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.
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.
