The general Bernstein function: Application to χ‐fractional differential equations
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DOI: 10.1002/mma.9910
Abstract: In this paper, we present the general Bernstein functions for the first time. The properties of generalized Bernstein basis functions are given and demonstrated. The classical Bernstein polynomial bases are merely a subset of the… read more here.
Keywords: bernstein function; differential equations; fractional differential; general bernstein ... See more keywords
Approximation and Geometric Properties of Complex $$\alpha $$α-Bernstein Operator
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DOI: 10.1007/s00025-018-0953-z
Abstract: In this paper, we consider the complex form of a new generalization of the Bernstein operator, depending on a non-negative real parameter. We obtain quantitative upper estimate for simultaneous approximation, a qualitative Voronovskaja type result… read more here.
Keywords: alpha bernstein; complex alpha; properties complex; bernstein ... See more keywords
RETRACTED ARTICLE: On eigenstructure of q-Bernstein operators
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DOI: 10.1007/s13324-020-00443-7
Abstract: The quantum analogue of Bernstein operators $${\mathcal {B}}_{m,q}$$ reproduce the linear polynomials which are therefore eigenfunctions corresponding to the eigenvalue $$1,~\forall ~ q>0$$ . In this article the rest of eigenstructure of q-Bernstein operators and… read more here.
Keywords: bernstein; eigenstructure bernstein; bernstein operators; retracted article ... See more keywords
Comparison of Two-Parameter Bernstein Operator and Bernstein–Durrmeyer Variants
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Iranian Mathematical Society"
DOI: 10.1007/s41980-018-0101-2
Abstract: The quantum calculus and the post-quantum calculus have recently gained broad popularity in computational science and engineering due to their applications to diverse areas such as solution of differential equations, approximation theory and computer-aided geometric… read more here.
Keywords: bernstein; bernstein durrmeyer; bernstein operator; two parameter ... See more keywords
Approximation of functions by a new family of generalized Bernstein operators
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2016.12.075
Abstract: Abstract The main object of this paper is to construct a new generalization of the Bernstein operator, depending on a non-negative real parameter. We investigate some elementary properties of this operator, such as end point… read more here.
Keywords: bernstein; bernstein operators; generalized bernstein; approximation functions ... See more keywords
Overlapping of the harmonics of the cyclotron frequency in the Bernstein waves due to relativistic effects
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DOI: 10.1063/1.5027773
Abstract: By using the generalized expression for the plasma conductivity tensor, the general dispersion relation for the Bernstein waves is derived. To investigate the Bernstein waves for a weakly relativistic plasma, the Maxwell-Boltzmann-Juttner distribution function is… read more here.
Keywords: bernstein; propagation; cyclotron frequency; harmonics ... See more keywords
Pedagogic governance: theorising with/after Bernstein
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DOI: 10.1080/01425692.2015.1081052
Abstract: Researchers interested in new modes of social control and regulation through pedagogic means have increasingly drawn on Bernstein’s theories of social control through pedagogic means and the emergence of a totally pedagogised society. This article… read more here.
Keywords: bernstein; theorising bernstein; control; governance theorising ... See more keywords
BERN-NN-IBF: Enhancing Neural Network Bound Propagation Through Implicit Bernstein Form and Optimized Tensor Operations
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"
DOI: 10.1109/tcad.2024.3447577
Abstract: Neural networks have emerged as powerful tools across various domains, exhibiting remarkable empirical performance that motivated their widespread adoption in safety-critical applications, which, in turn, necessitates rigorous formal verification techniques to ensure their reliability and… read more here.
Keywords: bern ibf; tensor operations; bound propagation; optimized tensor ... See more keywords
A place for Basil Bernstein in the field: How applicable is Basil Bernstein’s theory of codes and social groups as a way of understanding educational inequity in upper secondary education in Iceland during the first year of the COVID-19 pandemic?
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DOI: 10.1177/14749041241235974
Abstract: In this article, key aspects of Basil Bernstein’s theory of elaborating and restricted codes are analysed within the Icelandic context to determine whether it can be employed when researching socio-economic inequities in upper-secondary education in… read more here.
Keywords: education; basil bernstein; bernstein; bernstein theory ... See more keywords
A Kantorovich type integral modification of q-Bernstein-Schurer operators
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DOI: 10.2298/fil1804335g
Abstract: The q− Bernstein-Schurer summation type operators are modified in order to make them applicable for approximation of integrable functions. The aim of the paper is twofold. Firstly, to find refined error estimates, |S n,p,q (… read more here.
Keywords: bernstein; type integral; kantorovich type; integral modification ... See more keywords
Convergence of iterates of q-Bernstein and (p,q)-Bernstein operators and the Kelisky-Rivlin type theorem
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DOI: 10.2298/fil1812351r
Abstract: Recently, Radu [Note on the iterates of q and (p, q)-Bernstein operators, Scientific Studies and Research, Series Mathematics and Informatics, 26(2) (2016) 83-94] has investigated the convergence of iterates of q-Bernstein polynomial and (p, q)-Bernstein… read more here.
Keywords: bernstein; convergence iterates; bernstein operators; rivlin type ... See more keywords