Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Incomplete inverse spectral and nodal problems for differential pencils

[[abstract]]We prove uniqueness theorems for so-called half inverse spectral problem (and also for some its modification) for second order differential pencils on a finite interval with Robin boundary conditions. Using the obtained result we show that for unique determination of the pencil it is sufficient to specify the nodal points only on a part of the interval slightly exceeding its half.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

Escherichia coli RuvBL268S: A mutant RuvB protein that exhibits wild-type activities in vitro but confers a UV-sensitive ruv phenotype in vivo

The RuvABC proteins of Escherichia coli process recombination intermediates during genetic recombination and DNA repair. RuvA and RuvB promote branch migration of Holliday junctions, a process that extends heteroduplex DNA. Together with RuvC, they form a RuvABC complex capable of Holliday junction resolution. Branch migration by RuvAB is mediated by RuvB, a hexameric ring protein that acts as an ATP-driven molecular pump. To gain insight into the mechanism of branch migration, random mutations were introduced into the ruvB gene by PCR and a collection of mutant alleles were obtained. Mutation of leucine 268 to serine resulted in a severe UV-sensitive phenotype, characteristic of a ruv defect. Here, we report a biochemical analysis of the mutant protein RuvBL268S. Unexpectedly, the purified protein is fully active in vitro with regard to its ATPase, DNA binding and DNA unwinding activities. It also promotes efficient branch migration in combination with RuvA, and forms functional RuvABC-Holliday junction resolvase complexes. These results indicate that RuvB may perform some additional, and as yet undefined, function that is necessary for cell survival after UV-irradiatio

Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

[[abstract]]The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]CH