On Polynomial Solutions of Pell’s Equation
Journal of Mathematics, 2021 Polynomial Pell’s equation is x2−Dy2=±1, where D is a quadratic polynomial with integer coefficients and the solutions X,Y must be quadratic polynomials with integer coefficients. Let D=a2x2+a1x+a0 be a polynomial in Zx.
Hasan Sankari, Ahmad Abdo
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A NOVEL CONCEPT: THE SOLUTION OF ANY QUADRATIC EQUATION IN ONE UNKNOWN QUANTITY IN REAL NUMBERS [PDF]
Journal of Mechanics of Continua and Mathematical SciencesConventionally the solution of any quadratic equation in one unknown quantity (say x) is represented in real or complex numbers. Instead of finding the solution of any quadratic equation in one unknown in complex numbers, the author introduced ...
Prabir Chandra Bhattacharyya
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Stability of the Popoviciu type functional equations on groups [PDF]
Opuscula Mathematica, 2011 We consider the stability problem for a class of functional equations related to the Popoviciu equation.
Małgorzata Chudziak
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Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity [PDF]
Journal of the European Mathematical Society (Print), 2018 Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain ...
Massimiliano Gubinelli +2 more
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Chapman-Enskog expansion of the Boltzmann equation and its diagrammatic interpretation [PDF]
, 2001 We perform a Chapman-Enskog expansion of the Boltzmann equation keeping up to quadratic contributions. We obtain a generalized nonlinear Kubo formula, and a set of integral equations which resum ladder and extended ladder diagrams. We show that these two
Carrington, M. E., Defu, Hou, Kobes, R.
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Soliton-like Solutions of General Variable Coefficient Cylindrical/Spherical KdV Equation
Mathematics, 2022 The general variable coefficient cylindrical/spherical KdV equation has been investigated by using the simplified homogeneous balance method. It has been proven that if its coefficients satisfy certain constraint conditions, then the cylindrical ...
Lingxiao Li, Mingliang Wang
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Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state [PDF]
, 2015 Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H(z) and cosmic microwave background constraints are described with different
G. S. Sharov
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European Physical Journal C: Particles and Fields, 2021 We investigate the stability and enhancement of the physical characteristics of compact, relativistic objects which follow a quadratic equation of state. To achieve this, we make use of the Vaidya–Tikekar metric potential.
S. Thirukkanesh +3 more
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Classification of generalized ternary quadratic quasigroup functional equations of the length three
Karpatsʹkì Matematičnì Publìkacìï, 2019 A functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are ...
F.M. Sokhatsky, A.V. Tarasevych
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The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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