Results 11 to 20 of about 269,808 (267)
On Equational Definability of Function Classes [PDF]
2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011 We propose a notion of functional equation for functions of a fixed arity, which is based on a pair of clones. We present necessary conditions for aclass of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.
Miguel Couceiro +2 more
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A CLASS OF DIOPHANTINE EQUATIONS [PDF]
Proceedings of the National Academy of Sciences, 1959 Nach Verf. hat \[ \alpha^x+\beta^x=\alpha^n+\beta^n,\quad \alpha,\beta=\tfrac 12 (1\pm\sqrt{-7}), \] für gegebene \(n\) höchstens zwei Lösungen und für \(n=2^m\) genau die triviale Lösung \(x=2^m\).
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Integro-differential equations in Banach spaces and analytic resolving families of operators
Современная математика: Фундаментальные направления, 2023 We study a class of equations in Banach spaces with a Riemann–Liouville-type integro-differential operator with an operator-valued convolution kernel. The properties of \(k\)-resolving operators of such equations are studied and the class \(\mathcal A_ ...
V. E. Fedorov, A. D. Godova
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An evaluation of the U.S. EPA's correction equation for PurpleAir sensor data in smoke, dust, and wintertime urban pollution events [PDF]
Atmospheric Measurement Techniques, 2023 PurpleAir sensors (PASs) are low-cost tools to measure fine particulate matter (PM) concentrations and are now widely used, especially in regions with few regulatory monitors.
D. A. Jaffe +9 more
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Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
Partial Differential Equations in Applied Mathematics, 2021 In this paper, Lagrangians and the first integrals of a new class of Liénard-type equations have been investigated. This class can be obtained using the traveling wave reduction of the generalized Camassa–Holm equation.
H. Elzehri +2 more
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To the solution of one pseudo-Volterra integral equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 In this paper, we study a homogeneous singular integral Volterra equation of the second kind (pseudoVolterra integral equation). The singularity of the integral equation is shown. Properties of its kernel are proved.
M.T. Jenaliyev +3 more
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Gevrey class regularity for analytic differential-delay equations
Electronic Journal of Qualitative Theory of Differential Equations, 2016 This paper considers differential-delay equations of the form \[x'(t)=p(t)x(t-1),\] where the coefficient function $p\colon\mathbb{R}\rightarrow\mathbb{C}$ is analytic and not bounded on any $\delta$-neighborhood of the intervals $\left(-\infty,\gamma ...
Roger Nussbaum, Gabriella Vas
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Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels
Mathematics, 2022 The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined.
Oleg Avsyankin
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On a class of diophantine equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Cohn (1971) has shown that the only solution in positive integers of the equation Y(Y + 1)(Y + 2)(Y + 3) = 2X(X + 1)(X + 2)(X + 3) is X = 4, Y = 5. Using this result, Jeyaratnam (1975) has shown that the equation Y(Y + m)(Y + 2m)(Y + 3m) = 2X(X + m)(X + 2m)(X + 3m) has only four pairs of nontrivial solutions in integers given by X = 4m or −7m, Y = 5m ...
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Oscillation for a Class of Fractional Differential Equation
Discrete Dynamics in Nature and Society, 2013 We consider the oscillation for a class of fractional differential equation [r(t)g(D-αy)(t)]'-p(t)f∫t∞(s-t)-αy(s)ds=0, for t>0, where ...
Zhenlai Han +3 more
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