Whereas autism spectrum condition is known for its social and communicative challenges,some autistic children demonstrate unusual islets of abilities including those related to mathematics,the neurobiological underpin...Whereas autism spectrum condition is known for its social and communicative challenges,some autistic children demonstrate unusual islets of abilities including those related to mathematics,the neurobiological underpinnings of which are increasingly becoming the focus of research.Here we describe an 8-year-old autistic boy with intellectual and language challenges,yet exceptional arithmetic ability.He can perform verbal-based multiplication of three-and even four-digit numbers within 20 seconds.To gain insights into the neural basis of his talent,we investigated the gray matter in the child's brain in comparison to typical development,applying voxel-based morphometry to magnetic resonance imaging data.The case exhibited reduced gray matter volume in regions associated with arithmetic,which may suggest an accelerated development of brain regions with arithmetic compared to typically developing individuals:potentially a key factor contributing to his exceptional talent.Taken together,this case report describes an example of the neurodiversity of autism.Our research provides valuable insights into the potential neural basis of exceptional arithmetic abilities in individuals with the autism spectrum and its potential contribution to depicting the diversity and complexity of autism.展开更多
Let R be a commutative ring having nonzero identity and M be a unital R-module.Assume that S⊆R is a multiplicatively closed subset of R.Then,M satisfies S-Noetherian spectrum condition if for each submodule N of M,ther...Let R be a commutative ring having nonzero identity and M be a unital R-module.Assume that S⊆R is a multiplicatively closed subset of R.Then,M satisfies S-Noetherian spectrum condition if for each submodule N of M,there exist s∈S and afinitely generated submodule F⊆N such that sN⊆radM(F),where radM(F)is the prime radical of F in the sense(McCasland and Moore in Commun Algebra 19(5):1327–1341,1991).Besides giving many properties and characterizations of S-Noetherian spectrum condition,we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition.Moreover,we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.展开更多
基金supported by the National Natural Science Foundation of China(62273076,82121003,and 62036003)Fundamental Research Funds for Central Universities(ZYGX2019Z017)National Social Science Foundation of China(20&ZD296).
文摘Whereas autism spectrum condition is known for its social and communicative challenges,some autistic children demonstrate unusual islets of abilities including those related to mathematics,the neurobiological underpinnings of which are increasingly becoming the focus of research.Here we describe an 8-year-old autistic boy with intellectual and language challenges,yet exceptional arithmetic ability.He can perform verbal-based multiplication of three-and even four-digit numbers within 20 seconds.To gain insights into the neural basis of his talent,we investigated the gray matter in the child's brain in comparison to typical development,applying voxel-based morphometry to magnetic resonance imaging data.The case exhibited reduced gray matter volume in regions associated with arithmetic,which may suggest an accelerated development of brain regions with arithmetic compared to typically developing individuals:potentially a key factor contributing to his exceptional talent.Taken together,this case report describes an example of the neurodiversity of autism.Our research provides valuable insights into the potential neural basis of exceptional arithmetic abilities in individuals with the autism spectrum and its potential contribution to depicting the diversity and complexity of autism.
文摘Let R be a commutative ring having nonzero identity and M be a unital R-module.Assume that S⊆R is a multiplicatively closed subset of R.Then,M satisfies S-Noetherian spectrum condition if for each submodule N of M,there exist s∈S and afinitely generated submodule F⊆N such that sN⊆radM(F),where radM(F)is the prime radical of F in the sense(McCasland and Moore in Commun Algebra 19(5):1327–1341,1991).Besides giving many properties and characterizations of S-Noetherian spectrum condition,we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition.Moreover,we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.
