The notion of relative derived category with respect to a subcategory is introduced. A triangle-equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived categories, emph{J. Algebra} textbf{323} (2010) 2041-2057] to the bounded below
case, is obtained. Moreover, we interpret the relative derived functor $mathrm{Ext}_{mathcal{X}mathcal {A}}(-,-)$ as the morphisms in such derived category and give two applications.
Let $R$ be a commutative noetherian ring with a semi-dualizing module $C$. The Auslander categories with respect to $C$ are related through Foxby equivalence: $xymatrix@C=50pt{mathcal {A}_C(R) ar@<0.4ex>[r]^{Cotimes^{mathbf{L}}_{R} -} & mathcal {B}_C
(R) ar@<0.4ex>[l]^{mathbf{R}mathrm{Hom}_{R}(C, -)}}$. We firstly intend to extend the Foxby equivalence to Cartan-Eilenberg complexes. To this end, C-E Auslander categories, C-E $mathcal{W}$ complexes and C-E $mathcal{W}$-Gorenstein complexes are introduced, where $mathcal{W}$ denotes a self-orthogonal class of $R$-modules. Moreover, criteria for finiteness of C-E Gorenstein dimensions of complexes in terms of resolution-free characterizations are considered.
Epitaxial strain plays an important role in determining physical properties of perovskite ferroelectric oxide thin films. However, it is very challenging to directly measure properties such as polarization in ultrathin strained films using traditiona
l sandwich capacitor devices, because of high leakage current. We employed a planar electrode device with different crystallographical orientations between electrodes along different electric field orientation to directly measure the in-plane polarization-electric field (P-E) hysteresis loops in fully strained thin films. At high misfit strains such as -4.4%, the pure Tetrogonal-like phase is obtained and its polarization vector is constrained to lie in the (010) plane with a significantly large in-plane component, ~44 {mu}C/cm2. First-principle calculations are carried out in parallel, and provide a good agreement with the experimental results. Our results pave the way to design in-plane devices based on T-like BFO and the strategy proposed here can be expanded to study all other similar strained multiferroic ultrathin films.
We report a first principles analysis of electronic transport characteristics for (n,n) carbon nanotube bundles. When n is not a multiple of 3, inter-tube coupling causes universal conductance suppression near Fermi level regardless of the rotational
arrangement of individual tubes. However, when n is a multiple of 3, the bundles exhibit a diversified conductance dependence on the orientation details of the constituent tubes. The total energy of the bundle is also sensitive to the orientation arrangement only when n is a multiple of 3. All the transport properties and band structures can be well understood from the symmetry consideration of whether the rotational symmetry of the individual tubes is commensurate with that of the bundle.
In this paper, we propose a novel semi-parametric probabilistic model which considers interactions between different communities and can provide more information about the network topology besides correctly detecting communities. By using an addition
al parameter, our model can not only detect community structure but also detect pattern which is a generalization of common sense network community structure. The prior parameter in our model reveals the characteristics of patterns inside the network. Results on some widely known data sets prove the efficiency of our model.
