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DISTRIBUTION OF ROOTS OF CUBIC EQUATIONS
"... Abstract. In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations. Cubic equations are frequently encountered in many important problems in physics, applied mathematics, and engi ..."
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Abstract. In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations. Cubic equations are frequently encountered in many important problems in physics, applied mathematics
Cubic equations for the hyperelliptic locus
 Asian J. Math
"... Abstract. We prove a conjecture from [BK2] that the multidimensional vector addition formula for BakerAkhiezer functions obtained there characterizes Jacobians among principally polarized abelian varieties. We also show that this addition formula is equivalent to Gunning’s multisecant formula for ..."
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for the Kummer variety obtained in [Gu2]. We then use this addition formula to obtain cubic relations among theta functions that characterize the locus of hyperelliptic Jacobians among irreducible abelian varieties. In genus 3 our equations are equivalent to the vanishing of one thetanull, and thus
Solving Cubic Equations By the Quadratic Formula
"... Let p(z) be a monic cubic complex polynomial with distinct roots and distinct critical points. We say a critical point has the Voronoi property if it lies in the Voronoi cell of a root θ, V (θ), i.e. the set of points that are closer to θ than to the other roots. We prove at least one critical point ..."
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by the Voronoi property, there is a solution c of p′(z) = 0 where Bm(c) converges to a root of p(z). The speed of convergence is dependent on the ratio of the distances between c and the closest and the second closest roots of p(z). This results in a different algorithm for solving a cubic equation than
NonHomogeneous Cubic Equation with Three Unknowns
"... The nonhomogeneous cubic equation with three unknowns represented by 322 274)(25)(3 zyxxyyx is analyzed for finding its nonzero distinct integral solutions. Three different methods have been presented for determining the integral solutions of the nonhomogeneous cubic equation under considerati ..."
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The nonhomogeneous cubic equation with three unknowns represented by 322 274)(25)(3 zyxxyyx is analyzed for finding its nonzero distinct integral solutions. Three different methods have been presented for determining the integral solutions of the nonhomogeneous cubic equation under
Solution Formulas for Cubic Equations Without or With Constraints
, 2011
"... We present a convention (for square/cubic root) which provides correct interpretations of Lagrange’s formula for all cubic polynomial equations with real coefficients. Using this convention, we also present a real solution formulas for the general cubic equation with real coefficients under equality ..."
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We present a convention (for square/cubic root) which provides correct interpretations of Lagrange’s formula for all cubic polynomial equations with real coefficients. Using this convention, we also present a real solution formulas for the general cubic equation with real coefficients under
A Cubic Equation of State for Methanol and Ethanol Vapours
"... Vapourphase thermodynamic properties of methanol and ethanol have been fitted to a cubic equation of state with two temperaturedependent parameters. The parameter a(T) is fitted to the second virial coefficient, and the parameter c(T) is fitted to saturated vapour densities. The equation gives goo ..."
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Vapourphase thermodynamic properties of methanol and ethanol have been fitted to a cubic equation of state with two temperaturedependent parameters. The parameter a(T) is fitted to the second virial coefficient, and the parameter c(T) is fitted to saturated vapour densities. The equation gives
EXPERIENCE IN NORSK HYDRO WITH CUBIC EQUATIONS OF STATE
"... The paper presents some specific applications of cubic equations of state (EOS) in Norak Hydro and points out some aspects of such equations that one should be aware of when using them or when developing new equations. Is is emphasized that the use of EOS to calculate vaporliquid equilibrium is inh ..."
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The paper presents some specific applications of cubic equations of state (EOS) in Norak Hydro and points out some aspects of such equations that one should be aware of when using them or when developing new equations. Is is emphasized that the use of EOS to calculate vaporliquid equilibrium
A Cubic Equation of State for Mixtures Containing Steam
"... A cubic equation of state and combining rules for mixtures containing steam has been developed. The equation is based on the earlier equations of Clausius, Martin and Kubic, and contains two temperaturedependent parameters, which give it enough flexibility to fit the residual properties of both ste ..."
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A cubic equation of state and combining rules for mixtures containing steam has been developed. The equation is based on the earlier equations of Clausius, Martin and Kubic, and contains two temperaturedependent parameters, which give it enough flexibility to fit the residual properties of both
Results 1  10
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195,533