scholarly journals The reduction number and degree bound of projective subschemes

2019 ◽  
Vol 373 (2) ◽  
pp. 1153-1180 ◽  
Author(s):  
Đoàn Trung Cường ◽  
Sijong Kwak
Keyword(s):  
Reduction Number ◽  
Degree Bound

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

scholarly journals Lee-Yang zeros of the antiferromagnetic Ising model

2021 ◽  
pp. 1-35
Author(s):  
FERENC BENCS ◽  
PJOTR BUYS ◽  
LORENZO GUERINI ◽  
HAN PETERS
Keyword(s):  
Ising Model ◽  
Partition Functions ◽  
Cayley Trees ◽  
Circular Arcs ◽  
Precise Characterization ◽  
Ferromagnetic Ising Model ◽  
Location Of Zeros ◽  
Antiferromagnetic Ising Model ◽  
Recursively Defined Trees ◽  
Degree Bound

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

scholarly journals Borel-fixed ideals and reduction number

2003 ◽  
Vol 270 (1) ◽  
pp. 335-346 ◽  
Author(s):  
Lê Tuân Hoa ◽  
Ngô Viêt Trung
Keyword(s):  
Reduction Number

scholarly journals Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fatmawati ◽  
Muhammad Altaf Khan ◽  
Cicik Alfiniyah ◽  
Ebraheem Alzahrani
Keyword(s):  
Statistical Data ◽  
Dengue Infection ◽  
Fractional Operator ◽  
Novel Approach ◽  
Reduction Number ◽  
Best Fitting ◽  
The Stability ◽  
Parameter Values ◽  
Graphical Illustration ◽  
Stability Results

AbstractIn this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings

1992 ◽  
Vol 111 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Yinghwa Wu
Keyword(s):  
Local Ring ◽  
Residue Field ◽  
Primary Ideal ◽  
Local Rings ◽  
Hilbert Polynomials ◽  
Higher Dimensional ◽  
Reduction Number ◽  
Minimal Reduction ◽  
System Of Parameters

Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.

scholarly journals DELAUNAY AND DIAMOND TRIANGULATIONS CONTAIN SPANNERS OF BOUNDED DEGREE

2009 ◽  
Vol 19 (02) ◽  
pp. 119-140 ◽  
Author(s):  
PROSENJIT BOSE ◽  
MICHIEL SMID ◽  
DAMING XU
Keyword(s):  
Unit Disk ◽  
Delaunay Triangulation ◽  
Maximum Degree ◽  
Time Algorithm ◽  
Connected Subgraph ◽  
Unit Disk Graph ◽  
Bounded Degree ◽  
Vertex Set ◽  
Range Of Values ◽  
Degree Bound

Given a triangulation G, whose vertex set V is a set of n points in the plane, and given a real number γ with 0 < γ < π, we design an O(n)-time algorithm that constructs a connected subgraph G' of G with vertex set V whose maximum degree is at most 14 + ⌈2π/γ⌉. If G is the Delaunay triangulation of V, and γ = 2π/3, we show that G' is a t-spanner of V (for some constant t) with maximum degree at most 17, thereby improving the previously best known degree bound of 23. If G is a triangulation satisfying the diamond property, then for a specific range of values of γ dependent on the angle of the diamonds, we show that G' is a t-spanner of V (for some constant t) whose maximum degree is bounded by a constant dependent on γ. If G is the graph consisting of all Delaunay edges of length at most 1, and γ = π/3, we show that a modified version of the algorithm produces a plane subgraph G' of the unit-disk graph which is a t-spanner (for some constant t) of the unit-disk graph of V, whose maximum degree is at most 20, thereby improving the previously best known degree bound of 25.

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