'GAUSS' THEOREMA EGREGIUM FOR TRIANGULATED SURFACES

The paper deals with fundamental geometric assumptions of the static-kinematic analysis of triangulated surfaces. First. intrinsic and extrinsic properties of triangulated surfaces as analogues of those of smooth surfaces are introduced, then static-kinematic analogies between triangulated surfaces and pin-jointed single-layer space grids are dealt with. It is shown that Gaussian curvature of smooth surfaces cannot be interpreted for triangulated surfaces. and space grids. however, statements of Gauss' Theorema Egregium can be replaced for statements concerning simple and useful connections between their intrinsic and extrinsic measures

The linker region of breast cancer resistance protein ABCG2 is critical for coupling of ATP-dependent drug transport.

The ATP-binding cassette (ABC) transporters of class G display a different domain organisation than P-glycoprotein/ABCB1 and bacterial homologues with a nucleotide-binding domain preceding the transmembrane domain. The linker region connecting these domains is unique and its function and structure cannot be predicted. Sequence analysis revealed that the human ABCG2 linker contains a LSGGE sequence, homologous to the canonical C-motif/ABC signature present in all ABC nucleotide-binding domains. Predictions of disorder and of secondary structures indicated that this C2-sequence was highly mobile and located between an alpha-helix and a loop similarly to the C-motif. Point mutations of the two first residues of the C2-sequence fully abolished the transport-coupled ATPase activity, and led to the complete loss of cell resistance to mitoxantrone. The interaction with potent, selective and non-competitive, ABCG2 inhibitors was also significantly altered upon mutation. These results suggest an important mechanistic role for the C2-sequence of the ABCG2 linker region in ATP binding and/or hydrolysis coupled to drug efflux

Extensive Spectroscopy and Photometry of the Type IIP Supernova 2013ej

We present extensive optical (UBVRI, g′r′i′z′, and open CCD) and near-infrared (ZYJH) photometry for the very nearby Type IIP SN ~2013ej extending from +1 to +461 days after shock breakout, estimated to be MJD 56496.9±0.3. Substantial time series ultraviolet and optical spectroscopy obtained from +8 to +135 days are also presented. Considering well-observed SNe IIP from the literature, we derive UBVRIJHK bolometric calibrations from UBVRI and unfiltered measurements that potentially reach 2\% precision with a B−V color-dependent correction. We observe moderately strong Si II λ6355 as early as +8 days. The photospheric velocity (vph) is determined by modeling the spectra in the vicinity of Fe II λ5169 whenever observed, and interpolating at photometric epochs based on a semianalytic method. This gives vph=4500±500 km s−1 at +50 days. We also observe spectral homogeneity of ultraviolet spectra at +10--12 days for SNe IIP, while variations are evident a week after explosion. Using the expanding photosphere method, from combined analysis of SN 2013ej and SN 2002ap, we estimate the distance to the host galaxy to be 9.0+0.4−0.6 Mpc, consistent with distance estimates from other methods. Photometric and spectroscopic analysis during the plateau phase, which we estimated to be 94±7 days long, yields an explosion energy of 0.9±0.3×1051 ergs, a final pre-explosion progenitor mass of 15.2±4.2~M⊙ and a radius of 250±70~R⊙. We observe a broken exponential profile beyond +120 days, with a break point at +183±16 days. Measurements beyond this break time yield a 56Ni mass of 0.013±0.001~M⊙

Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG${}^{+}$ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary $S$ matrix, and find that it coincides with the one proposed by Bajnok, Palla and Tak\'acs for the Dirichlet BSSG${}^{+}$ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary $S$ matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.Comment: correcting the title of the pape