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1. The Furstenberg–Poisson boundary and CAT(0) cube complexes

   https://doi.org/10.1017/etds.2016.124  

   FERNÓS, TALIA (September 2018, Ergodic Theory and Dynamical Systems)

   We show under weak hypotheses that$$\unicode[STIX]{x2202}X$$, the Roller boundary of a finite-dimensional CAT(0) cube complex$$X$$is the Furstenberg–Poisson boundary of a sufficiently nice random walk on an acting group$$\unicode[STIX]{x1D6E4}$$. In particular, we show that if$$\unicode[STIX]{x1D6E4}$$admits a non-elementary proper action on$$X$$, and$$\unicode[STIX]{x1D707}$$is a generating probability measure of finite entropy and finite first logarithmic moment, then there is a$$\unicode[STIX]{x1D707}$$-stationary measure on$$\unicode[STIX]{x2202}X$$making it the Furstenberg–Poisson boundary for the$$\unicode[STIX]{x1D707}$$-random walk on$$\unicode[STIX]{x1D6E4}$$. We also show that the support is contained in the closure of the regular points. Regular points exhibit strong contracting properties. 

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2. Simple Topological Drawings of k-Planar Graphs.

   https://doi.org/10.1007/978-3-030-68766-3_31  

   Hoffmann, Michael; Liu, Chih-Hung; Reddy, Meghana M.; Toth, Csaba D. (February 2021, Graph Drawing and Network Visualization)

   null (Ed.)

   Every finite graph admits a simple (topological) drawing, that is, a drawing where every pair of edges intersects in at most one point. However, in combination with other restrictions simple drawings do not universally exist. For instance, k-planar graphs are those graphs that can be drawn so that every edge has at most k crossings (i.e., they admit a k-plane drawing). It is known that for k≤3 , every k-planar graph admits a k-plane simple drawing. But for k≥4 , there exist k-planar graphs that do not admit a k-plane simple drawing. Answering a question by Schaefer, we show that there exists a function Open image in new window such that every k-planar graph admits an f(k)-plane simple drawing, for all Open image in new window. Note that the function f depends on k only and is independent of the size of the graph. Furthermore, we develop an algorithm to show that every 4-planar graph admits an 8-plane simple drawing. 

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3. JUNO sensitivity on proton decay p → ν K ⁺ searches*

   https://doi.org/10.1088/1674-1137/ace9c6  

   Abusleme, Angel; Adam, Thomas; Ahmad, Shakeel; Ahmed, Rizwan; Aiello, Sebastiano; Akram, Muhammad; An_安, Fengpeng 丰鹏; An_安, Qi 琪; Andronico, Giuseppe; Anfimov, Nikolay; et al (November 2023, Chinese Physics C)

   Abstract The Jiangmen Underground Neutrino Observatory (JUNO) is a large liquid scintillator detector designed to explore many topics in fundamental physics. In this study, the potential of searching for proton decay in themode with JUNO is investigated. The kaon and its decay particles feature a clear three-fold coincidence signature that results in a high efficiency for identification. Moreover, the excellent energy resolution of JUNO permits suppression of the sizable background caused by other delayed signals. Based on these advantages, the detection efficiency for the proton decay viais 36.9% ± 4.9% with a background level ofevents after 10 years of data collection. The estimated sensitivity based on 200 kton-years of exposure isyears, which is competitive with the current best limits on the proton lifetime in this channel and complements the use of different detection technologies. 

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4. On classification of non-unital amenable simple C*-algebras, II

   https://doi.org/doi.org/10.1016  

   Gong, G.; Lin, Huaxin (December 2020, Journal of geometry and physics)

   null (Ed.)

   We present a classification theorem for separable amenable simple stably projectionless C -algebras with finite nuclear dimension whose K0 vanish on traces which satisfy the Universal Coefficient Theorem. One of C -algebras in the class is denoted by Z0 which has a unique tracial state, K_0(Z_0) = Z and K1(Z_0) = {0}. Let A and B be two separable amenable simple C -algebras satisfying the UCT. We show that A ⊗ Z_0 = B ⊗ Z_0 if and only if Ell(A ⊗ Z_0 ) = Ell(B ⊗ Z_0 ). A class of simple separable C -algebras which are approximately sub-homogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for C -algebras of the form A ⊗ Z_0 , where A is any finite separable simple amenable C -algebras. 

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5. The utility of mechanical objects: Aiding students' learning of abstract and difficult engineering concepts

   https://doi.org/10.1002/jee.20573  

   Mitropoulos, Tanya; Bairaktarova, Diana; Huxtable, Scott (December 2023, Journal of Engineering Education)

   Abstract BackgroundUndergraduate students consistently struggle with mastering concepts related to thermodynamics. Prior work has shown that haptic technology and intensive hands‐on workshops help improve learning outcomes relative to traditional lecture‐based thermodynamics instruction. The current study takes a more feasible approach to improving thermal understanding by incorporating simple mechanical objects into individual problem‐solving exercises. Purpose/HypothesesThis study tests the impact of simple mechanical objects on learning outcomes (specifically, problem‐solving performance and conceptual understanding) for third‐year undergraduate engineering students in a thermodynamics course across a semester. Design/MethodDuring the semester, 119 engineering students in two sections of an undergraduate thermodynamics course completed three 15‐min, self‐guided problem‐solving tasks, one section without and the other with a simple and relevant physical object. Performance on the tasks and improvements in thermodynamics comprehension (measured via Thermal and Transport Concept Inventory scores) were compared between the two sections. ResultsStudents who had a simple, relevant object available to solve three thermodynamics problems consistently outperformed their counterparts without objects, although only to statistical significance when examining the simple effects for the third problem. At the end of the semester, students who had completed the tasks with the objects displayed significantly greater improvements in thermodynamics comprehension than their peers without the relevant object. Higher mechanical aptitude facilitated the beneficial effect of object availability on comprehension improvements. ConclusionFindings suggest that the incorporation of simple mechanical objects into active learning exercises in thermodynamics curricula could facilitate student learning in thermodynamics and potentially other abstract domains. 

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