Zobrazeno 1 - 10
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pro vyhledávání: '"YOST, DAVID"'
We establish a lower bound theorem for the number of $k$-faces ($1\le k\le d-2$) in a $d$-dimensional polytope $P$ (abbreviated as a $d$-polytope) with $2d+2$ vertices, building on the known case for $k=1$. There are two distinct lower bounds dependi
Externí odkaz:
http://arxiv.org/abs/2409.14294
We study the existence and structure of $d$-polytopes for which the number $f_1$ of edges is small compared to the number $f_0$ of vertices. Our results are more elegantly expressed in terms of the excess degree of the polytope, defined as $2f_1-df_0
Externí odkaz:
http://arxiv.org/abs/2405.16838
The problem of calculating exact lower bounds for the number of $k$-faces of $d$-polytopes with $n$ vertices, for each value of $k$, and characterising the minimisers, has recently been solved for $n\le2d$. We establish the corresponding result for $
Externí odkaz:
http://arxiv.org/abs/2102.12813
Autor:
Wang, Jie, Yost, David
It is possible for a combinatorial type of polytope to have both decomposable and indecomposable realizations; here decomposability is meant with respect to Minkowski addition. Such polytopes are called conditionally decomposable. We show that the mi
Externí odkaz:
http://arxiv.org/abs/2102.10868
We define an analogue of the cube and an analogue of the 5-wedge in higher dimensions, each with $2d+2$ vertices and $d^2+2d-3$ edges. We show that these two are the only minimisers of the number of edges, amongst d-polytopes with $2d+2$ vertices, fo
Externí odkaz:
http://arxiv.org/abs/2005.06746
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope of a family
Externí odkaz:
http://arxiv.org/abs/1910.08156
Autor:
Yost, David M.
Research shows that stress in the workplace can contribute to negative physical and mental health outcomes among workers in a variety of settings, while the personality disposition of Hardiness can serve as a protective factor against those outcomes.
Externí odkaz:
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1466085691
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the notion of
Externí odkaz:
http://arxiv.org/abs/1708.09743
It is known that polytopes with at most two nonsimple vertices are reconstructible from their graphs, and that $d$-polytopes with at most $d-2$ nonsimple vertices are reconstructible from their 2-skeletons. Here we close the gap between 2 and $d-2$,
Externí odkaz:
http://arxiv.org/abs/1704.00854
We define the excess degree $\xi(P)$ of a $d$-polytope $P$ as $2f_1-df_0$, where $f_0$ and $f_1$ denote the number of vertices and edges, respectively. This parameter measures how much $P$ deviates from being simple. It turns out that the excess degr
Externí odkaz:
http://arxiv.org/abs/1703.10702