A Pedagogical Discussion on Neutrino Wave-Packet Evolution

We present a pedagogical discussion on the time evolution of a Gaussian neutrino wave packet in free space. A common treatment is to keep momentum terms up to the quadratic order in the expansion of the energy-momentum relation so that the Fourier transform can be evaluated analytically via Gaussian integrals. This leads to a solution representing a flat Gaussian distribution with a constant longitudinal width and a spreading transverse width, which suggests that special relativity would be violated if the neutrino wave packet were detected on its edge. However, we demonstrate that by including terms of higher order in momentum the correct geometry of the wave packet is restored. The corrected solution has a spherical wave front so that it complies with special relativity.Comment: submitted to 2013 TAUP Conference Proceeding

Rotationally symmetric harmonic diffeomorphisms between surfaces

In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.Comment: Minor typos correcte

The Differentiation Balance of Bone Marrow Mesenchymal Stem Cells Is Crucial to Hematopoiesis.

Bone marrow mesenchymal stem cells (BMSCs), the important component and regulator of bone marrow microenvironment, give rise to hematopoietic-supporting stromal cells and form hematopoietic niches for hematopoietic stem cells (HSCs). However, how BMSC differentiation affects hematopoiesis is poorly understood. In this review, we focus on the role of BMSC differentiation in hematopoiesis. We discussed the role of BMSCs and their progeny in hematopoiesis. We also examine the mechanisms that cause differentiation bias of BMSCs in stress conditions including aging, irradiation, and chemotherapy. Moreover, the differentiation balance of BMSCs is crucial to hematopoiesis. We highlight the negative effects of differentiation bias of BMSCs on hematopoietic recovery after bone marrow transplantation. Keeping the differentiation balance of BMSCs is critical for hematopoietic recovery. This review summarises current understanding about how BMSC differentiation affects hematopoiesis and its potential application in improving hematopoietic recovery after bone marrow transplantation