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Hot Games
Published in Michael H. Albert, Richard J. Nowakowski, David Wolfe, Lessons in Play, 2019
Michael H. Albert, Richard J. Nowakowski, David Wolfe
This means that the sequence LS(n · G) is a subadditive sequence. It is well known that for any subadditive sequence an, the limit as n tends to infinity of ann exists and is either −∞ or the lower bound of ann. But dually in our case, the sequence RS(n · G) is superadditive and RS(n · G)/n has a limit that is either ∞ or the upper bound of this sequence. However, RS(n • G) ≤ LS(n · G) and their difference is bounded, so both the limits must actually exist and be a single common number, which we dub m(G).
Privatisation and Regulation of Amsterdam Airport
Published in Peter Forsyth, David W. Gillen, Andreas Knorr, Otto G. Mayer, Hans-Martin Niemeier, David Starkie, The Economic Regulation of Airports, 2017
Although the concept of the natural monopoly may well apply to the network component of most network industries (gas, electricity, water, railroads etc), it can be questioned whether this is the case for airports. A natural monopoly requires the firm's cost function to be subadditive over the entire range of outputs. Actually, this is quite a demanding condition, since we have to determine whether single-firm production of y is cheaper than its production by any combination of smaller firms. That is, we must know C(y*) for every y* ≤ y (Baumol et al, 1982). This requires a constantly decreasing long-run average cost curve. For airports however, this characteristic is unlikely. Doganis (1992), for example, indicates that, beyond a level of about three million passengers, unit costs flatten out and do not seem to vary much with airport size. As pointed out by Starkie (2002), it is even more likely that the cost curve will increase for larger airports, due to the increasing scarcity of one input factor, i.e. land in the neighbouring area of the airport. Thus, competitive entry is not frustrated by returns to scale but rather by other entry barriers, especially the availability of land. Also, other factors may stimulate the airport's market power, such as the lock-in effects for airline operators. This will be addressed in the analysis of relevant markets for airport services of Amsterdam airport.
Preliminary results: Basic theory of elliptic operators
Published in Takao Nambu, Theory of Stabilization for Linear Boundary Control Systems, 2017
in a Banach space is called well posed on (0, ∞), if (i) there is a unique solution u(t) to the problem for each u0∈D(L), and (ii) u(t) continuously depends on u0 in the topology of the space for each t > 0. The semigroup generated by the problem is called a C0-semigroup. The problem (4.6) in L2(Ω) is thus well posed on (0, ∞). When e–tL is a C0-semigroup, the function log ║e–tL║ is subadditive in t > 0. Thus we see that [3, 16, 26, 71], ω*=limt→∞log‖e−tL‖t=inft>0log‖e−tL‖t.
Quantitative recurrence properties in the historic set for symbolic systems
Published in Dynamical Systems, 2021
Recall that a continuous map T on a topological space X is called topologically mixing if for every pair of open sets there is a number s.t. We call the subshift of finite type of is topological mixing if there exists such that for any and any , we have an admissible word w of length n such that awb is admissible. For any continuous define We introduce the topological pressure for shift dynamic systems as a special form of the topological pressure for general dynamical systems in [20]. Define the topological pressure for any by In fact, the above limit exits, because the sequence is subadditive. When , we write by the topological entropy of The variational principle states that where denotes the measure-theoretic entropy of σ-invariant measure μ.
The K-property for subadditive equilibrium states
Published in Dynamical Systems, 2021
The key result used to prove this theorem is Theorem 3.5, which shows that for subadditive equilibrium states, weak mixing is equivalent to the K-property under some suitable assumptions, similar to those used in [6]. This holds even for non-symbolic systems, and we expect it to be of independent interest. The remaining results in this paper are obtained by applying Theorem A to -cocycles, including locally constant cocycles and fibre-bunched cocycles. For any cocycle , we define its norm potential as From the submultiplicativity of the operator norm , it is clear that is subadditive. The singular value potentials are natural generalizations of the norm potentials (see Section 2 for the precise definition).
Characterizing quasi-metric aggregation functions
Published in International Journal of General Systems, 2019
Juan-José Miñana, Oscar Valero
Let and let be a subadditive function. Then the following assertions are equivalent: There exists satisfying the following: for each with we have that ;If such that , then .