We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we inve...We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we investigate the maximal and minimal ranks and inertias of Y and Z in the above system of matrix equations. As a special case of the results, we solve the problem proposed in Farid, Moslehian, Wang and Wu's recent paper (Farid F O, Moslehian M S, Wang Q W, et al. On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl, 2012, 437: 1854-1891).展开更多
In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is...In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.展开更多
Two benzo[1,2-b:4,5-b￠]dithiophene(BDT)-based small molecule(SM) donor materials with identical conjugated backbones but different substitution groups, named as DRTB-O and DRTB-T, were well explored to demonstrate th...Two benzo[1,2-b:4,5-b￠]dithiophene(BDT)-based small molecule(SM) donor materials with identical conjugated backbones but different substitution groups, named as DRTB-O and DRTB-T, were well explored to demonstrate the influence of the replacement of alkoxy with alkylthienyl on their photovoltaic properties in fullerene-based and fullerene-free organic solar cells(OSCs). The study shows that the two SM donors possess similar absorption spectra and energy levels but different crystalline structures in solid films. The carrier transport property and phase separation morphologies of the blend films have also been fully investigated.By employing PC71 BM as the acceptor, the power conversion efficiency(PCE) of DRTB-O:PC71BM and DRTB-T:PC71BM based devices were 4.91% and 7.08%, respectively. However, by blending with IDIC, the two SM donors exhibited distinctly different photovoltaic properties in fullerene-free OSCs, and the PCE of DRTB-O:IDIC and DRTB-T:IDIC based devices were 0.15% and9.06%, respectively. These results indicate that the replacement of alkoxyl with alkylthienyl in designing SM donor materials plays an important role in the application of fullerene-free OSCs.展开更多
基金National Natural Science Foundation of China (Grant No. 11171205)Natural Science Foundation of Shanghai (Grant No. 11ZR1412500)+2 种基金the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)Shanghai Leading Academic Discipline Project (Grant No. J50101)Innovation Foundation of Shanghai University (Grant No. SHUCX120109)
文摘We derive the solvability conditions and an expression of the general solution to the system of matrix equations A 1X=C1 , A2Y=C2 , YB2=D2 , Y=Y*, A3Z=C3 , ZB3=D3 , Z=Z*, B4X+(B4X)+C4YC4*+D4ZD4*=A4 . Moreover, we investigate the maximal and minimal ranks and inertias of Y and Z in the above system of matrix equations. As a special case of the results, we solve the problem proposed in Farid, Moslehian, Wang and Wu's recent paper (Farid F O, Moslehian M S, Wang Q W, et al. On the Hermitian solutions to a system of adjointable operator equations. Linear Algebra Appl, 2012, 437: 1854-1891).
基金supported by National Natural Science Foundation of China (Grant No.10971040)the AV foundation of the Institute of Mathematical Sciences of Hong Kong Chinese University
文摘In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.
基金supported by the Ministry of Science and Technology of China (2014CB643501)the National Natural Science Foundation of China (21325419, 51373181, 91333204, 91633301)
文摘Two benzo[1,2-b:4,5-b￠]dithiophene(BDT)-based small molecule(SM) donor materials with identical conjugated backbones but different substitution groups, named as DRTB-O and DRTB-T, were well explored to demonstrate the influence of the replacement of alkoxy with alkylthienyl on their photovoltaic properties in fullerene-based and fullerene-free organic solar cells(OSCs). The study shows that the two SM donors possess similar absorption spectra and energy levels but different crystalline structures in solid films. The carrier transport property and phase separation morphologies of the blend films have also been fully investigated.By employing PC71 BM as the acceptor, the power conversion efficiency(PCE) of DRTB-O:PC71BM and DRTB-T:PC71BM based devices were 4.91% and 7.08%, respectively. However, by blending with IDIC, the two SM donors exhibited distinctly different photovoltaic properties in fullerene-free OSCs, and the PCE of DRTB-O:IDIC and DRTB-T:IDIC based devices were 0.15% and9.06%, respectively. These results indicate that the replacement of alkoxyl with alkylthienyl in designing SM donor materials plays an important role in the application of fullerene-free OSCs.
