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Separating Polynomial $$\chi $$-Boundedness from $$\chi $$-Boundedness [PDF]
AbstractExtending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function $$f:\mathbb {N}\rightarrow \mathbb {N}\cup \{\infty \}$$ f : N → N ∪ {
Briański, M, Davies, J, Walczak, B
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Adjectives and boundedness [PDF]
This paper examines the significance of the schematic domain of BOUNDEDNESS in adjectives. It is proposed that boundedness in adjectives is a fundamental characteristic associated with gradability. Cross-categorial correspondences are made to nouns and verbs, where boundedness is a feature of countability and aktionsart respectively. Two basic types of
Carita Paradis
exaly +4 more sources
AbstractIf a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? András Gyárfás made a number of challenging conjectures about this in the early 1980s, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are
Alex Scott, Paul Seymour
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$R$ -Boundedness versus $\gamma$ -boundedness [PDF]
It is well-known that in Banach spaces with finite cotype, the $R$-bounded and $\gamma$-bounded families of operators coincide. If in addition $X$ is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that $R$-boundedness implies $\gamma$-boundedness.
Kwapien, Stanislaw+2 more
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boundedness of solutions [PDF]
This chapter presents the concepts of uniform boundedness, quasiuniform boundedness, and uniform ultimate boundedness in the scenery of generalized ordinary differential equations (ODEs). It includes criteria of uniform boundedness and uniform ultimate boundedness for the generalized ODE.
Afonso, Suzete M.+6 more
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Reuniting $χ$-boundedness with polynomial $χ$-boundedness
A class $\mathcal F$ of graphs is $χ$-bounded if there is a function $f$ such that $χ(H)\le f(ω(H))$ for all induced subgraphs $H$ of a graph in $\mathcal F$. If $f$ can be chosen to be a polynomial, we say that $\mathcal F$ is polynomially $χ$-bounded.
Chudnovsky, Maria+3 more
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On boundedness of semistable sheaves
We give a new simple proof of boundedness of the family of semistable sheaves with fixed numerical invariants on a fixed smooth projective variety. In characteristic zero our method gives a quick proof of Bogomolov's inequality for semistable sheaves on a smooth projective variety of any dimension \ge 2
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Boundedness of Faber operators [PDF]
In this work, we prove the boundedness of the Faber operators that transform the Hardy-Orlicz class HM(D) into the Smirnov-Orlicz class EM(G).
Yıldırır, Yunus Emre+1 more
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Amalgams and χ-Boundedness [PDF]
A class of graphs is hereditary if it is closed under isomorphism and induced subgraphs. A class G of graphs is -bounded if there exists a function f : N ! N such that for all graphs G 2 G, and all induced subgraphs H of G, we have that (H) f(!(H)). We prove that proper homogeneous sets, clique-cutsets, and amalgams together preserve -boundedness. More
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