Zobrazeno 1 - 10
of 40
pro vyhledávání: '"52Axx"'
Autor:
Indrei, Emanuel, Karakhanyan, Aram
In this paper we completely settle the Almgren problem in $\mathbb R^3$ under some generic conditions on the potential and tension functions. The problem, among other things, appears in classical thermodynamics when one is to understand if minimizing
Externí odkaz:
http://arxiv.org/abs/2406.00241
Autor:
Kazarnovskii, Boris
We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex vector bundle a
Externí odkaz:
http://arxiv.org/abs/2404.07596
Autor:
Schweighofer, Markus
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and 10 are the
Externí odkaz:
http://arxiv.org/abs/2205.04211
Autor:
Ryabogin, Dmitry
We give a negative answer to Ulam's Problem 19 from the Scottish Book asking {\it is a solid of uniform density which will float in water in every position a sphere?} Assuming that the density of water is $1$, we show that there exists a strictly con
Externí odkaz:
http://arxiv.org/abs/2102.01787
Autor:
Ryabogin, Dmitry
Let $d\ge 2$ and let $K$ and $L$ be two convex bodies in ${\mathbb R^d}$ such that $L\subset \textrm{int}\,K$ and the boundary of $L$ does not contain a segment. If $K$ and $L$ satisfy the $(d+1)$-equichordal property, i.e., for any line $l$ supporti
Externí odkaz:
http://arxiv.org/abs/2010.09864
Autor:
Ryabogin, Dmitry
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
Comment: 6 figures, 16 pages
Comment: 6 figures, 16 pages
Externí odkaz:
http://arxiv.org/abs/2010.09565
Autor:
Akian, Jean-Luc
In this paper we show that the proof of the convexity of the set of lamination parameters given by J.L. Grenestedt and P. Gudmundson, which is extensively cited in the literature, is not correct. We give a proof of the convexity of this set when the
Externí odkaz:
http://arxiv.org/abs/2010.07707
Autor:
Weis, Stephan, Shirokov, Maksim
Publikováno v:
Journal of Convex Analysis, 28:3 (2021), 847-870
We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex set with a sublevel or level set of a generalized affine functional, t
Externí odkaz:
http://arxiv.org/abs/2003.14302
Autor:
Weis, Stephan, Shirokov, Maksim
Publikováno v:
Russian Math. Surveys, 76:1 (2021), 190-192
We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy in terms of a continuous convex combination of pure states of bounded
Externí odkaz:
http://arxiv.org/abs/2002.03969
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations.
Externí odkaz:
http://arxiv.org/abs/1701.01990