Results 21 to 30 of about 988,651 (350)
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 Generalization of the Hopf-Cole Transformation [PDF]
, 2012 A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented.
Miskinis, Paulius
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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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Demonstratio Mathematica, 2021 In this work, we study the existence of one and exactly one solution x∈C[0,1]x\in C\left[0,1], for a delay quadratic integral equation of Volterra-Stieltjes type.
El-Sayed Ahmed M. A., Omar Yasmin M. Y.
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Quadratic Liénard Equations with Quadratic Damping
Journal of Differential Equations, 1997 AbstractIn this paper we study the generalized Liénard equations x+f(x)x+g(x)=0 with quadratic polynomialsfandg. We prove that these kind of equations can have at most one limit cycle, and we give the complete bifurcation diagram and classification of the phase portraits. The paper also contains a shorter proof for the result in A. Lins, W.
Dumortier, Freddy, Li, C.
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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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On reducing the Heun equation to the hypergeometric equation [PDF]
, 2004 The reductions of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable are enumerated and classified.
Babister +20 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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On the Stability of Quadratic Functional Equations [PDF]
Abstract and Applied Analysis, 2008 Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.
Lee, Jung Rye +2 more
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