Zobrazeno 1 - 10
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pro vyhledávání: '"Hakopian A"'
Autor:
Hakopian, Hakop
Let a set of nodes $\mathcal X$ in the plane be $n$-independent, i.e., each node has a fundamental polynomial of degree $n.$ Assume that\\ $\#\mathcal X=d(n,n-3)+3= (n+1)+n+\cdots+5+3.$ In this paper we prove that there are at most three linearly ind
Externí odkaz:
http://arxiv.org/abs/2209.08576
A two-dimensional $n$-correct set is a set of nodes admitting unique bivariate interpolation with polynomials of total degree at most ~$n$. We are interested in correct sets with the property that all fundamental polynomials are products of linear fa
Externí odkaz:
http://arxiv.org/abs/2208.06784
Autor:
Matthew Bergosh, Sasha Medvidovic, Nancy Zepeda, Lindsey Crown, Jennifer Ipe, Lauren Debattista, Luis Romero, Eimon Amjadi, Tian Lam, Erik Hakopian, Wooseong Choi, Kevin Wu, Jack Yu Tung Lo, Darrin Jason Lee
Publikováno v:
Frontiers in Neuroscience, Vol 18 (2024)
IntroductionBoth ketamine (KET) and medial prefrontal cortex (mPFC) deep brain stimulation (DBS) are emerging therapies for treatment-resistant depression, yet our understanding of their electrophysiological mechanisms and biomarkers is incomplete. T
Externí odkaz:
https://doaj.org/article/d64cfc2b3b684938a375926f997e82ed
Autor:
Gharibyan, Anna R., Hakopian, Hakop A.
In this paper we prove that the PDE $p(D)f=q,$ where $p$ and $q$ are multivariate polynomials, has a solution in the space of polynomials of total degree not exceeding ${n+s},$ where $n$ is the degree of $q$ and $s$ is the zero order of $O=(0,\ldots,
Externí odkaz:
http://arxiv.org/abs/2106.00272
Let a set of nodes $\mathcal X$ in the plane be $n$-independent, i.e., each node has a fundamental polynomial of degree $n.$ Assume that $\#\mathcal X=d(n,k-3)+3= (n+1)+n+\cdots+(n-k+5)+3$ and $4 \le k\le n-1.$ In this paper we prove that there are a
Externí odkaz:
http://arxiv.org/abs/2105.13863
Autor:
Hakopian, Hakop, Vardanyan, Navasard
In this paper, we prove the Noether theorem with the multiplicities described by PD operators. Despite the known analogue versions in this case the provided conditions are necessary and sufficient. We also prove the Cayley-Bacharach theorem with PD m
Externí odkaz:
http://arxiv.org/abs/2004.01262
Autor:
Hakopian, Hakop, Vardanyan, Navasard
A planar node set $\mathcal X,$ with $\#\mathcal X=\binom{n+2}{2},$ is called $GC_n$ set if each node possesses fundamental polynomial in form of a product of $n$ linear factors. We say that a node uses a line if the line is a factor of the fundament
Externí odkaz:
http://arxiv.org/abs/2001.05306
Akademický článek
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Akademický článek
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Autor:
Hakopian, Hakop, Kloyan, Harutyun
Let a set of nodes $\mathcal X$ in plain be $n$-independent, i.e., each node has a fundamental polynomial of degree $n.$ Suppose also that $|\mathcal X|= d(n,k-2)+2,$ where $d(n,k-2) = (n+1)+n+\cdots+(n-k+4)$ and $\ k\le n-1.$ In this paper we prove
Externí odkaz:
http://arxiv.org/abs/1903.10874