Z_{12-I} Orbifold Compactification toward SUSY Standard Model

We explain the orbifold compactification in string models and present a Z_{12-I} orbifold compactification toward supersymmetric standard models. We also point out an effective R-parity from this string construction. The VEVs of gauge singlets are chosen such that phenomenological constraints are satisfied.Comment: 13 pages with 5 figure. Talk presented at "CTP Symposium on SUSY at LHC", Cairo, 11-14 March 200

Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

In this paper, we consider noncompact ancient solutions to the mean curvature flow in $\mathbb{R}^{n+1}$ ($n \geq 3$) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.Comment: In this paper, we extend the result in arxiv:1711.00823 to higher dimensions, assuming uniform two-convexit

Cosmological constant is probably adjustable in brane worlds

In the brane world scenario, possessing the self-tuning property of the cosmological constant, we study the probability amplitude for an initial state of the Universe to transform to final states with some curvatures. In the Kim, Kyae and Lee model, there exists a finite range of parameters such that the transition amplitude to a near flat universe is exponentially dominated by the smallness of curvature, > e^{positive number}/{Lambda-bar}^2}, i.e. is dominated by an almost flat universe of |Lambda-bar|<epsilon.Comment: 6 pages with 2 figure