In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...

This paper studies the variation diminishing property of k-positive linear time-invariant (LTI) systems, which diminish number sign changes (variation) from input to output, if is at most k?1. We characterize this for discrete-time Toeplitz and Hankel operators finite-dimensional causal systems. Our main result that these have a dominant approximation in form series or parallel interconnections...

We define inequality aversion as a decision-maker disliking it when his opponents’ payoffs differ from his own, diminishing sensitivity as this effect increasing less-than-proportionately as the opponents’ payoffs move further from the decision-maker’s, and a preference for Robin Hood redistributions as a preference for taking money from a high-payoff opponent and giving it to a low-payoff oppo...

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero (Dupuis and Ellis, 1995, The large deviations principle for a general class of queueing systems I. Trans. Amer. Math. Soc. 347 2689–2751; Ignatiouk-Robert, 2002, Sample path large deviations and convergence parameters. Ann. Appl. Probab. 11 1292–1329; Shwartz...

Let $\Gamma$ be a group and $\mathscr{C}$ class of groups endowed with bi-invariant metrics. We say that is $\mathscr{C}$-stable if every $\varepsilon$-homomorphism $\Gamma \rightarrow G$, $(G,d) \in \mathscr{C}$, $\delta_\varepsilon$-close to homomorphism, $\delta_\varepsilon\to 0$ when $\varepsilon\to 0$. If $\delta_\varepsilon < C \varepsilon$ for some $C$ we $ \mathscr{C} $-stable linear ra...