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Displaying 161 –
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498
We investigate functional equations where and are given real functions defined on the set of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions which are strictly increasing and continuous on . In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present a construction...
We consider the lowest-order Raviart–Thomas mixed finite element
method for second-order elliptic problems on simplicial meshes in
two and three space dimensions. This method produces saddle-point
problems for scalar and flux unknowns. We show how to easily and
locally eliminate the flux unknowns, which implies the equivalence
between this method and a particular multi-point finite volume
scheme, without any approximate numerical integration. The matrix
of the final linear system is sparse, positive...
We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system is star-like with centre if...
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...
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498