Grilliot's trick in Nonstandard Analysis [PDF]
Logical Methods in Computer Science, 2017 The technique known as Grilliot's trick constitutes a template for explicitly defining the Turing jump functional $(\exists^2)$ in terms of a given effectively discontinuous type two functional. In this paper, we discuss the standard extensionality trick:
Sam Sanders
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Describing limits of integrable functions as grid functions of nonstandard analysis [PDF]
Partial Differential Equations and Applications, 2021 AbstractIn functional analysis, there are different notions of limit for a bounded sequence of$$L^1$$L1functions. Besides the pointwise limit, that does not always exist, the behaviour of a bounded sequence of$$L^1$$L1functions can be described in terms of its weak-$$\star $$⋆limit or by introducing a measure-valued notion of limit in the sense of ...
E. Bottazzi
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Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response [PDF]
AIP Conference Proceedings, 2017 In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties.
Agus Suryanto, Isnani Darti
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Solution of Inhomogeneous Fractional Differential Equations with Polynomial Coefficients in Terms of the Green’s Function, in Nonstandard Analysis [PDF]
Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the framework of distribution theory.
Morita, Tohru, Sato, Ken-ichi
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Body response to primary joint replacement after proximal femur injuries in patients with an increased body mass index (preliminary study) [PDF]
Гений oртопедии, 2020 Introduction Injuries of the proximal femur remains a significant problem of management in the elderly persons. The traditional approach comprising osteosynthesis of bone fragments is a method of choice in standard situations but showed to be ...
Hao Zhi Han +4 more
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Analysis of the mathematical model of cutaneous Leishmaniasis disease
Alexandria Engineering Journal, 2023 Mathematical models are powerful tools to study various real-world problems from different perspectives. This branch has been given much more popularity over the last several decades.
Muhammad Sinan +6 more
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Local analysis of nonstandard $C^∞$ functions of pre-distributional type [PDF]
Annales Polonici Mathematici, 1984 The authors define pre-distributions as equivalence classes of non- standard \(^*C^{\infty}\) functions, and analyze the classes of the so- called K-pre-distributions. Discrete oscillation, essential oscillation and other properties are defined in the monad of a standard point.
Komkov, V., McLaughlin, T. G.
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Determination of the synthetic hydroxyapatite life circle used in dental practice [PDF]
Chemical Industry and Chemical Engineering Quarterly, 2012 Dental materials are specific materials that were developed as a general materials for specific aplication in oral environment. To determinate the functional properties of this materials, we are obligated to use nonstandard approach and specific ...
Teodorović Nevenka, Jovanić Predrag
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Ultrafunctions and Applications [PDF]
, 2014 This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works.
Baglini, Lorenzo Luperi, Benci, Vieri
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On Some Types of Functions in Nonstandard Analysis
Science Journal of University of Zakho, 2016 In this paper, by using some nonstandard concepts given by Robinson and axiomatized by Nelson we study the behavior of functions defined on a discrete intervals, whose points are of infinitesimal distances. This study leads to introduce and define some new types of functions in nonstandard analysis and we get some nonstandard results for different ...
Ibrahim O. Hamad, Sebar H. Jumha
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