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Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
We report a recent paper of Witt Nystrom, where he proved the differentiability of volume functions using deformation to the normal cone.
When two balls in a metric space have small intersection? We give some natural conditions to guarantee an exponential decay on the volume of such intersections. Our proof is conceptually simple, makin...
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
Our knowledge of dwindling sea ice coverage in the Arctic Ocean comes mostly through satellites, which have imaged sea ice from above since 1979. The University of Washington Pan-Arctic Ice Ocean and ...
In order to evaluate the fluctuation of Taihui Lake, ICESat/Hydroweb and Landsat data recorded from 1975 to 2015 were used to examine changes in lake level and area, derived from Normalized Difference...
Plasma volume expansion is an important component of a successful pregnancy. The failure of maternal plasma volume expansion has been implicated in adverse obstetric outcomes such as pre-eclampsia, fe...
Scientists at the University of California, Davis have discovered that DNA sequences thought to be essential for gene activity can be expendable. Sequences once called junk sometimes call the shots in...
Durable proteins make life possible in the crushing depths of the ocean, and may have evolved in life below the surface of ice-bound oceanic exo-planets. These proteins stay folded – allowing them to ...
For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a parametrization of the set of conjugacy classes of boundary-unipotent representations of π1(M) into SL(n, C). Our param...
We give an e ient simpli ial formula for the volume and ChernSimons invariant of a boundary-paraboli PSL(2,C)representation of a tame 3manifold
Since Stein’s original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribu...
In this study, we demonstrate the use of a geo-spatial information system for volume estimation of fallout deposits and for identification of syn-eruptive and post-eruptive depositional mechanisms. Fo...
The objective of this paper is to improve the cost-effectiveness (accuracy of estimates versus applied costs) of present ITC (Individual Tree Crown) approaches which are based on 1) aerial imagery or...

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