This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained b...This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.展开更多
A reversible dual-responsive luminescent material was introduced by our group to show the simultaneous color and lifetime switching in response to external stimuli.Pristine crystalline powder of(E)-2-(benzo[d]thiazol-...A reversible dual-responsive luminescent material was introduced by our group to show the simultaneous color and lifetime switching in response to external stimuli.Pristine crystalline powder of(E)-2-(benzo[d]thiazol-2-yl)-3-(pyren-1-yl)acrylonitrile(Py-BZTCN)shows the orderedπ–πstacking with only near-monomer-normal orange-yellow fluorescence,but it exhibits red emission with thermally activated delayed fluorescence(TADF)after grinding,which can be reversibly recovered by heating or fuming treatment.Grinding disturbs the orderedπ–πstacking of pristine powder,leading to the formation of small aggregates with compressed distance and increased overlap ofπ–πstacking between adjacent molecules.The cause of switching was verified by single-crystal X-ray diffraction experiments of two corresponding crystals.This strongπ–πinteraction effectively promotes the excited-state energy splitting and substantially decreases the singlet–triplet energy gap(ΔEST)of aggregates,resulting in the red TADF emission of aggregates through reverse intersystem crossing.This finding proposes a new route to realizing the TADF emission of aggregates through strong intermolecular interactions based on non-TADF monomer,thereby enabling a novel high-contrast dualresponsive luminescence switching.展开更多
基金supported by Ministry of Human Resource and Development(MHR-02-23-200-429/304)
文摘This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.
基金This work is supported by the National Natural Sciences Foundation of China under Grant 10361006 the Natural Sciences Foundation of Yunnan Province under Grant 2003A0001M.
文摘We use Krasnosel'skii's fixed point theorem to show that the following BAM networks with state dependent delays has a periodic solution.
基金supported by the National Natural Science Foundation of China(nos.52073117,91833304,51873077,and 51803071)the National Basic Research Program of China(no.2016YFB0401001)+1 种基金the Postdoctoral Innovation Talent Support Project(no.BX20180121)the China Postdoctoral Science Foundation(nos.2018M641767 and 2019TQ0198).
文摘A reversible dual-responsive luminescent material was introduced by our group to show the simultaneous color and lifetime switching in response to external stimuli.Pristine crystalline powder of(E)-2-(benzo[d]thiazol-2-yl)-3-(pyren-1-yl)acrylonitrile(Py-BZTCN)shows the orderedπ–πstacking with only near-monomer-normal orange-yellow fluorescence,but it exhibits red emission with thermally activated delayed fluorescence(TADF)after grinding,which can be reversibly recovered by heating or fuming treatment.Grinding disturbs the orderedπ–πstacking of pristine powder,leading to the formation of small aggregates with compressed distance and increased overlap ofπ–πstacking between adjacent molecules.The cause of switching was verified by single-crystal X-ray diffraction experiments of two corresponding crystals.This strongπ–πinteraction effectively promotes the excited-state energy splitting and substantially decreases the singlet–triplet energy gap(ΔEST)of aggregates,resulting in the red TADF emission of aggregates through reverse intersystem crossing.This finding proposes a new route to realizing the TADF emission of aggregates through strong intermolecular interactions based on non-TADF monomer,thereby enabling a novel high-contrast dualresponsive luminescence switching.
