We show that for any given norm ball or proper cone, weak membership in its dual ball or dual cone is polynomial-time reducible to weak membership in the given ball or cone. A consequence is that the weak membership or membership problem for a ball or cone is NP-hard if and only if the corresponding problem for the dual ball or cone is NP-hard. In a similar vein, we show that computation of the...

N-polar AlGaN epi-layer was realized on AlN seeding layer grown with a novel flow-modulation method. The polarity reversion from Al(Ga)-polar to for AlGaN/AlN films confirmed by KOH etching and subsequent observation optical microscope as well high-resolution X-ray diffraction (HR-XRD) measurement. In particular, the dependence of crystalline quality defect size in epi-layers V/III ratio invest...

A central idea of minimal model theory as formulated by Mori is to study algebraic varieties using convex geometry. The cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves; the dual cone is the cone of nef line bundles. For Fano varieties (varieties with ample anticanonical bundle), these cones are rational polyhe...

Mouse embryos with an additional maternally inherited X chromosome, i.e., disomic for XM (DsXM), cease to grow early in development and have a deficient extraembryonic region. We hypothesized that the underdeveloped extraembryonic region is attributed to two copies of XM that escape inactivation due to maternal imprinting. To examine the validity of this hypothesis and throw more light on the s...

ABSTRACT Recent observations have shown that a large portion of the mid-infrared (MIR) spectrum active galactic nuclei (AGNs) stems from polar regions. In this paper, we investigate effects gas on X-ray AGNs using ray-tracing simulations. Two geometries for are considered, (1) hollow cone corresponding to best-fitting MIR model and (2) filled cone, both with varying column densities (ranging 10...

Basic electrowetting theory predicts that a continued increase in applied voltage will allow contact angle modulation to zero degrees. In practice, the effect of contact angle saturation has always been observed to limit the contact angle modulation, often only down to a contact angle of 60 to 70. The physical origins of contact angle saturation have not yet been explained successfully and uneq...

Tropical polyhedra are known to be representable externally, as intersections of finitely many tropical half-spaces. However, unlike in the classical case, the extreme rays of their polar cones provide external representations containing in general superfluous half-spaces. In this paper, we prove that any tropical polyhedral cone in R (also known as “tropical polytope” in the literature) admits...

A new oogenus and oospecies of the Elongatoolithidae, Undulatoolithus pengi oogen. et oosp. nov., is described on the basis of specimens from the Upper Cretaceous Zhoutian Formation of the Pingxiang Basin, Jiangxi Province, China. The eggs are slightly asymmetrical, paired, and lay radially-oriented in a circular configuration within the clutch, and most suggestive of Macroolithus of the Elonga...

A fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. Instances of this problem arise often in mesh parameterization and 3D deformation. A related problem is to express a vector lying in a convex cone as a non-negative combination of edge rays of this cone. This problem also arises in many applic...

The computation burden of cone-beam forward and back-projectors is one of the greatest challenges facing iterative methods for 3D image reconstruction in CT. This paper describes a new separable footprint (SF) projector. It takes advantage of small polar angles of X-rays in cone-beam geometry to approximate the voxel footprint functions as 2D separable functions with simple rectangular function...