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作者:Tadahito Harima , Akihito Wachi , Junzo Watanabe
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.371-383
摘要:Let $F$ be a homogeneous polynomial in $n$ variables of degree $d$ over a field $K$. Let $A(F)$ be the associated Artinian graded $K$-algebra. If $B\subset A(F)$ is a subalgebra of $A(F)$ which is Gorenstein with the same socle degree as $A(F)$, we describe the Macaulay dual gene...
作者:Federico Galetto , Yong-Su Shin , Adam Van Tuyl
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.415-441
摘要:A $\Bbbk$-configuration is a set of points $\mathbb{X}$ in $\mathbb{P}^{2}$ that satisfies a number of geometric conditions. Associated to a $\Bbbk$-configuration is a sequence $(d_{1},\ldots,d_{s})$ of positive integers, called its type, which encodes many of its homological inv...
作者:Inasa Nakamura
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.497-515
摘要:A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot $F$, where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram ...
作者:Ryan M. Causey
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2018, Vol.62 (1-4), pp.381-426
摘要:For each ordinal $\xi$ and each $1\leqslant q<\infty$, we define the notion of $\xi$-$q$-summable Szlenk index. When $\xi=0$ and $q=1$, this recovers the usual notion of summable Szlenk index. We define for an arbitrary weak$^{*}$-compact set a transfinite, asymptotic analogue $\...
作者:Daowei Ma , Xin Wei , Zhi-Ying Wen
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.443-477
摘要:A connected compact subset $E$ of $\mathbb{R}^{N}$ is said to be a strict Whitney set if there exists a real-valued $C^{1}$ function $f$ on $\mathbb{R}^{N}$ with $\nabla f|_{E}\equiv 0$ such that $f$ is constant on no non-empty relatively open subsets of $E$. We prove that e...
作者:Nishant Suri , Mark Tomforde
来源:[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.479-495
摘要:Naimark’s problem asks whether a $C^{*}$-algebra that has only one irreducible $*$-representation up to unitary equivalence is isomorphic to the $C^{*}$-algebra of compact operators on some (not necessarily separable) Hilbert space. This problem has been solved in special ca...

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