Results 91 to 100 of about 25,354 (185)

Border Basis of an Ideal of Points and its Application in Experimental Design and Regression

پژوهش‌های ریاضی, 2020
Introduction Border bases are a generalization of Gröbner bases for zero-dimensional ideals which have attracted the interest of many researchers recently. More precisely, border bases provide a new method to find a structurally stable monomial basis for
Samira Poukhajouei, Sare Goli, Amir Hashemi   +2 more
doaj  

An algorithm to compute the Stanley depth of monomial ideals

Le Matematiche, 2008
In this article we describe an algorithm to compute the Stanley depth of I=J where I and J are monomial ideals. We describe also an implementation in CoCoA.
Giancarlo Rinaldo
doaj  

Gotzmann monomial ideals

Illinois Journal of Mathematics, 2007
A Gotzmann monomial ideal of the polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. A subset $V$ is said to be a Gotzmann subset if the ideal generated by $V$ is a Gotzmann monomial ideal.
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Algebraic invariants of edge ideals of some circulant graphs

AIMS Mathematics
Let $ S $ be a polynomial ring over a field and $ I $ be an edge ideal associated with some classes of circulant graphs. We discussed the algebraic invariants, namely, regularity, projective dimension, depth, and the Stanley depth of $ S/I. $
Bakhtawar Shaukat, Muhammad Ishaq, Ahtsham Ul Haq   +2 more
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On the Hilbert depth of the Hilbert function of a finitely generated graded module

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Let K be a field, A a standard graded K-algebra and M a finitely generated graded A-module. Inspired by our previous works, see [2] and [3], we study the invariant called Hilbert depth of hM, that is hdepth(hM)=max{d:∑j≤k(-1)k-j(d-jk-j)hM(j)≥0  for  all ...
Bălănescu Silviu, Cimpoeaş Mircea
doaj   +1 more source

Efficient next-generation reservoir computing: An analog in-memory implementation using memristor crossbar arrays

iScience
Summary: Reservoir computing has garnered significant attention for its efficiency in processing temporal signals, while the proposed next-generation reservoir computing (NG-RC) further enhances computational efficiency.
Zhuosheng Lin, Xiaona Wu, Zaofeng Chen, Jilong Zhang, Jingliang Deng, Yue Feng   +5 more
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Monomial ideals and $n$-lists

Illinois Journal of Mathematics, 2004
Generalizing a construction of \textit{A. V. Geramita}, \textit{T. Harima} and \textit{Y. S. Shin} [Ill. J. Math 45, 1--23 (2001; Zbl 1095.13500)], the author introduces so-called \(n\)-lists: A \(1\)-list is a natural number, and for \(n\geq 1\) an \(n\)-list is a decreasing infinite sequence of \((n- 1)\)-lists, where \(A\geq B\) for two \(n\)-lists \
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Increasing subsequences, matrix loci and Viennot shadows

Forum of Mathematics, Sigma
Let ${\mathbf {x}}_{n \times n}$ be an $n \times n$ matrix of variables, and let ${\mathbb {F}}[{\mathbf {x}}_{n \times n}]$ be the polynomial ring in these variables over a field ${\mathbb {F}}$ .
Brendon Rhoades
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Higher Polynomial Identities for Mutations of Associative Algebras. [PDF]

Results Math, 2023
Bremner MR, Brox J, Sánchez-Ortega J.
europepmc   +1 more source

Local Cohomology at Monomial Ideals

Journal of Symbolic Computation, 2000
For a reduced monomial ideal B in R=k[X_1,...,X_n], we write H^i_B(R) as the union of {Ext^i(R/B^[d],R)}_d, where {B^[d]}_d are the "Frobenius powers of B". We describe H^i_B(R)_p, for every p in Z^n, in the spirit of the Stanley-Reisner theory. As a first application we give an isomorphism Tor_i(B', k)_p\iso Ext^{|p|-i}(R/B,R)_{-p} for all p in {0,1 ...
openaire   +3 more sources