作者：Yuval Z. Flicker , Piotr Krasoń 来源：[J].Bulletin Polish Acad. Sci. Math., 2017, Vol.65, pp.125-138IMPAS 摘要：Our aim here is to restructure the area of multiplicative relations on points and congruences, by proposing a novel conjecture in the context of general reductive linear algebraic groups. To support our conjecture we check it in a few elementary but new cases, and claim this...
 作者：Agnieszka Borowiecka , Piotr Mizerka 来源：[J].Bulletin Polish Acad. Sci. Math., 2018, Vol.66, pp.167-177IMPAS 摘要：According to Laitinen and Morimoto (1998), a finite group $G$ has a smooth effective one fixed point action on some sphere if and only if $G$ is an Oliver group. For some finite Oliver groups $G$ of order up to $216$, and for $G=A_5\times C_p$, where $p=3,5,7$, we present a strat...
 作者：Adam Osękowski 来源：[J].Bulletin Polish Acad. Sci. Math., 2017, Vol.65, pp.165-175IMPAS 摘要：Let $X=(X_t)_{t\geq 0}$ be a bounded martingale and let $Y=(Y_t)_{t\geq 0}$ be differentially subordinate to $X$. We prove that if $1\leq p \lt \infty$ and $W=(W_t)_{t\geq 0}$ is an $A_p$ weight of characteristic $[W]_{A_p}$, then  \| Y\| _{L^{p,\infty }(W)}\leq C_p[W]_{A_p}\|...
 作者：James H. Schmerl 来源：[J].Bulletin Polish Acad. Sci. Math., 2019, Vol.67, pp.31-35IMPAS 摘要：The Kotlarski–Krajewski–Lachlan Theorem says that every resplendent model of Peano Arithmetic has a full satisfaction class. Enayat and Visser gave a more model-theoretic proof of this theorem. We redo their proof using kernels of directed graphs.
 作者：Kyriakos Keremedis 来源：[J].Bulletin Polish Acad. Sci. Math., 2018, Vol.66, pp.99-113IMPAS 摘要：In the realm of metric spaces we show, in the Zermelo–Fraenkelset theory $\mathbf{ZF}$, that:;;(a) A metric space $\mathbf{X}=(X,d)$ is countably compact iff it ispseudocompact.;;(b) Given a metric space $\mathbf{X}=(X,d),$ the following statements areequivalent:;;$\hskip2em...  作者：Saronsad Sokantika , Athipat Thamrongthanyalak 来源：[J].Bulletin Polish Acad. Sci. Math., 2017, Vol.65, pp.97-105IMPAS 摘要：Let$T$be a set-valued map from a subset of$\mathbb {R}^n$to$\mathbb {R}^m$. Suppose$(\mathbb {R};+,\cdot ,T)$is o-minimal. We prove that (1) if for every$x\in \mathbb {R}^n$, each connected component of$T(x)$is convex, then$T$has a continuous selection if and only if ...  作者：Christophe Cuny , Michel Weber 来源：[J].Bulletin Polish Acad. Sci. Math., 2018, Vol.66, pp.69-85IMPAS 摘要：We show that if${\bf a}=(a_n)_{n\in {\mathbb N}}$is a good weight for the dominated weighted ergodic theorem in$L^p$,$p \gt 1$, then the Nörlund matrix$N_{\bf a}=\{a_{i-j}/A_i\}_{0\le j\le i}$,$A_i=\sum_{k=0}^i |a_k|$, is bounded on$\ell ^p({\mathbb N})$. We study the...  作者：Tomasz Cieślak , Michał Gaczkowski , Mariusz Kubkowski ... 来源：[J].Bulletin Polish Acad. Sci. Math., 2017, Vol.65, pp.153-164IMPAS 摘要：We adress the problem of qualitative properties of multipeakons, particular solutions of the Camassa–Holm equation. Our approach makes use of the well-known fact that the evolution of multipeakons is governed by the geodesic motion of a particle on an$N$-dimensional surface...  作者：Zbigniew Lipecki 来源：[J].Bulletin Polish Acad. Sci. Math., 2017, Vol.65, pp.93-95IMPAS 摘要：A theorem of E. Szpilrajn (Marczewski) (1936) on equivalent functions is recalled and its relation to subsequent results published by M. Morayne and C. Ryll-Nardzewski (1999) and M. Kysiak (2005) is briefly discussed.  作者：Rafael Espínola , Andrzej Wiśnicki 来源：[J].Bulletin Polish Acad. Sci. Math., 2018, Vol.66, pp.1-7IMPAS 摘要：Let$X$be a partially ordered set with the property that each family of order intervals of the form$[a,b],[a,\rightarrow )$with the finite intersection property has a nonempty intersection. We show that every directed subset of$X\$ has a supremum. Then we apply the above ...