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Cubic Diophantine Equations with Reducible Cubic Part
Proceedings of the London Mathematical Society, 1970Summary: An equation of the type considered can, by suitably transforming the variables, written as \[ yQ + Q_1 + L + N = 0, \tag{1} \] where \(N\) is an integer and \(Q,Q_1, L\) are forms of degrees \(2,2,1\) in \(n\) variables \(x_1,\ldots,x_{n-1}, y\).
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A Generalized Cubic Functional Equation
Acta Mathematica Sinica, English Series, 2005The author solves the functional equation \[ f_1(2x+y)+f_2(2x-y)=f_3(x+y)+f_4(x-y)+f_5(x), \qquad x,y \in \mathbb R, \] where \(f_1, f_2, f_3, f_4, f_5: \mathbb R \to \mathbb R\). The general solution, obtained by elementary methods, is made up via diagonal of multiadditive symmetric functions. This result is then extended to the case of functions from
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The Cubic and Quartic Equations
1995Cardano was the first person to use imaginary numbers in print. In this chapter, we shall use imaginary numbers to present what is essentially Cardano’s solution to the cubic equation. We shall also give Ludovico Ferrari’s solution to the fourth degree polynomial equation.
W. S. Anglin, J. Lambek
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Cubic Derivative Nonlinear Schrödinger Equations*
SUT Journal of Mathematics, 2000The paper studies the Cauchy problem for the cubic derivative nonlinear Schrödinger equation, whose nonlinear term is a linear combination of all possible cubic differential polynomials but not only polynomials of the unknown function. The global existence in time of solutions to the Cauchy problem is proved, and the modified asymptotics is constructed
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2018
For a quadratic field of discriminant D, the units of norm 1 are in one-to-one correspondence with the integer points of the equation X2 − DY2 = 4, often called the Pell equation. This makes it possible, as many throughout history have done, to study some aspects of quadratic fields through consideration of this associated Diophantine equation.
Samuel A. Hambleton, Hugh C. Williams
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For a quadratic field of discriminant D, the units of norm 1 are in one-to-one correspondence with the integer points of the equation X2 − DY2 = 4, often called the Pell equation. This makes it possible, as many throughout history have done, to study some aspects of quadratic fields through consideration of this associated Diophantine equation.
Samuel A. Hambleton, Hugh C. Williams
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AIChE Journal, 1973
AbstractLimitations and capabilities of a generic cubic equation of state are analyzed in light of observed real‐fluid behavior, and criteria are presented for classification of specializations of the generic equation. An example is worked out which illustrates the application of these criteria to the development of new equations of state.
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AbstractLimitations and capabilities of a generic cubic equation of state are analyzed in light of observed real‐fluid behavior, and criteria are presented for classification of specializations of the generic equation. An example is worked out which illustrates the application of these criteria to the development of new equations of state.
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