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2019
Let α be an algebraic integer of degree n ≥ 3, \(K={\mathbb Q}(\alpha )\), and let \(0\neq m\in {\mathbb Z}\). In some applications for index form equations in sextic and octic fields (cf. Sects. 11.2.1, 11.2.2, and 14.2.3) we shall need to solve equations of type $$\displaystyle N_{K/{\mathbb Q}}(x+\alpha y +\lambda )=m \;\;\; \mathrm {in ...
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Let α be an algebraic integer of degree n ≥ 3, \(K={\mathbb Q}(\alpha )\), and let \(0\neq m\in {\mathbb Z}\). In some applications for index form equations in sextic and octic fields (cf. Sects. 11.2.1, 11.2.2, and 14.2.3) we shall need to solve equations of type $$\displaystyle N_{K/{\mathbb Q}}(x+\alpha y +\lambda )=m \;\;\; \mathrm {in ...
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Toward solving the inhomogeneous Bloch equation
Journal of Mathematical Physics, 2003The homogeneous Bloch equation reduces to the Riccati equation. By linearizing the Riccati equation, a set of three solutions of the homogeneous Bloch equation is found. The fundamental matrix becomes singular. We clarify the utility and limitation of our approach to solve the homogeneous Bloch equation.
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Inhomogenous infinite dimensional langevin equations
Stochastic Analysis and Applications, 1988A criterion for an infinite dimensional Gaussian process to satisfy a Langevin equation i s extended to the case where the evolution term is time ...
Tomasz Bojdecki, Luis G. Gorostiza
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Temporally inhomogeneous Timoshenko beam equations
Annali di Matematica Pura ed Applicata, 1993We provide a well-posedness result for a fourth order evolution equation in Hilbert space, which is the temporally inhomogeneous version of the Timoshenko beam equation. The method consists in transforming the equation to a convenient second order equation, which is a perturbation, by lower order terms, of a standard wave equation.
AROSIO, Alberto Giorgio +2 more
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Inhomogeneous semi-linear wave equations
2021In this thesis we study semi-linear wave equations with spatial inhomogeneity. The spatial inhomogeneity corresponds to a localised spatially dependent scaling of the nonlinear potential term. This thesis will consider the existence of stationary fronts and the dynamics of travelling solutions.
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An inhomogeneous Landau-like equation
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1981The problem of the mixing of two plasmas is very difficult to solve if the methods of statistical mechanics are used. When both plasmas are homogeneous in space, and the limit of weak coupling is appropriate, the Landau equation describes the motion.
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Systems of Inhomogeneous Linear Equations
2010Many problems in physics and especially computational physics involve systems of linear equations, which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the system is nonsingular and has full rank, a formal solution is given by matrix inversion. If the matrix is singular or the number of
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Inhomogeneous Cauchy exponential functional equations
Publicationes Mathematicae Debrecen, 2005Summary: We show that equations of the form \(f(x)f(y)-f(x+y)=\Gamma (x,y)\), termed here inhomogeneous Cauchy exponential functional equations, can be solved quite easily. Furthermore, their solutions are almost always unique. Both of these results contrast starkly with the situation for the inhomogeneous Cauchy additive functional equation \(f(x)+f(y)
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Integral Equations for Inhomogeneous Fluids
1993Useful theories of inhomogeneous fluids can be obtained either from the singlet Ornstein-Zernike (OZ1) equation (Henderson et al, 1976).
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