Optional Decomposition and Lagrange Multipliers

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption

A model of inversion of DNA charge by a positive polymer: fractionization of the polymer charge

Charge inversion of a DNA double helix by an oppositely charged flexible polyelectrolyte (PE) is considered. We assume that, in the neutral state of the DNA-PE complex, each of the DNA charges is locally compensated by a PE charge. When an additional PE molecule is adsorbed by DNA, its charge gets fractionized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized DNA. These charges spread all over the DNA eliminating the self-energy of PE. This fractionization mechanism leads to a substantial inversion of the DNA charge, a phenomenon which is widely used for gene delivery.Comment: 4 pages, 2 figures. Improved figures and various corrections to tex

Investigation of the properties of quantum-dimensional semiconductor particles A3B5 by scanning probe microscopy, obtained by liquid chemical etching

The study was carried out with the financial support of the Russian Foundation for Basic Research in the framework of scientific projects 17-07-00407-а and 17-07-00139

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

Localized charged states and phase separation near second order phase transition

Localized charged states and phase segregation are described in the framework of the phenomenological Ginzburg-Landau theory of phase transitions. The Coulomb interactions determines the charge distribution and the characteristic length of the phase separated states. The phase separation with charge segregation becomes possible because of the large dielectric constant and the small density of extra charge in the range of charge localization. The phase diagram is calculated and the energy gain of the phase separated state is estimated. The role of the Coulomb interaction is elucidated

Vortex matter in the charged Bose liquid at absolute zero

The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in the external magnetic field at zero temperature. There is a vortex lattice with locally broken charge neutrality. The boson density is modulated in real space and each vortex is charged. Remarkably, there is no upper critical field at zero temperature, so the density of single flux-quantum vortices monotonously increases with the magnetic field up to B=infinity and no indication of a phase transition. The size of each vortex core decreases as about 1/sqrt(B) keeping the system globally charge neutral. If bosons are composed of two fermions, a phase transition to a spin-polarized Fermi liquid at some magnetic field larger than the pair-breaking field is predicted.Comment: 4 pages, 4 figures, references update

Quasiparticle dynamics and gap structure in Hg1223 investigated with femtosecond spectroscopy

Measurements of the temperature dependence of the quasiparticle (QP) dynamics in Hg1223 with femtosecond time-resolved optical spectroscopy are reported. From the temperature dependence of the amplitude of the photoinduced reflection, the existence of two gaps is deduced, one temperature dependent Dc that closes at Tc, and another temperature independent ''pseudogap'' Dp. The zero-temperature magnitudes of the two gaps are Dc/kTc = 6 +/- 0.5 and Dp/kTc = 6.4 +/- 0.5 respectively. The quasiparticle lifetime is found to exhibit a divergence as T -> Tc from below, which is attributed to the existence of a superconducting gap which closes at Tc. Above Tc the relaxation time is longer than expected for metallic relaxation, which is attributed to the presence of the ''pseudogap''. The QP relaxation time is found to increase significantly at low temperatures. This behavior is explained assuming that at low temperatures the relaxation of photoexcited quasiparticles is governed by a bi-particle recombination process.Comment: accepted for publication in Phys.Rev.

Filamentation of collimated Ti:sapphire-laser pulses in water

The results of experimental studies of the spatial characteristics of multiple filamentation terawatt femtosecond Ti:Salaser in water are presented. With an increase in initial power laser pulses increases the number of filaments, the length of the field is increased filamentation and reducing the length of the filaments have been shown. The distribution of the filaments in the longitudinal direction of the field of multiple filamentation has a maximum cross-sectional filament is shifted from the center to the periphery of the beam at the end region of filamentation. The minimum diameter of the beam on the track corresponds to the position of the maximum number of filaments. After the point of maximum impulse essentially loses energy in the initial direction of propagation. Upon reaching the pulse power 2 104 Pcr of multiple filamentation area is formed of a hollow cone, the apex directed to the radiation source