Polydimethylsilylenes bearing pyrenyl groups exhibit emissions fromtwisted intramolecular charge transfer state between the aromatic ring and thesilicon backbone both in polar and nonpolar solvents.
In this study,a novel series of chiral 1,2-propanediol derivatives with different electron-donating and electron-withdrawing groups were synthesized and characterized by FT-IR and ~1H NMR.The helical twisting properti...In this study,a novel series of chiral 1,2-propanediol derivatives with different electron-donating and electron-withdrawing groups were synthesized and characterized by FT-IR and ~1H NMR.The helical twisting properties of all the chiral dopants were investigated by doping the chiral dopants into a nematic liquid crystal host（SLC-1717）.The results indicate that the donor-acceptor electron effect have a prominent influence on helical twisting property of the chiral nematic phase induced by the chiral dopants. Introducing electron-withdrawing groups into the terminal ends of chiral 1,2-propanediol can decrease the absolute values of the helical twisting power.In addition,the helix inversion temperatures of the induced chiral nematic phase are variational with the change of terminal groups.展开更多
All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as ...All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.展开更多
We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-al...We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.展开更多
文摘Polydimethylsilylenes bearing pyrenyl groups exhibit emissions fromtwisted intramolecular charge transfer state between the aromatic ring and thesilicon backbone both in polar and nonpolar solvents.
基金supported in part by the National Natural Science Foundation of China(No.51173155)the Hebei Province Science Foundation of China(No.E2010001182)
文摘In this study,a novel series of chiral 1,2-propanediol derivatives with different electron-donating and electron-withdrawing groups were synthesized and characterized by FT-IR and ~1H NMR.The helical twisting properties of all the chiral dopants were investigated by doping the chiral dopants into a nematic liquid crystal host（SLC-1717）.The results indicate that the donor-acceptor electron effect have a prominent influence on helical twisting property of the chiral nematic phase induced by the chiral dopants. Introducing electron-withdrawing groups into the terminal ends of chiral 1,2-propanediol can decrease the absolute values of the helical twisting power.In addition,the helix inversion temperatures of the induced chiral nematic phase are variational with the change of terminal groups.
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.
基金supported by National Natural Science Foundation of China(Grant Nos.11171109 and 11801177)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
