365 research outputs found
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
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