On the large values of the Riemann zeta-function on short segments of the critical line

In this paper, we obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, the conditional solution of one problem of A.A.Karatsuba is given. Some typos of the previous versions are corrected (in particular, the important remark of Prof. Yan Fyodorov is taken into account). The reference to the grant of Russian Scientific Fund is also added.Comment: 40 pages, 4 figure

Nonlocal pseudopotentials and magnetic fields

We show how to describe the coupling of electrons to non-uniform magnetic fields in the framework of the widely used norm-conserving pseudopotential appro ximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules. Our results are compared with high quality all electron quantum chemical results, and another recently proposed formalism.Comment: 4 pages, submitted to Physical Review Letter

Competition and cooperation in one-dimensional stepping stone models

Cooperative mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well-known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a distinct selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, mutualism is generically lost via a directed percolation process, with a phase diagram strongly influenced by an exceptional DP2 transition.Comment: 8 pages, 4 figure

Exact analytical expression for the electromagnetic field in a focused laser beam or pulse

We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These solutions are derived by the use of a modification of the "complex source method", investigated and visualized.Comment: 10 pages, 4 figures, an extended version of the talk at the International Conference on Coherent and Nonlinear Optics (ICONO 2007

\u3cem\u3ePlasmodium falciparum\u3c/em\u3e SSB Tetramer Wraps Single-Stranded DNA with Similar Topology but Opposite Polarity to \u3cem\u3eE. coli\u3c/em\u3e SSB

Single-stranded DNA binding (SSB) proteins play central roles in genome maintenance in all organisms. Plasmodium falciparum, the causative agent of malaria, encodes an SSB protein that localizes to the apicoplast and likely functions in the replication and maintenance of its genome. P. falciparum SSB (Pf-SSB) shares a high degree of sequence homology with bacterial SSB proteins but differs in the composition of its C-terminus, which interacts with more than a dozen other proteins in Escherichia coli SSB (Ec-SSB). Using sedimentation methods, we show that Pf-SSB forms a stable homo-tetramer alone and when bound to single-stranded DNA (ssDNA). We also present a crystal structure at 2.1 Å resolution of the Pf-SSB tetramer bound to two (dT)35 molecules. The Pf-SSB tetramer is structurally similar to the Ec-SSB tetramer, and ssDNA wraps completely around the tetramer with a “baseball seam” topology that is similar to Ec-SSB in its “65 binding mode”. However, the polarity of the ssDNA wrapping around Pf-SSB is opposite to that observed for Ec-SSB. The interactions between the bases in the DNA and the amino acid side chains also differ from those observed in the Ec-SSB–DNA structure, suggesting that other differences may exist in the DNA binding properties of these structurally similar proteins

On the kinetic equation approach to pair production by time-dependent electric field

We investigate the quantum kinetic approach to pair production from vacuum by time-dependent electric field. Equivalence between this approach and the more familiar S-matrix approach is explicitly established for both scalar and fermion cases. For the particular case of a constant electric field exact solution for kinetic equations is provided and the accuracy of low-density approximation is estimated.Comment: 8 pages, 4 figure