Optimal Switching for Hybrid Semilinear Evolutions

We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed

A Theory of Ex Post Inefficient Renegotiation

We propose a theory of ex post inefficient renegotiation that is based on loss aversion. When two parties write a long-term contract that has to be renegotiated after the realization of the state of the world, they take the initial contract as a reference point to which they compare gains and losses of the renegotiated transaction. We show that loss aversion makes the renegotiated outcome sticky and materially inefficient. The theory has important implications for the optimal design of long-term contracts. First, it explains why parties often abstain from writing a beneficial long-term contract or why some contracts specify transactions that are never ex post efficient. Second, it shows under what conditions parties should rely on the allocation of ownership rights to protect relationship-specific investments rather than writing a specific performance contract. Third, it shows that employment contracts can be strictly optimal even if parties are free to renegotiate

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.Comment: In press in Physical Review Letters; Revised arguments in the introductory part; 3 figure

XMM-Newton observations of GB B1428+4217: confirmation of intrinsic soft X-ray absorption

We report the results of XMM-Newton observations of the X-ray bright, radio-loud blazar GB B1428+4217 at a redshift of z=4.72. We confirm the presence of soft X-ray spectral flattening at energies <0.7 keV as reported in previous ROSAT and BeppoSAX observations. At hard X-ray energies the spectrum is consistent with a power-law although we find the spectral slope varied between both XMM-Newton observations and is also significantly different from that reported previously. Whilst we cannot rule-out intrinsic cold absorption to explain the spectral depression, we favour a dust-free warm absorber. Cold absorption requires a column density ~1.4-1.6 x 10^22 cm^-2 whilst a warm absorber could have up to ~10^23 cm^-2 and an ionization parameter ~10^2. The spectrum of GB B1428+4217 shows remarkable parallels with that of the z=4.4 blazar PMN J0525-3343, in which the available evidence is also most consistent with a warm absorber model.Comment: 5 pages, 5 figures, MNRAS accepted. Minor changes to sections 3.1 and

Upper limit on the critical strength of central potentials in relativistic quantum mechanics

In the context of relativistic quantum mechanics, where the Schr\"odinger equation is replaced by the spinless Salpeter equation, we show how to construct a large class of upper limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant, $g$, of the central potential, $V(r)=-g v(r)$. This critical value is the value of $g$ for which a first $\ell$-wave bound state appears.Comment: 8 page

Chandra observations of Abell 2199

We present results from an analysis of two Chandra observations of the rich, nearby galaxy cluster Abell 2199. We find evidence (having corrected for projection effects) for radial gradients in temperature and metallicity in the X-ray emitting gas: the temperature drops from kT~4.2 keV at R=200 kpc to 1.6 keV within R=5 kpc of the centre. The metallicity rises from ~0.3 solar at R=200 kpc to ~0.7 solar at R=30 kpc before dropping to 0.3 solar within the central 5 kpc. We find evidence for structure in the surface brightness distribution associated with the central radio source 3C338. No evidence is found for the gas having a large spread in temperature at any particular location despite the cooling time being short (<10**9yr) within the central ~15 kpc. Heating and mass cooling rates are calculated for various assumptions about the state of the gas.Comment: 10 pages, 12 figures. Accepted by MNRAS. Minor changes following referee's comment