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A Note on Rational Approximation [PDF]
p(x) = qo(x) * Tn +1 (x) + ro(x) YTn~l(x =-q1(x)W ro(x) + r1(x) ro(x) = q2-(X) * ri(x) + r2(x) r1() = q3(x) *r2(x) + r3(X), etc., where the (degrees of thie ri formr a strictly decreasing sequence. From these equations we may write r,(Q) = i(x) -.p(.x) + bi(x) . T.+1(x), where ai and bi are defined recursively by (a,=ai-. -qiai-?, a-1=O, a2= 1 lbi = bi-
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Design and analysis strategies for robust microbiome ageing research
The gut microbiome changes with age and associates with age‐related morbidity and mortality, establishing it as a potential biomarker and intervention target for ageing. Realising this potential requires methodological rigour, yet distinguishing biological signals from methodological artefacts remains challenging across cohorts. This review provides an
Mark Olenik +5 more
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Reconstructing enzyme evolution by protein engineering
Natural enzyme evolution can be retraced by protein engineering methods such as directed evolution, rational design, and ancestral sequence reconstruction. These approaches reveal how enzymes emerged from ligand‐binding scaffolds, developed varying substrate preferences, formed oligomeric complexes, adapted to environmental changes, and evolved novel ...
Lukas Drexler +2 more
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Approximation performance analysis of Oustaloup rational approximation of ideal fractance
:Starting from operational characteristics, in this paper, the operational characteristics localization of zero-pole subsystem of Oustaloup was analyzed based on order-frequency and phase-frequency characteristic function.
Liu Panpan, Yuan Xiao
doaj
Algebraic and recursion equations are widely used in different areas of mathematics, so various objects and methods of research that are associated with them are very important.
I.I. Lishchynsky
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In this paper, we obtain the Complex Natural Resonances of an object from the backscattered response in the frequency domain with a novel rational function approximation method based on both Vector Fitting and Cauchy methods.
Andres Gallego +2 more
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On monotone Rational Approximation
In this chapter,we focus on the shape preserving approximation using rational polynomials, for rational in _spaces, . In our work, we solve a problem raised by R. DeVore in several lectures for many years ago.
Bhaya, Eman S., Ahmed, Dhay Basim
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The process of internalization of the Shiga toxin A subunit via formation of a complex with the Shiga toxin B subunit, which specifically binds to the Gb3 receptor. The peptide is designed to act as a carrier of drugs into cancer cells. Here, we explored the potential of peptides derived from the catalytic A subunit of Shiga toxin (STxA) to be drug ...
Giulia Opassi +6 more
wiley +1 more source
On rational approximation in a ball in ℂN
We study rational approximations of elements of a special class of meromorphic functions which are characterized by their holomorphic behavior near the origin in balls in ℂN by means of their rational approximants. We examine two modes of convergence for
P. W. Darko +2 more
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A complete MAPLE procedure is designed to effectively implement an algorithm for approximating trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its ...
Le Phuong Quan
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