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

\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

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

On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes

On Karatsuba's Problem Concerning the Divisor Function τ(n)\tau(n)

We study an asymptotic behavior of the sum \sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.Comment: 32 page

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