Assessing Negotiation Outcomes Matters in Classroom Settings

It is hardly disputable that negotiation outcomes count in real world negotiation settings. In classroom settings, however, the negotiation outcomes often do not count. In many negotiation courses, for the negotiators it does not really matter in any tangible dimensions what kind of outcomes they achieve through the negotiation – not only that they do not need to bear the (hypothetical) consequence of the agreement (or its lack of), but also that the negotiation outcomes do not affect their performance assessment in the negotiation course. Thus on the issue of whether negotiation outcomes count, this type of class-room negotiation is drastically different from those in real world settings. But does that difference really matter? Would it make any difference in terms of student learning? These are the question the current study aims to address

New Hamiltonian constraint operator for loop quantum gravity

A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method, so that its regulated version in the kinematical Hilbert space is diffeomorphism covariant and creates new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.Comment: 5 pages; a few modification

A Remark on Soliton Equation of Mean Curvature Flow

In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension. We show that the following is true: Let $F(x) = (x,f(x)), x \in \mathbb{R}^{n}$ be a graph solution to the soliton equation $$\bar{H}(x) + F^{\bot}(x) = 0.$$ Assume $\sup_{\mathbb{R}^{n}}|Df(x)| \le C_{0} < + \infty$. Then there exists a unique smooth function $f_{\infty}: \mathbb{R}^{n}\to \mathbb{R}^k$ such that $$f_{\infty}(x) = \lim_{\lambda \to \infty}f_{\lambda}(x)$$ and $$f_{\infty}(r x)=r f_{\infty}(x)$$ for any real number $r\not= 0$, where $$f_{\lambda}(x) = \lambda^{-1}f(\lambda x).$$Comment: 6 page