作者：Agnid Banerjee , Bernd Kawohl 来源：[J].Proceedings of the American Mathematical Society, Series B, 2018, Vol.5 (3), pp.18-24AMS 摘要：We extend the symmetry result of Serrin [ 21 ] and Weinberger [ 24 ] from the Laplacian operator to the highly degenerate game-theoretic $p$-Laplacian operator and show that viscosity solutions of $-\Delta _p^Nu=1$ in $\Omega$, $u=0$ and $\tfrac {\partial u}{\partial \nu }=...  作者：G. Lusztig 来源：[J].Representation Theory of the American Mathematical Society, 2018, Vol.22 (2), pp.27-44AMS 摘要：Let$ N$be the normalizer of a maximal torus$ T$in a split reductive group over$ F_q$, and let$ w$be an involution in the Weyl group$ N/T$. We explicitly construct a lifting$ n$of$ w$in$ N$such that the image of$ n$under the Frobenius map is equal to the inverse of...  作者：Christoph Thäle , Nicola Turchi , Florian Wespi 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (7), pp.3063-3071AMS 摘要：Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability theory.  作者：Mohamed Elhamdadi , Mustafa Hajij , Masahico Saito 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (7), pp.5155-5177AMS 摘要：We prove that the coefficients of the colored Jones polynomial of alternating links stabilize under increasing the number of twists in the twist regions of the link diagram. This gives us an infinite family of$ q$-power series derived from the colored Jones polynomial parametriz...  作者：Jason Fulman , Robert Guralnick 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (7), pp.4601-4622AMS 摘要：This is the fourth paper in a series. We prove a conjecture made independently by Boston et al. and Shalev. The conjecture asserts that there is an absolute positive constant$ \delta $such that if$ G$is a finite simple group acting transitively on a set of size$ n > 1$, then...  作者：Alexandru A. Popa 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (7), pp.2749-2764AMS 摘要：We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of modular forms, and it generalizes an app...  作者：Marcel Jackson , Edmond W. H. Lee 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (7), pp.4785-4812AMS 摘要：Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and, surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is shown that there are, nevertheless, man...  作者：Katrin Fässler , Tuomas Orponen 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (7), pp.4909-4926AMS 摘要：A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in$ \mathbb{R}^{2}$of length one. The classical worm problem'' of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M...  作者：Ruiyuan Chen 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (7), pp.3085-3096AMS 摘要：We show that every countable Borel equivalence relation structurable by$ n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most$ M_n := 2^{n-1}(n^2+3n+2)-2$edges; th...  作者：Wataru Yuasa 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (7), pp.3153-3166AMS 摘要：The colored Jones polynomial is a$ q$-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A$ q$-series called a tail is obtained as the limit of the$ \mathfrak{sl}_2$colored Jones polynomials$ \{J_n(K;q)\}_n$for some link$ K\$, for ...