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A Gauss type functional equation
Published 2001-01-01“…Gauss' functional equation (used in the study of the arithmetic-geometric mean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means.…”
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Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals
Published 2011-01-01“…By using a generalized arithmetic-geometric mean inequality on time scales, we study the forced oscillation of second-order dynamic equations with nonlinearities given by Riemann-Stieltjes integrals of the form [p(t)ϕα(xΔ(t))]Δ+q(t)ϕα(x(τ(t)))+∫aσ(b)r(t,s)ϕγ(s)(x(g(t,s)))Δξ(s)=e(t), where t∈[t0,∞)T=[t0,∞) ⋂ T, T is a time scale which is unbounded from above; ϕ*(u)=|u|*sgn u; γ:[a,b]T1→ℝ is a strictly increasing right-dense continuous function; p,q,e:[t0,∞)T→ℝ, r:[t0,∞)T×[a,b]T1→ℝ, τ:[t0,∞)T→[t0,∞)T, and g:[t0,∞)T×[a,b]T1→[t0,∞)T are right-dense continuous functions; ξ:[a,b]T1→ℝ is strictly increasing. …”
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Achieving Fair Spectrum Allocation and Reduced Spectrum Handoff in Wireless Sensor Networks: Modeling via Biobjective Optimization
Published 2014-01-01“…To tackle this intractability, we first convexify the original problem using arithmetic-geometric mean approximation and logarithmic change of the decision variables and then deploy weighted Chebyshev norm-based scalarization method in order to collapse the multiobjective problem into a single objective one. …”
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Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions
Published 2012-01-01“…To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.…”
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