Statistics of Gaussian packets on metric and decorated graphs

VL Chernyshev, AI Shafarevich - … Transactions of the …, 2014 - royalsocietypublishing.org
We study a semiclassical asymptotics of the Cauchy problem for a time-dependent
Schrödinger equation on metric and decorated graphs with a localized initial function. A …

A sharp lower bound for the geometric genus and Zariski multiplicity question

SST Yau, H Zuo - Mathematische Zeitschrift, 2018 - Springer
It is well known that the geometric genus and multiplicity are two important invariants for
isolated singularities. In this paper we give a sharp lower estimate of the geometric genus in …

A sharp estimate of positive integral points in 6-dimensional polyhedra and a sharp estimate of smooth numbers

A Liang, S Yau, HQ Zuo - Science China Mathematics, 2016 - Springer
Abstract Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number
theoretic conjecture (see Conjecture 1.3) which gives a sharp polynomial upper bound of …

[HTML][HTML] On the polynomial sharp upper estimate conjecture in 7-dimensional simplex

SST Yau, B Yuan, H Zuo - Journal of Number Theory, 2016 - Elsevier
Because of its importance in number theory and singularity theory, the problem of finding a
polynomial sharp upper estimate of the number of positive integral points in an n …

How the permutation of edges of a metric graph affects the number of points moving along the edges

VL Chernyshev, AA Tolchennikov - arXiv preprint arXiv:1410.5015, 2014 - arxiv.org
We consider a dynamical system on a metric graph, that corresponds to a semiclassical
solution of a time-dependent Schr\" odinger equation. We omit all details concerning …

Proposing a New Theorem to Determine If an Algebraic Polynomial Is Nonnegative in an Interval

KP Lin, YF Wang, RY Wang, A Yang - Mathematics, 2021 - mdpi.com
We face the problem to determine whether an algebraic polynomial is nonnegative in an
interval the Yau Number Theoretic Conjecture and Yau Geometric Conjecture is proved. In …

Proposing a New Theorem To Determine If an Algebraic Polynomial Is Nonnegative in an Interval. Mathematics 2021, 9, 167

KP Lin, YF Wang, RY Wang, A Yang - 2021 - search.proquest.com
We face the problem to determine whether an algebraic polynomial is nonnegative in an
interval the Yau Number Theoretic Conjecture and Yau Geometric Conjecture is proved. In …

[PDF][PDF] Уравнения Шрёдингера на графах и сингулярных пространствах: спектральные свойства и квазиклассическая динамика локализованных пакетов

АА Толченников, ВЛ Чернышев… - Наноструктуры …, 2014 - nano-journal.ru
Уравнения Шрёдингера на геометрических графах изучаются, начиная с 30-х годов
прошлого века; изначально они использовались в модели свободных электронов в …

Количество точек, движущихся по метрическому графу: зависимость от перестановки ребер

ВЛ Чернышев, АА Толченников - … и компьютерные технологии, 2012 - cyberleninka.ru
Рассматривается дискретная задача о движении точек на метрическом графе,
связанная с задачей об изучении статистики гауссовых пакетов на пространственной …

Sharp upper estimate of geometric genus and coordinate-free characterization of isolated homogeneous hypersurface singularities

KP Lin, S Raghuvanshi, SST Yau… - Asian Journal of …, 2018 - intlpress.com
The subject of counting positive lattice points in $ n $-dimensional simplexes has interested
mathematicians for decades due to its applications in singularity theory and number theory …