An Exact Solution Method for Binary Equilibrium Problems with Compensation and the Power Market Uplift Problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity

The waiting time paradox: population based retrospective study of treatment delay and survival of women with endometrial cancer in Scotland

No abstract available

Uniqueness of Flat Spherically Symmetric Spacelike Hypersurfaces Admitted by Spherically Symmetric Static Spactimes

It is known that spherically symmetric static spacetimes admit a foliation by {\deg}at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of {\deg}at foliations for studying black hole physics. Here {\deg}at spherically symmetric spacelike hy- persurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit {\deg}at spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the time- like Killing vector. This result guarantees the uniqueness of {\deg}at spherically symmetric foliations for such spacetimes.Comment: 10 page

N-(4-Hydroxy­phen­yl)-2-(1,1,3-trioxo-2,3-di­hydro-1,2-benzothia­zol-2-yl)­acet­amide

In the title compound, C15H12N2O5S, the benzisothia­zole group is approximately planar (r.m.s. deviation excluding H atoms and the two O atoms bonded to S = 0.023 Å). The dihedral angle between the benzisothia­zole ring and the terminal phenol ring is 84.9 (1)°. In the crystal, mol­ecules are joined by N—H⋯O and O—H⋯O hydrogen bonds, and π-stacking inter­actions are observed between alternating phenol and benzisothia­zole rings [centroid–centroid distances = 3.929 (3) and 3.943 (3) Å]

Asymptotic Behaviour of the Proper Length and Volume of the Schwarzschild Singularity

Though popular presentations give the Schwarzschild singularity as a point it is known that it is spacelike and not timelike. Thus it has a "length" and is not a "point". In fact, its length must necessarily be infinite. It has been proved that the proper length of the Qadir-Wheeler suture model goes to infinity [1], while its proper volume shrinks to zero, and the asymptotic behaviour of the length and volume have been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture". The question arises whether a similar analysis could provide the asymptotic behaviour of the Schwarzschild black hole near the singularity. It is proved here that, unlike the behaviour for the suture model, for the Schwarzschild essential singularity $\Delta s$ $\thicksim$ $K^{1/3}\ln K$ and $V\thicksim$ $K^{-1}\ln K$, where $K$ is the mean extrinsic curvature, or the York time.Comment: 13 pages, 1 figur

Auction-Based Allocation of Shared Electricity Storage Resources through Physical Storage Rights

This article proposes a new electricity storage business model based on multiple simultaneously considered revenue streams, which can be attributed to different market activities and players. These players thus share electricity storage resources and compete to obtain the right to use them in a dynamic allocation mechanism. It is based on the design of anew periodically organized auction to allocate shared storage resources through physical storage rights between different market players and ac-companying applications. Through such a flexibility platform owners of flexible resources can commercialize their flexible capacity over different applications, while market players looking for additional flexibility can obtain this through a pay-per-use principle and thus not having to make long-term investment commitments. As such, they can quickly adapt their portfolio according to the market situation. Alternatively, through such an allocation mechanism players can effectively share storage re-sources. Players may be incentivized to participate as they can share the investment cost, mitigate risk, exploit economies of scale, overcome regulatory barriers, and merge time-varying and player-dependent flexibility needs. The mechanism allocates the limited storage resources to the most valuable application for each market-clearing, based on the competing players' willingness-to-pay. An illustrative case study is provided in which three players share storage resources that are allocated through a daily auction with hourly market-clearings

Phonon runaway in nanotube quantum dots

We explore electronic transport in a nanotube quantum dot strongly coupled with vibrations and weakly with leads and the thermal environment. We show that the recent observation of anomalous conductance signatures in single-walled carbon nanotube (SWCNT) quantum dots can be understood quantitatively in terms of current driven `hot phonons' that are strongly correlated with electrons. Using rate equations in the many-body configuration space for the joint electron-phonon distribution, we argue that the variations are indicative of strong electron-phonon coupling requiring an analysis beyond the traditional uncorrelated phonon-assisted transport (Tien-Gordon) approach.Comment: 8 pages, 6 figure