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Runge–Kutta–Nyström symplectic splitting methods of order 8
(Elsevier, 2022-12)
Different families of Runge–Kutta–Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better ...
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
(Elsevier, 2023-11-10)
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and ...
MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes
(Springer Nature, 2024-03-01)
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. ...
Archetypal Curves in the Shape and Size Space: Discovering the Salient Features of Curved Big Data by Representative Extremes
(Springer, 2023)
Curves are complex data. Tools for visualizing, exploring, and discovering the structure
of a data set of curves are valuable. In this paper, we propose a scalable methodology to
solve this challenge. On the one hand, ...
On the existence of non-norm-attaining operators
(Cambridge University Press, 2021-07-09)
In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in L(E,F)
. By using a theorem due to Pfitzner on James boundaries, we show that if there exists a ...
Smooth and Polyhedral Norms via Fundamental Biorthogonal Systems
(Oxford University Press, 2022-08-04)
Let X be a Banach space with a fundamental biorthogonal system, and let Y be the dense subspace spanned by the vectors of the system. We prove that Y admits a C∞-smooth norm that locally depends on finitely many coordinates ...
Optimal approximation to unitary quantum operators with linear optics
(Springer Nature, 2021-09-21)
Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov’s theorem from differential geometry, we ...
On interpolating sequences for Bloch type spaces
(ElsevierAcademic Press, 2022-02-14)
When we deal with , it is known that interpolating sequences are interpolating and it is sufficient to interpolate idempotents of in order to interpolate the whole . We will extend these results to the frame of interpolating ...
No-go theorems for photon state transformations in quantum linear optics
(Elsevier, 2023)
We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity ...
Optimal (r,δ)-LRCs from monomial-Cartesian codes and their subfield-subcodes
(Springer, 2024-05-02)
We study monomial-Cartesian codes (MCCs) which can be regarded as (r,δ)-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to (r,δ)-optimal ...