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Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…

Three dimensional bosonization is a conjectured duality between non-supersymmetric Chern-Simons theories coupled to matter fields in the fundamental representation of the gauge group. There is a well-established supersymmetric version of…

This is the text of a talk given by the first author at the Harish-Chandra centenary meeting held in Allahabad in October 2023. It reviews Harish-Chandra's isomorphism and its many applications to representation theory and mathematical…

In a recent paper, Hassoul et al.[1], the authors proposed an analysis of the quantum dynamics for general time-dependent three coupled oscillators through an approach based on their decouplement using the unitary transformation method.…

This is the second part in a series of two papers. The $k$-Dirac complex is a complex of differential operators which are natural to a particular $|2|$-graded parabolic geometry. In this paper we will consider the $k$-Dirac complex over a…

We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the…

We find a family of solutions to Zamolodchikov's tetrahedral algebra corresponding to the fermionic R-operator for the free fermion model of the difference type in one of the spectral parameters, construct an extension of the R-operator for…

There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…

Erroneous statements on the mathematical and physical properties of the double-Kerr solution made in a recent paper (Class. Quantum Grav. 21 (2004) 2723) are commented.

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was…

Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Virtually all other textbooks on numerical analysis and…

The critical behavior of the 1/5-depleted square-lattice Ising model with nearest neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field…

The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very…

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects…

We show that the modern theory of fully nonlinear operators had been started by the skew symmetry of minors in cooperation with the symmetry of symmetric functions. The paper presents some consequences of this interaction for the m-Hessian…

This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors…

In this paper, we consider the Cauchy problem for a compressible Oldroyd-B model in three dimensions. Under some smallness assumptions on the initial data, we obtain the global wellposedness of strong solution with uniform regularity.…

This paper introduces an efficient high-order numerical method for solving the 1D stationary Schr\"odinger equation in the highly oscillatory regime. Building upon the ideas from [Arnold, Ben Abdallah, Negulescu, SIAM J. Numer. Anal.,…

This note presents a correction to the paper ``Hardy and BMO spaces associated to divergence form elliptic operators" by Steve Hofmann and Svitlana Mayboroda