Generalized Projective Representations for sl(n+1)

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of $sl(n+1)$ to a non-homogenous representation on the tensor space of any finite-dimensional irreducible $gl(n)$-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible $sl(n+1)$-modules, which are in general not highest-weight type, for any given finite-dimensional irreducible $sl(n)$-module. The results could also be used to study the quantum field theory with the projective group as the symmetry.Comment: 24page

Deep sequencing of HPV E6/E7 genes reveals loss of genotypic diversity and gain of clonal dominance in high-grade intraepithelial lesions of the cervix

Table S2. HPV E6/E7 sequencing: dideoxy (Sanger) vs. deep (Illumina). (PDF 236 kb

Stress-induced permeability evolution in coal: Laboratory testing and numerical simulations

Mining operations produce a multiscale network of fractures in the coal seams. Permeability evolution in rocks is important for coal bed methane (CBM) and shale gas exploitation as well as for greenhouse gas storage. Therefore, this work presents laboratory tests and a coupled model using PFC3D and FLAC3D to simulate the stress induced permeability evolution in coal samples. Basic mechanical properties are determined via lab testing. The spatial distributions of different components inside the reconstructed samples produce a significant heterogeneity based on CT technique. A newly developed experimental system is employed to perform 3-dimensional loading and to measure the flow rate simultaneously. The evolution process is described by 5 distinct phases in terms of permeability and deformation. Triaxial tests are simulated with PFC3D using a novel flexible wall boundary method. Gas seepage simulations are performed with FLAC3D. Relations between hydraulic properties and fracture data are established. Permeability and volumetric strain show good nonlinear exponential relation after a newly introduced expansion point. Piecewise relations fit the whole process, the expansion point can be treated as critical point. The structural characteristics of the samples influence this relation before and after the expansion point significantly