment on solvability claims for Sylvester-type operator equations

This independent technical comment checks four groups of claims in A. Yakoub and A. Mennouni, “New results on the solvability of Sylvester-type operator equations,” Filomat 40 (2026), 371–396, DOI: 10.2298/FIL2602371Y. Bounded-operator counterexamples on the infinite-dimensional...

A counterexample to a homotopy-equivalence criterion for topological categories

Roberts' Theorem 4.2 states that a fully faithful, essentially O_num-surjective functor between well-pointed topological categories induces a homotopy equivalence of classifying spaces. In the published formulation, however, the space of algebraically invertible arrows is only eq...

A counterexample to a homotopy-equivalence criterion for topological categories

Roberts' Theorem 4.2 states that a fully faithful, essentially O_num-surjective functor between well-pointed topological categories induces a homotopy equivalence of classifying spaces. In the published formulation, however, the space of algebraically invertible arrows is only eq...

An Axial Obstruction to the Uniform High-Order Matrix Damping Criterion in "Stable Singularity of the Euler Equations on R^3"

This technical note examines the full-domain high-order matrix negativity condition (S248) in the 107-page manuscript "Stable Singularity of the Euler Equations on R^3" by Adarsh Ganeshram, Valentin Duruisseaux and Anima Anandkumar, retrieved on 8 September 2026. From the normali...

The Sharp First-Angular Symmetry-Breaking Threshold for the Planar Lane–Emden Equation with Robin Boundary Conditions

This note sharpens the first-angular symmetry-breaking analysis for the planar Lane--Emden equation with positive Robin boundary conditions. We prove the existence of a unique sharp transition exponent\[p_{\mathrm{sb}}\in(5,8).\]For \(1 p_{\mathrm{sb}}\), it has exactly two simpl...

The Sharp First-Angular Symmetry-Breaking Threshold for the Planar Lane–Emden Equation with Robin Boundary Conditions

This note sharpens the first-angular symmetry-breaking analysis for the planar Lane--Emden equation with positive Robin boundary conditions. We prove the existence of a unique sharp transition exponent\[p_{\mathrm{sb}}\in(5,8).\]For \(1 p_{\mathrm{sb}}\), it has exactly two simpl...

Minimal Real Generalized Trisecants

Ranestad, Seigal, and Wang asked whether, for every admissible triple (d,n,m)(d,n,m), there exists a smooth, irreducible, non-degenerate real projective variety of dimension mm, codimension nn, and degree dd, whose maximum number of real points in a transverse complementary linea...