On Order Ideal Convergence in a Metric Additive System

2016 ◽  
Vol 4 (2) ◽  
pp. 159-164
Author(s):  
Bablu Biswas ◽  
D. K. Ganguly
Keyword(s):  
Order Ideal ◽  
Ideal Convergence ◽  
Additive System

scholarly journals The close relation between border and Pommaret marked bases

2021 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi
Keyword(s):  
Finite Order ◽  
Polynomial Ring ◽  
Group Actions ◽  
Close Relation ◽  
Open Covering ◽  
Order Ideal ◽  
Lower Dimension ◽  
Hilbert Schemes ◽  
Affine Spaces ◽  
The Ideal

AbstractGiven a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Finite Difference Method on Non-Uniform Meshes for Time Fractional Diffusion Problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Haili Qiao ◽  
Aijie Cheng
Keyword(s):  
Theoretical Analysis ◽  
Fractional Derivative ◽  
Time Discretization ◽  
Summation Formula ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Initial Moment ◽  
Central Difference ◽  
Ideal Convergence ◽  
Derivative Term

AbstractIn this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence rate when the time discretization is performed on uniform meshes. Therefore, in order to improve the convergence order, the Caputo time fractional derivative term is discretized by the {L2-1_{\sigma}} format on non-uniform meshes, with {\sigma=1-\frac{\alpha}{2}}, while the spatial derivative term is approximated by the classical central difference scheme on uniform meshes. According to the summation formula of positive integer k power, and considering {k=3,4,5}, we propose three non-uniform meshes for time discretization. Through theoretical analysis, different time convergence orders {O(N^{-\min\{k\alpha,2\}})} can be obtained, where N denotes the number of time splits. Finally, the theoretical analysis is verified by several numerical examples.

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

Λ-strongly summable sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Ayhan Esi ◽  
M. Kemal Özdemir
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Summable Sequence ◽  
Inclusion Results

AbstractIn this paper we introduce some certain new sequence spaces via ideal convergence, λ-sequence and an Orlicz function in n-normed spaces and study different properties of these spaces and also establish some inclusion results among them.

scholarly journals Facile Deoxygenation of Dicarbonyl Compounds Using a Samarium Diiodide–Additive System

2005 ◽  
Vol 53 (8) ◽  
pp. 1017-1020 ◽  
Author(s):  
Yasuko Kamochi ◽  
Tadahiro Kudo ◽  
Toshinobu Masuda ◽  
Akira Takadate
Keyword(s):  
Samarium Diiodide ◽  
Dicarbonyl Compounds ◽  
Additive System

scholarly journals Catalytic defluorinative [3 + 2] cycloaddition of trifluoromethylalkenes with alkynes via reduction of nickel(ii) fluoride species

2015 ◽  
Vol 44 (45) ◽  
pp. 19460-19463 ◽  
Author(s):  
Takeshi Fujita ◽  
Tomohiro Arita ◽  
Tomohiro Ichitsuka ◽  
Junji Ichikawa
Keyword(s):  
Nickel Catalyst ◽  
Catalytic Synthesis ◽  
Additive System ◽  
System P

A catalytic synthesis of 2-fluoro-1,3-cyclopentadienes was achieved via [3 + 2] cycloaddition of 2-trifluoromethyl-1-alkenes and alkynes using a nickel catalyst and a diboron-based ternary additive system.

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