scholarly journals Monomial ideals whose depth function has any given number of strict local maxima

2014 ◽  
Vol 52 (1) ◽  
pp. 11-19 ◽  
Author(s):  
Somayeh Bandari ◽  
Jürgen Herzog ◽  
Takayuki Hibi
2015 ◽  
Vol 25 (4) ◽  
pp. 633-640
Author(s):  
HUNTER SPINK

How many strict local maxima can a real quadratic function on {0, 1}n have? Holzman conjectured a maximum of $\binom{n }{ \lfloor n/2 \rfloor}$. The aim of this paper is to prove this conjecture. Our approach is via a generalization of Sperner's theorem that may be of independent interest.


2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Qingsong Tang

A proper cluster is usually defined as maximally coherent groups from a set of objects using pairwise or more complicated similarities. In general hypergraphs, clustering problem refers to extraction of subhypergraphs with a higher internal density, for instance, maximal cliques in hypergraphs. The determination of clustering structure within hypergraphs is a significant problem in the area of data mining. Various works of detecting clusters on graphs and uniform hypergraphs have been published in the past decades. Recently, it has been shown that the maximum 1,2 -clique size in 1,2 -hypergraphs is related to the global maxima of a certain quadratic program based on the structure of the given nonuniform hypergraphs. In this paper, we first extend this result to relate strict local maxima of this program to certain maximal cliques including 2-cliques or 1,2 -cliques. We also explore the connection between edge-weighted clusters and strictly local optimum solutions of a class of polynomials resulting from nonuniform 1,2 -hypergraphs.


2015 ◽  
Vol 22 (01) ◽  
pp. 23-34 ◽  
Author(s):  
Anda Olteanu

In this paper we characterize all the lexsegment ideals which are normally torsion-free. This will provide a large class of normally torsion-free monomial ideals which are not square-free. Our characterization is given in terms of the ends of the lexsegment. We also prove that, for lexsegment ideals, the property being normally torsion-free is equivalent to the property of the depth function being constant.


2013 ◽  
Vol 217 (9) ◽  
pp. 1764-1772 ◽  
Author(s):  
Jürgen Herzog ◽  
Marius Vladoiu

2000 ◽  
Vol 179 ◽  
pp. 201-204
Author(s):  
Vojtech Rušin ◽  
Milan Minarovjech ◽  
Milan Rybanský

AbstractLong-term cyclic variations in the distribution of prominences and intensities of green (530.3 nm) and red (637.4 nm) coronal emission lines over solar cycles 18–23 are presented. Polar prominence branches will reach the poles at different epochs in cycle 23: the north branch at the beginning in 2002 and the south branch a year later (2003), respectively. The local maxima of intensities in the green line show both poleward- and equatorward-migrating branches. The poleward branches will reach the poles around cycle maxima like prominences, while the equatorward branches show a duration of 18 years and will end in cycle minima (2007). The red corona shows mostly equatorward branches. The possibility that these branches begin to develop at high latitudes in the preceding cycles cannot be excluded.


2020 ◽  
Vol 1515 ◽  
pp. 042105
Author(s):  
D M Malinichev ◽  
E A Melnikova ◽  
Y V Prus

PLoS ONE ◽  
2018 ◽  
Vol 13 (12) ◽  
pp. e0208256
Author(s):  
Shuhan Wang ◽  
Xiaoli Zhang ◽  
Mohammed Abdelmanan Hassan ◽  
Qi Chen ◽  
Chaokui Li ◽  
...  

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 757
Author(s):  
Tianyi Su ◽  
Wenqing Zhang ◽  
Zhijun Zhang ◽  
Xiaowei Wang ◽  
Shiwei Zhang

A 2D axi-symmetric theoretical model of dielectric porous media in intermittent microwave (IMW) thermal process was developed, and the electromagnetic energy, multiphase transport, phase change, large deformation, and glass transition were taken into consideration. From the simulation results, the mass was mainly carried by the liquid water, and the heat was mainly carried by liquid water and solid. The diffusion was the dominant mechanism of the mass transport during the whole process, whereas for the heat transport, the convection dominated the heat transport near the surface areas during the heating stage. The von Mises stress reached local maxima at different locations at different stages, and all were lower than the fracture stress. A material treated by a longer intermittent cycle length with the same pulse ratio (PR) tended to trigger the phenomena of overheat and fracture due to the more intense fluctuation of moisture content, temperature, deformation, and von Mises stress. The model can be extended to simulate the intermittent radio frequency (IRF) process on the basis of which one can select a suitable energy source for a specific process.


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