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of 106
pro vyhledávání: '"ALKAUSKAS, Giedrius"'
Consider a subset [1,2,...,n]x[1,2,...,n] of the plane integer lattice. Take any non self-intersecting n^2-gon built on it (straight angles are allowed). The square of a side length is a positive integer. It is thus natural to ask how large the sum o
Externí odkaz:
http://arxiv.org/abs/2311.03011
Autor:
Alkauskas, Giedrius
For a given finite subset P of points of the lattice Z^2, a friendly path is a monotone (uphill or downhill) lattice path which splits points in half; points lying on the path itself are discarded. The purpose of this paper (and its sequel) is to ful
Externí odkaz:
http://arxiv.org/abs/2302.01137
Autor:
Alkauskas, Giedrius
In this paper we demonstrate a new phenomenon in the area of tilings: a direct analogue of 1D interface and 1D grain boundary.
Comment: 12 pages, 19 figures
Comment: 12 pages, 19 figures
Externí odkaz:
http://arxiv.org/abs/2301.10975
Autor:
Alkauskas, Giedrius
Publikováno v:
Journal of Geometry and Physics (153) July 2020, 103655
A vector field is called a Beltrami vector field, if $B\times(\nabla\times B)=0$. In this paper we construct two unique Beltrami vector fields $\mathfrak{I}$ and $\mathfrak{Y}$, such that $\nabla\times\mathfrak{I}=\mathfrak{I}$, $\nabla\times\mathfra
Externí odkaz:
http://arxiv.org/abs/1706.09295
Autor:
Alkauskas, Giedrius
Publikováno v:
Acta Linguistica Lithuanica. (86):227-257
Externí odkaz:
https://www.ceeol.com/search/article-detail?id=1064952
Autor:
Alkauskas, Giedrius
A 3-dimensional vector field $B$ is said to be Beltrami vector field (force free-magnetic vector field in physics), if $B\times(\nabla\times B)=0$. Motivated by our investigations on projective an polynomial superflows, and as an important side resul
Externí odkaz:
http://arxiv.org/abs/1701.04218
Autor:
Alkauskas, Giedrius
Publikováno v:
Aequationes Math. 91 (2017), no. 5, 871--907
In this second part of the work, we correct the flaw which was left in the proof of the main Theorem in the first part. This affects only a small part of the text in this first part and two consecutive papers. Yet, some additional arguments and addit
Externí odkaz:
http://arxiv.org/abs/1610.05106
Autor:
Alkauskas, Giedrius
In this note we list a number of open problems in the fields of number theory, combinatorics, and representation theory: algebraic functions with Fermat property; power product expansion of the generating function for the partition function; relation
Externí odkaz:
http://arxiv.org/abs/1609.09842
Autor:
Alkauskas, Giedrius
Let $X\in\mathbb{R}^{n}$ or $\mathbb{C}^{n}$. For $\phi:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ (respectively, $\phi:\mathbb{C}^{n}\mapsto\mathbb{C}^{n}$) and $t\in\mathbb{R}$ (respectively, $\mathbb{C}$), we put $\phi^{t}=t^{-1}\phi(Xt)$. A projective
Externí odkaz:
http://arxiv.org/abs/1608.02522
Autor:
Alkauskas, Giedrius
Let $X\in\mathbb{R}^{n}$. For $\phi:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ and $t\in\mathbb{R}$, we put $\phi^{t}=t^{-1}\phi(Xt)$. A projective flow is a solution to the projective translation equation $\phi^{t+s}=\phi^{t}\circ\phi^{s}$, $t,s\in\mathbb
Externí odkaz:
http://arxiv.org/abs/1606.05772