404 research outputs found
General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
We consider discrete self-adjoint Dirac systems determined by the potentials
(sequences) such that the matrices are positive definite and
-unitary, where is a diagonal matrix and has entries
and entries () on the main diagonal. We construct
systems with rational Weyl functions and explicitly solve inverse problem to
recover systems from the contractive rational Weyl functions. Moreover, we
study the stability of this procedure. The matrices (in the potentials)
are so called Halmos extensions of the Verblunsky-type coefficients .
We show that in the case of the contractive rational Weyl functions the
coefficients tend to zero and the matrices tend to the indentity
matrix .Comment: This paper is a generalization and further development of the topics
discussed in arXiv:math/0703369, arXiv:1206.2915, arXiv:1508.07954,
arXiv:1510.0079
Discrete Dirac system: rectangular Weyl functions, direct and inverse problems
A transfer matrix function representation of the fundamental solution of the
general-type discrete Dirac system, corresponding to rectangular Schur
coefficients and Weyl functions, is obtained. Connections with Szeg\"o
recurrence, Schur coefficients and structured matrices are treated.
Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the
interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on
Halmos extension are added and arguments are simplifie
Unraveling the Differences of the Hydrolytic Activity of Trypanosoma cruzi trans-Sialidase and Trypanosoma rangeli Sialidase: A Quantum Mechanics–Molecular Mechanics Modeling Study
Chagas’ disease, also known as American trypanosomiasis, is a lethal, chronic disease that currently affects more than 10 million people in Central and South America. The trans-sialidase from Trypanosoma cruzi (T. cruzi, TcTS) is a crucial enzyme for the survival of this parasite: sialic acids from the host are transferred to the cell surface glycoproteins of the trypanosome, thereby evading the host’s immune system. On the other hand, the sialidase of T. rangeli (TrSA), which shares 70% sequence identity with TcTS, is a strict hydrolase and shows no trans-sialidase activity. Therefore, TcTS and TrSA represent an excellent framework to understand how different catalytic activities can be achieved with extremely similar structures. By means of combined quantum mechanics–molecular mechanics (QM/MM, SCC-DFTB/Amberff99SB) calculations and umbrella sampling simulations, we investigated the hydrolysis mechanisms of TcTS and TrSA and computed the free energy profiles of these reactions. The results, together with our previous computational investigations, are able to explain the catalytic mechanism of sialidases and describe how subtle differences in the active site make TrSA a strict hydrolase and TcTS a more efficient trans-sialidase.Fil: Bueren Calabuig, Juan A.. University of Florida; Estados UnidosFil: Pierdominici Sottile, Gustavo. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Roitberg, Adrián. University of Florida; Estados Unido
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