Open case: Closed

2021 ◽  
Author(s):  
Anveez Azeez ◽  
Diksha Shirodkar ◽  
K S Sahana ◽  
Gautham Pai
Keyword(s):  
Open Case

scholarly journals Toughness, Forbidden Subgraphs and Pancyclicity

2021 ◽  
Vol 37 (3) ◽  
pp. 839-866
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang
Keyword(s):  
Recent Article ◽  
Forbidden Subgraph ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Complete Answer ◽  
Open Case

AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Rings whose additive endomorphisms are ring endomorphisms

1990 ◽  
Vol 42 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Gary Birkenmeier ◽  
Henry Heatherly
Keyword(s):  
Subdirectly Irreducible ◽  
Finiteness Conditions ◽  
Chain Conditions ◽  
Open Questions ◽  
Open Case ◽  
Ring Endomorphism ◽  
Substantial Progress ◽  
Additive Endomorphism ◽  
Made In

A ring R is said to be an AE-ring if every additive endomorphism is a ring endomorphism. In this paper further steps are made toward solving Sullivan's Problem of characterising these rings. The classification of AE-rings with. R3 ≠ 0 is completed. Complete characterisations are given for AE-rings which are either: (i) subdirectly irreducible, (ii) algebras over fields, or (iii) additively indecomposable. Substantial progress is made in classifying AE-rings which are mixed – the last open case – by imposing various finiteness conditions (chain conditions on special ideals, height restricting conditions). Several open questions are posed.

TOPOS: A Prototyping-Oriented Open CASE System

1993 ◽  
pp. 209-225
Author(s):  
R. Plösch ◽  
H. Rumerstorfer ◽  
R. Weinreich
Keyword(s):  
Case System ◽  
Open Case

Thinking Regional on Peace Missions in Latin America

2017 ◽  
Vol 21 (3-4) ◽  
pp. 177-196
Author(s):  
Monica Hirst
Keyword(s):  
Latin America ◽  
Latin American ◽  
The United States ◽  
Post Cold War ◽  
Peace Processes ◽  
Post Conflict ◽  
Open Case ◽  
Response Capacity ◽  
Latin America And Caribbean ◽  
The Caribbean

As is the case with other regions, in Latin America and the Caribbean, multilateral peace missions are subordinated to norms and expectations of specific mandates. Yet, post-Cold War peace missions in Latin America and the Caribbean share circumstances that are unique to this region. This article seeks to offer a sequenced overview of three scenarios – Central America, Haiti and Colombia – to show how these circumstances interplay as shaping factors in regional peace missions. Three circumstances are highlighted: i) the strategic irrelevance of the region; ii) the preeminence of the United States in Latin America and the Caribbean; iii) the response capacity of Latin American governments. These three are addressed as the core cast of determinants in post-conflict contexts in Latin America and Caribbean. This article explores how these circumstances have adapted in time producing reiterative dynamics attuned to international and regional changing landscapes. Even though the Colombian experience should be considered “an open case”, its inclusion contributes to enrich this argument. Final reflections raise the question if these circumstances explain as well the failures and reversed expectations of regional peace processes.

Analysis and Simulation of Inner Flow Condition of a Novel Rotary on/off Valve

2012 ◽  
Vol 220-223 ◽  
pp. 1698-1702
Author(s):  
Jian Chen ◽  
Zhu Ming Su ◽  
Qi Zhou ◽  
Jian Ping Shu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Flow Condition ◽  
High Speed ◽  
Ansys Fluent ◽  
Revolution Speed ◽  
Pressure Profiles ◽  
Open Case ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Method

A novel hydraulic rotary high speed on/off valve is investigated. The function of the outlet turbine and the effect on revolution speed of valve spool are analyzed. The inner fluid flow condition under full open case of the on/off valve is simulated using computational fluid dynamics(CFD) method based on Ansys/Fluent and velocity and pressure profiles of fluid inside valve are obtained. Suggestions on optimizing the geometry of valve to decrease transition losses are given.

scholarly journals A skew Hadamard matrix of order 36

1970 ◽  
Vol 11 (3) ◽  
pp. 343-344 ◽  
Author(s):  
J. M. Goethals ◽  
J. J. Seidel
Keyword(s):  
Present Note ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Open Case

Hadamard matrices exist for infinitely many orders 4m, m ≧ 1, m integer, including all 4m < 100, cf. [3], [2]. They are conjectured to exist for all such orders. Skew Hadamard matrices have been constructed for all orders 4m < 100 except for 36, 52, 76, 92, cf. the table in [4]. Recently Szekeres [6] found skew Hadamard matrices of the order 2(pt +1)≡ 12 (mod 16), p prime, thus covering the case 76. In addition, Blatt and Szekeres [1] constructed one of order 52. The present note contains a skew Hadamard matrix of order 36 (and one of order 52), thus leaving 92 as the smallest open case.

scholarly journals Upper Bounds on the Minimum Size of Hamilton Saturated Hypergraphs

10.37236/5252 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Andrzej Ruciński ◽  
Andrzej Żak
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Minimum Size ◽  
Uniform Hypergraph ◽  
Open Case ◽  
Vertex Ordering

For $1\leqslant \ell< k$,  an $\ell$-overlapping $k$-cycle is a $k$-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of $k$ consecutive vertices and every two consecutive edges share exactly $\ell$ vertices.A $k$-uniform hypergraph $H$ is $\ell$-Hamiltonian saturated if $H$ does not contain an $\ell$-overlapping Hamiltonian $k$-cycle but every hypergraph obtained from $H$ by adding one edge does contain such a cycle. Let $\mathrm{sat}(n,k,\ell)$ be the smallest number of edges in an $\ell$-Hamiltonian saturated $k$-uniform hypergraph on $n$ vertices. In the case of graphs Clark and Entringer showed in 1983 that $\mathrm{sat}(n,2,1)=\lceil \tfrac{3n}2\rceil$. The present authors proved that for $k\geqslant 3$ and $\ell=1$, as well as for all $0.8k\leqslant \ell\leq k-1$, $\mathrm{sat}(n,k,\ell)=\Theta(n^{\ell})$. In this paper we prove two upper bounds which cover the remaining range of $\ell$. The first, quite technical one, restricted to $\ell\geqslant\frac{k+1}2$, implies in particular that for $\ell=\tfrac23k$ and $\ell=\tfrac34k$ we have $\mathrm{sat}(n,k,\ell)=O(n^{\ell+1})$. Our main result provides an upper bound $\mathrm{sat}(n,k,\ell)=O(n^{\frac{k+\ell}2})$ valid for all $k$ and $\ell$. In the smallest open case we improve it further to $\mathrm{sat}(n,4,2)=O(n^{\frac{14}5})$.

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