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2. Anharmonic Frequencies of (MO) 2 and Related Hydrides for M = Mg, Al, Si, P, S, Ca, and Ti and Heuristics for Predicting Anharmonic Corrections of Inorganic Oxides

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3. A remark on the number field analogue of Waring's constant g(k): A remark on the number field analogue of Waring's constant g(k)

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4. Verbal counting and the timing of number acquisition in an indigenous Amazonian group

   https://doi.org/10.1371/journal.pone.0270739  

   Boni, Isabelle ; Jara-Ettinger, Julian ; Sackstein, Sophie ; Piantadosi, Steven T. ( August 2022 , PLOS ONE)

   Perlman, Marcus (Ed.)

   Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words. 

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5. THE NUMBER OF SET ORBITS OF PERMUTATION GROUPS AND THE GROUP ORDER

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   GINTZ, MICHAEL ; KELLER, THOMAS M. ; KORTJE, MATTHEW ; WANG, ZILI ; YANG, YONG ( August 2022 , Bulletin of the Australian Mathematical Society)

   Abstract If G is permutation group acting on a finite set $\Omega $ , then this action induces a natural action of G on the power set $\mathscr{P}(\Omega )$ . The number $s(G)$ of orbits in this action is an important parameter that has been used in bounding numbers of conjugacy classes in finite groups. In this context, $\inf ({\log _2 s(G)}/{\log _2 |G|})$ plays a role, but the precise value of this constant was unknown. We determine it where G runs over all permutation groups not containing any ${{\textrm {A}}}_l, l> 4$ , as a composition factor. 

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