Related papers: Reply to comment on "Exact Solution for Three-Dime…
We respond to the recent comment [arXiv:1105.1593] on our Letter [G. G. Plunk and T. Tatsuno, Phys. Rev. Lett. 106, 165003 (2011)]. The comment claims that our argument for spectral transfer direction is incomplete. The comment gives an…
We consider four-dimensional Riemannian manifolds with commuting higher order Jacobi operators defined on two-dimensional orthogonal subspaces (polygons) and on their orthogonal subspaces. More precisely, we discuss higher order Jacobi…
Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer and results by D. Roy, we show that German's transference inequalities between the two most classical exponents of uniform Diophantine…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…
Finite size corrections to the pressure (free energy) of the Ising model on a 2 dimensional cylinder are calculated and shown to be consistent with the predictions of conformal field theory. The exact solution of the model is expressed in…
The Ising square lattice model with nearest-neighbor (nn) interactions ($J_1$) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions ($J_2$) or a magnetic field (or both) leads to the non…
We comment on the paper ``Numerical study of the SWKB condition of novel classes of exactly solvable systems'' [Y. Nasuda and N. Sawado, Mod. Phys. Lett. A 36, 2150025 (2021)]. We show that it misrepresents our prior work [J. Bougie, A.…
A general result is presented on the lack of second order corrections and on the form of the leading order Floquet quasi-energies in the high-frequency approximation for a two-level driven system. Then, by a perturbative approach in the…
We generalize the notion of Monk's schema in such a way to integrate finite dimensions. This allows us to lift a plathora of deep results proved for finite dimensions to the infinite dimensional case, like the solution to problem 2.12 in…
Image processing is an increasingly important aspect for analysis of data from X and $\gamma$-ray astrophysics missions. In this paper, I review a method proposed by Kebede (L. W. Kebede 1994, ApJ, 423, 878), and point out an error in the…
In Noor (2007)[Muhammad Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007) 937-943], proposed an algorithm namely \textbf{Algorithm 2.4} and established a proof to show cubic convergence. The presented…
We verify that a large portion of the theory of complex operator spaces and operator algebras (as represented by the 2004 book by the author and Le Merdy for specificity) transfers to the real case. We point out some of the results that do…
We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local…
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay,…
The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its "proof" is not correct. Here we change the statements and proofs of Lemma…
This work presents a novel strategy to address Navier-Stokes modelling errors arising on first-nearest neighbour lattice Boltzmann (LB) methods and introduces fully local corrections through Onsager-Regularized (OReg) non-equilibrium…
In this paper we identify some inaccuracies in the paper by R.R. Saxena and S.R. Arora, A Linearization technique for solving the Quadratic Set Covering Problem, Optimization, 39 (1997) 33-42. In particular, we observe that their algorithm…
In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for…
We investigate the convexity problem for the Parisi functional defined on the space of the so-called functional ordered parameters in the Sherrington-Kirkpatrick model. In the recent work of Panchenko [3], he proved that this functional is…
Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Ces\`aro summability of Fourier series, degree of approximation and best approximation by trigonometric…