BACKGROUND Nasal tip support is an essential consideration for rhinoplasty in East Asians. There are many techniques to improve tip projection, and among them, the columellar strut is the most popular technique. However, the conventional design is less supportive for rotating the tip. The amount of harvestable septal cartilage is relatively small in East Asians. For an optimal outcome, we propo...

In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...

Let K and L be compact convex sets in Rn. Suppose that, for a given dimension 1 ≤ d ≤ n − 1, every d-dimensional orthogonal projection of L contains a translate of the corresponding projection of K. Does it follow that the original set L contains a translate of K? In other words, if K can be translated to “hide behind” L from any perspective, does it follow that K can “hide inside” L? A compact...

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called flow tents. This allows us to establish weighted norm estimates for Bergman projection P such with respect Muckenhoupt weights. particular, result gives an alternative proof $$L^p$$ boundedness P. Moreover, using extrapolation, are also able derive vector-valued and modular inequalities projection.

This work gives an affirmative answer to a long time research problem. The weighted L projection is of optimal order in approximation measured in the weighted L norm, and stable in the weighted semi-H norm, independent of the jump of the constant weights, in 2D and 3D finite element spaces.

We derive a generalized counting rule for hard exclusive processes involving parton orbital angular momentum and hadron helicity flip. We start with a systematic way to enumerate the Fock components of a hadronic light-cone wave function with n partons and orbital angular momentum projection l(z). We show that the wave-function amplitude psi(n)(x(i),k(i perpendicular ),l(zi)) has a leading beha...

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.