Lax matrices for Yang-Baxter maps

It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quad-graphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff

On the anomalous mass defect of strange stars in the Field Correlator Method

We investigate general aspects of the mass defects of strange stars in the context of the Field Correlator Method, without magnetic field. The main parameters of the model that enter the corresponding nonperturbative equation of state of the quark gluon plasma are the gluon condensate $G_2$ and the large distance static $Q{\bar Q}$ potential $V_1$. We calculate mass defects of stellar configurations in the central density range $11<\log\rho_c<18$. In general, the mass defects are strongly dependent on the model parameters. For a large range of values of $G_2$ and $V_1$, we obtain anomalous mass defects with magnitudes around $10^{53}\,$erg\,, of the same order of the observed energies of gamma-ray bursts and neutrino emissions in SN1987A, and of the theoretically predicted energies of the quark-novae explosions.Comment: 24 pages, 6 figure

Strange stars properties calculated in the framework of the Field Correlator Method

We calculate the strange star properties in the framework of the Field Correlator Method. We find that for the values of the gluon condensate $G_2=0.006\;{\rm GeV}^4$ and $G_2=0.0068\;{\rm GeV}^4$, which give a critical temperature $T_c\sim170\;{\rm MeV}$ at $\mu_c=0$, the sequences of strange stars are compatible with some of the semi-empirical mass-radius relations and data obtained from astrophysical observations.Comment: 26 pages, 10 figure

Optimal portfolio and spending rules for endowment funds

We investigate the role of different spending rules in a dynamic asset allocation model for university endowment funds. In particular, we consider the fixed consumption-wealth ratio (CW) rule and the hybrid rule which smoothes spending over time. We derive the optimal portfolios under these two strategies and compare them with a theoretically optimal (Merton) strategy. We show that the optimal portfolio with habit is less risky compared to the optimal portfolio without habit. A calibrated numerical analysis on U.S. data shows, similarly, that the optimal portfolio under the hybrid strategy is less risky than the optimal portfolios under both the CW and the classical Merton strategies, in typical market conditions. Our numerical analysis also shows that spending under the hybrid strategy is less volatile than the other strategies. Thus, endowments following the hybrid spending rule use asset allocation to protect spending. However, in terms of the endowment’s wealth, the hybrid strategy comparatively outperforms the conventional Merton and CW strategies when the market is highly volatile but under-performs them when there is strong stock market growth and low volatility. Overall, the hybrid strategy is effective in terms of stability of spending and intergenerational equity because, even if it allows short-term fluctuation in spending, it ensures greater stability in the long run