67,502 research outputs found
Cocommutative Calabi-Yau Hopf algebras and deformations
The Calabi-Yau property of cocommutative Hopf algebras is discussed by using
the homological integral, a recently introduced tool for studying infinite
dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group
algebra of a universal enveloping algebra of a finite dimensional Lie algebra
\g with a finite subgroup of automorphisms of \g is Calabi-Yau if and
only if the universal enveloping algebra itself is Calabi-Yau and is a
subgroup of the special linear group SL(\g). The Noetherian cocommutative
Calabi-Yau Hopf algebras of dimension not larger than 3 are described. The
Calabi-Yau property of Sridharan enveloping algebras of finite dimensional Lie
algebras is also discussed. We obtain some equivalent conditions for a
Sridharan enveloping algebra to be Calabi-Yau, and then partly answer a
question proposed by Berger. We list all the nonisomorphic 3-dimensional
Calabi-Yau Sridharan enveloping algebras
Stabilized Schemes for the Hydrostatic Stokes Equations
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes
system or primitive equations of the ocean. It is known that the stability of the mixed formulation ap-
proximation for primitive equations requires the well-known LadyzhenskayaâBabuËskaâBrezzi condi-
tion related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical
velocity.
The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the
vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to
the primitive equations and some error estimates are provided using TaylorâHood P2 âP1 or miniele-
ment (P1 +bubble)âP1 FE approximations, showing the optimal convergence rate in the P2 âP1 case.
These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand,
by adding another residual term to the continuity equation, a better approximation of the vertical
derivative of pressure is obtained. In this case, stability and error estimates including this better
approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)âP1 case.
Finally, some numerical experiments are presented supporting previous results
Calabi-Yau coalgebras
We provide a construction of minimal injective resolutions of simple
comodules of path coalgebras of quivers with relations. Dual to Calabi-Yau
condition of algebras, we introduce the Calabi-Yau condition to coalgebras.
Then we give some descriptions of Calabi-Yau coalgebras with lower global
dimensions. An appendix is included for listing some properties of cohom
functors
Dualities of artinian coalgebras with applications to noetherian complete algebras
A duality theorem of the bounded derived category of quasi-finite comodules
over an artinian coalgebra is established. Let be a noetherian complete
basic semiperfect algebra over an algebraically closed field, and be its
dual coalgebra. If is Artin-Schelter regular, then the local cohomology of
is isomorphic to a shift of twisted bimodule with
a coalgebra automorphism. This yields that the balanced dualinzing
complex of is a shift of the twisted bimodule . If
is an inner automorphism, then is Calabi-Yau
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Highly Stable Luminous "snakes" from CsPbX3 Perovskite Nanocrystals Anchored on Amine-Coated Silica Nanowires
CsPbX3 (X = Cl, Br, and I) perovskite nanocrystals (NCs) are known for their exceptional optoelectronic properties, yet the material's instability toward polar solvents, heat, or UV irradiation greatly limits its further applications. Herein, an efficient in situ growing strategy has been developed to give highly stable perovskite NC composites (abbreviated CsPbX3@CA-SiO2) by anchoring CsPbX3 NCs onto silica nanowires (NWs), which effectively depresses the optical degradation of their photoluminescence (PL) and enhances stability. The preparation of surface-functionalized serpentine silica NWs is realized by a sol-gel process involving hydrolysis of a mixture of tetraethyl orthosilicate (TEOS), 3-aminopropyltriethoxysilane (APTES), and trimethoxy(octadecyl)silane (TMODS) in a water/oil emulsion. The serpentine NWs are formed via an anisotropic growth with lengths up to 8 ÎŒm. The free amino groups are employed as surface ligands for growing perovskite NCs, yielding distributed monodisperse NCs (âŒ8 nm) around the NW matrix. The emission wavelength is tunable by simple variation of the halide compositions (CsPbX3, X = Cl, Br, or I), and the composites demonstrate a high photoluminescence quantum yield (PLQY 32-69%). Additionally, we have demonstrated the composites CsPbX3@CA-SiO2 can be self-woven to form a porous 3D hierarchical NWs membrane, giving rise to a superhydrophobic surface with hierarchical micro/nano structural features. The resulting composites exhibit high stability toward water, heat, and UV irradiation. This work elucidates an effective strategy to incorporate perovskite nanocrystals onto functional matrices as multifunctional stable light sources
Quantum criticality and nodal superconductivity in the FeAs-based superconductor KFe2As2
The in-plane resistivity and thermal conductivity of
FeAs-based superconductor KFeAs single crystal were measured down to 50
mK. We observe non-Fermi-liquid behavior at =
5 T, and the development of a Fermi liquid state with when
further increasing field. This suggests a field-induced quantum critical point,
occurring at the superconducting upper critical field . In zero field
there is a large residual linear term , and the field dependence of
mimics that in d-wave cuprate superconductors. This indicates that
the superconducting gaps in KFeAs have nodes, likely d-wave symmetry.
Such a nodal superconductivity is attributed to the antiferromagnetic spin
fluctuations near the quantum critical point.Comment: 4 pages, 4 figures - replaces arXiv:0909.485
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