Domains of Positivity
نویسندگان
چکیده
A Domain of Positivity D is an open convex cone associated with a nonsingular symmetric matrix S, called the characteristic, such that xÇzD if and only if x'Sy>0 for all y(~D* As such they were introduced by Koecher (1) in generalization of the cone of positive definite matrices studied by Siegel. The automorphisms of D are the nonsingular linear transformations mapping D onto itself. The group of automorphisms {W] admits an anti-automorphism: W—>S~W'Sf where W' means W transposed. A norm N(x) is a function positive and continuous for x£J9 and satisfying there N(Wx) =||TF||N(X) for every automorphism W. A norm is given by:
منابع مشابه
Nonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملThe Relevance of Positivity in Spin Physics
Positivity reduces substantially the allowed domain for spin observables. We briefly recall some methods used to determine these domains and give some typical examples for exclusive and inclusive spin-dependent reactions.
متن کاملStability of Two Variable Interval Polynomials via Positivity
Stability criteria are proposed for two variable D polynomials having interval parameters in polynomic uncertain ty structures Both the left half plane and unit circle domains are considered Save for a minor condition the criteria reduce robust stability testing of D polynomials to testing positivity of only two polynomials The appealing feature of the new robustness criteria is that positivity...
متن کاملPositivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
متن کاملAn efficient nonstandard numerical method with positivity preserving property
Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The...
متن کاملEstimates of solutions and asymptotic symmetry for parabolic equations on bounded domains
We consider fully nonlinear parabolic equations on bounded domains under Dirichlet boundary condition. Assuming that the equation and the domain satisfy certain symmetry conditions, we prove that each bounded positive solution of the Dirichlet problem is asymptotically symmetric. Compared with previous results of this type, we do not assume certain crucial hypotheses, such as uniform (with resp...
متن کامل