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Near-equational and equational systems of logic for partial functions. II
The Journal of Symbolic Logic, 1989For the reader's convenience, we begin Part II by restating the rules for constructing Sq derivations given in §2:We let R be the set of 14 rules for Sq, R* the set of pure *-rules in R, R≃ the set of pure ≃-rules in R, and R− the set R ∩ − {Exs≃}. The closure of any F ⊆ Sq under R will be denoted by csRF, and the direct image of F under Cut*, for ...
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Stability in System of Impulsive Neutral Functional Differential Equations
Mediterranean Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Analytic solutions of systems of functional equations
Ukrainian Mathematical Journal, 1991The analytic properties of integral manifolds of systems of difference equations are studied. Analytic solutions of systems of functional equations are determined in the form of power series expansions.
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Continuous Solutions of Systems of Linear Difference-Functional Equations
Journal of Mathematical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Matrix Functions and Systems of Differential Equations
2015In this chapter we give an introduction to the area of matrix functions. We first define general matrix functions and derive their most important properties. Using the examples of network analysis and chemical reactions, we illustrate how matrix functions arise naturally in applications. The network analysis example involves the exponential function of
Jörg Liesen, Volker Mehrmann
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A remarkable system of eight functional equations
Aequationes mathematicae, 1999If \(\varphi:\mathbb R \to \mathbb R\) is continuous, \(1\)-periodic and even with respect to \(0\) and to \(1/2\), then the function \[ F_{\varphi}(x)=\sum_{k=0}^{+\infty} 2^{-k} \varphi(2^kx) \] satisfies a system \(\Omega\) of eight functional equations.
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Semicontinuous solutions of systems of functional equations.
2004The author considers the functional equation \[ F(\omega,u(\omega),u(g_1(\omega)),\dots,u(g_m(\omega)))=0 \leqno(1) \] where \(\omega \in \Omega\), \(\Omega\) metrizable topological space, \(g_j:\Omega \to \Omega\) (\(j=1,\dots,m\)) are given continuous functions, \(F:\Omega \times \mathbb R^{(1+m)n} \to \mathbb R^n\) and \(u\) is the unknown function.
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On Singular Systems of Parabolic Functional Equations
2011We consider systems consisting of an initial-boundary value problem for second-order quasilinear parabolic equation and an initial value problem for first-order ordinary differential equation where both equations contain functional dependence on the unknown functions.
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SARS-CoV-2 variants, spike mutations and immune escape
Nature Reviews Microbiology, 2021William T Harvey +2 more
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Mechanics and functional consequences of nuclear deformations
Nature Reviews Molecular Cell Biology, 2022Andrew D Stephens +2 more
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