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...
 来源：[J].Illinois Journal of Mathematics(IF 0.337), 2019, Vol.63 (1), pp.; 47 - 74
 来源：[J].Illinois Journal of Mathematics(IF 0.337), 2019, Vol.63 (2), pp.; 259 - 297
 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$. We prove that e...  来源：[J].Illinois Journal of Mathematics(IF 0.337), 2019, Vol.63 (3), pp.; 469 - 484  作者：Nishant Suri , Mark Tomforde 来源：[J].Illinois Journal of Mathematics(IF 0.337), 2017, Vol.61 (3-4), pp.479-495 摘要：Naimark’s problem asks whether a$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...
 来源：[J].Illinois Journal of Mathematics(IF 0.337), 2019, Vol.63 (3), pp.; 425 - 461