Biomorphic supramolecular assemblies formedthrough the collaboration of rigid and flexible elements,akin to bones and ligaments, play a crucialrole in constructing advanced functional structures.Non-intertwined ring–...Biomorphic supramolecular assemblies formedthrough the collaboration of rigid and flexible elements,akin to bones and ligaments, play a crucialrole in constructing advanced functional structures.Non-intertwined ring–ring assemblies that rely oninduced fitting between rigid rings and conformationallyflexible rings have emerged as thriving representativesof this process. However, detailing howrigid and flexible rings adapt to each other for preciseself-assembly evolution under solely weak noncovalentinteractions remains limited and oftenposes challenges in structural design. We offer adistinctive solution by distorting the rigid cyclophane,thereby providing not only unique dualrecognition sites for flexible vips but also intrinsicsolid-state emission for in-situ visualization ofdynamic processes. Three adaptive self-assembliesranging from ring-within-ring, to ring-bridge-ringand finally to ring-in-ring were constructed and demonstratedto be dynamically responsive in the solidstate through harnessing the high selectivity of theinner rings.展开更多
For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is ...For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is an α-skew McCoy ring,then the skew polynomial ring R[x;α] is α-skew McCoy.We also prove that if α（1） = 1 and R is α-rigid,then R[x;α]/ x 2 is αˉ-skew McCoy.展开更多
Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considere...Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.展开更多
基金supported by the National Natural Science Foundation of China(grant nos.22001006 and 22375002)the China Postdoctoral Science Foundation(grant no.2023M740010)+2 种基金the Anhui Provincial Natural Science Foundation(grant no.2308085Y10)the Shenzhen Key Laboratory of Functional Aggregate Materials(grant no.ZDSYS20211021111400001)the Science Technology Innovation Commission of Shenzhen Municipality(grant no.KQTD20210811090142053).
文摘Biomorphic supramolecular assemblies formedthrough the collaboration of rigid and flexible elements,akin to bones and ligaments, play a crucialrole in constructing advanced functional structures.Non-intertwined ring–ring assemblies that rely oninduced fitting between rigid rings and conformationallyflexible rings have emerged as thriving representativesof this process. However, detailing howrigid and flexible rings adapt to each other for preciseself-assembly evolution under solely weak noncovalentinteractions remains limited and oftenposes challenges in structural design. We offer adistinctive solution by distorting the rigid cyclophane,thereby providing not only unique dualrecognition sites for flexible vips but also intrinsicsolid-state emission for in-situ visualization ofdynamic processes. Three adaptive self-assembliesranging from ring-within-ring, to ring-bridge-ringand finally to ring-in-ring were constructed and demonstratedto be dynamically responsive in the solidstate through harnessing the high selectivity of theinner rings.
基金Supportd by the Natural Science Foundation of Gansu Province (Grant No. 3ZS061-A25-015)the Scientific Research Fund of Gansu Provincial Education Department (Grant No. 06021-21)
文摘For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is an α-skew McCoy ring,then the skew polynomial ring R[x;α] is α-skew McCoy.We also prove that if α（1） = 1 and R is α-rigid,then R[x;α]/ x 2 is αˉ-skew McCoy.
文摘Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.
