Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

QCD with dynamical Wilson fermions. II

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

Prediction of Shallow Landslide prone regions in Undulating Terrains

Genetic Algorithm for Rule-set Prediction (GARP) and Support Vector Machine (SVM) with free and open source software (FOSS) - Open Modeller were used to model the probable landslide occurrence points. Environmental layers such as aspect, digital elevation, flow accumulation, flow direction, slope, land cover, compound topographic index and precipitation have been used in modeling. Simulated output of these techniques is validated with the actual landslide occurrence points, which showed 92% (GARP) and 96% (SVM) accuracy considering precipitation in the wettest month and 91% and 94% accuracy considering precipitation in the wettest quarter of the year.

ATM- and ATR-mediated phosphorylation of XRCC3 regulates DNA double-strand break-induced checkpoint activation and repair

The RAD51 paralogs XRCC3 and RAD51C have been implicated in homologous recombination (HR) and DNA damage responses. However, the molecular mechanism(s) by which these paralogs regulate HR and DNA damage signaling remains obscure. Here, we show that an SQ motif serine 225 in XRCC3 is phosphorylated by ATR kinase in an ATM signaling pathway. We find that RAD51C but not XRCC2 is essential for XRCC3 phosphorylation, and this modification follows end resection and is specific to S and G(2) phases. XRCC3 phosphorylation is required for chromatin loading of RAD51 and HR-mediated repair of double-strand breaks (DSBs). Notably, in response to DSBs, XRCC3 participates in the intra-S-phase checkpoint following its phosphorylation and in the G(2)/M checkpoint independently of its phosphorylation. Strikingly, we find that XRCC3 distinctly regulates recovery of stalled and collapsed replication forks such that phosphorylation is required for the HR-mediated recovery of collapsed replication forks but is dispensable for the restart of stalled replication forks. Together, these findings suggest that XRCC3 is a new player in the ATM/ATR-induced DNA damage responses to control checkpoint and HR-mediated repair.