Implications in bounded systems

Abstract A consistent connective system generated by nilpotent operators is not necessarily isomorphic to Łukasiewicz-system. Using more than one generator function, consistent nilpotent connective systems (so-called bounded systems) can be obtained with the advantage of three naturally derived negations and thresholds. In this paper, implications in bounded systems are examined. Both R- and S-implications with respect to the three naturally derived negations of the bounded system are considered. It is shown that these implications never coincide in a bounded system, as the condition of coincidence is equivalent to the coincidence of the negations, which would lead to Łukasiewicz logic. The formulae and the basic properties of four different types of implications are given, two of which fulfill all the basic properties generally required for implications

Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems

This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion of projected dynamical systems to time-varying, possibly non-regular, domains and derive conditions for the existence of so-called Krasovskii solutions. The key insight is that for trajectories to exist, informally, the time-varying domain can only contract at a bounded rate whereas it may expand discontinuously. This condition is met, in particular, by feasible sets delimited via piecewise differentiable functions under appropriate constraint qualifications. To illustrate the necessity and usefulness of such a general framework, we consider a simple yet insightful power system example, and we discuss the implications of the proposed conditions for the design of feedback optimization schemes

Constraints on long-lived electrically charged massive particles from anomalous strong lens systems

We investigate anomalous strong lens systems, particularly the effects of weak lensing by structures in the line of sight, in models with long-lived electrically charged massive particles (CHAMPs). In such models, matter density perturbations are suppressed through the acoustic damping and the flux ratio of lens systems are impacted, from which we can constrain the nature of CHAMPs. For this purpose, first we perform $N$-body simulations and develop a fitting formula to obtain non-linear matter power spectra in models where cold neutral dark matter and CHAMPs coexist in the early Universe. By using the observed anomalous quadruple lens samples, we obtained the constraints on the lifetime ($\tau_{\rm Ch}$) and the mass density fraction ($r_{\rm Ch}$) of CHAMPs. We show that, for $r_{\rm Ch}=1$, the lifetime is bounded as $\tau_{\rm Ch} < 0.96\,$yr (95% confidence level), while a longer lifetime $\tau_{\rm Ch} = 10\,$yr is allowed when $r_{\rm Ch} < 0.5$ at the 95% confidence level. Implications of our result for particle physics models are also discussed.Comment: 20 pages, 6 figure

On the market viability under proportional transaction costs

This paper studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABPs). In particular, we show that the NUPBR and NLABP conditions in the robust sense are equivalent to the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144662/1/mafi12155.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144662/2/mafi12155_am.pd