Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energy

In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense)

Locally most powerful sequential tests of a simple hypothesis vs one-sided alternatives

Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$ versus a composite alternative $H_1:$ $\theta>\theta_0$, where $\theta_0\in\Theta$ is some fixed point. The main goal of this article is to characterize the structure of locally most powerful sequential tests in this problem. For any sequential test $(\psi,\phi)$ with a (randomized) stopping rule $\psi$ and a (randomized) decision rule $\phi$ let $\alpha(\psi,\phi)$ be the type I error probability, $\dot \beta_0(\psi,\phi)$ the derivative, at $\theta=\theta_0$, of the power function, and $\mathscr N(\psi)$ an average sample number of the test $(\psi,\phi)$. Then we are concerned with the problem of maximizing $\dot \beta_0(\psi,\phi)$ in the class of all sequential tests such that $$\alpha(\psi,\phi)\leq \alpha\quad{and}\quad \mathscr N(\psi)\leq \mathscr N,$$ where $\alpha\in[0,1]$ and $\mathscr N\geq 1$ are some restrictions. It is supposed that $\mathscr N(\psi)$ is calculated under some fixed (not necessarily coinciding with one of $P_\theta$) distribution of the process $X_1,X_2...$. The structure of optimal sequential tests is characterized.Comment: 30 page

A model calculation of the value of the electromagnetic coupling constant at q2=mZ2q^2 = m_{Z}^{2}

A QCD model with an infinite number of vector mesons suggested by one of the authors is used to derive the value of the correction $\delta\alpha_{hadr}$ for $\alpha(m_{Z}^{2})$ due to the strong interactions. The result is $\delta\alpha_{hadr} = 0.0275(2)$ ; thus $\alpha(m^{2}_{Z}) = (128.96(3))^{-1}$.Comment: in LaTeX, 6 pages, 0 figures, ITEP Preprint 49-9

Hopping transport of interacting carriers in disordered organic materials

Computer simulation of the hopping charge transport in disordered organic materials has been carried out explicitly taking into account charge-charge interactions. This approach provides a possibility to take into account dynamic correlations that are neglected by more traditional approaches like mean field theory. It was found that the effect of interaction is no less significant than the usually considered effect of filling of deep states by non-interacting carriers. It was found too that carrier mobility generally increases with the increase of carrier density, but the effect of interaction is opposite for two models of disordered organic materials: for the non-correlated random distribution of energies with Gaussian DOS mobility decreases with the increase of the interaction strength, while for the model with long range correlated disorder mobility increases with the increase of interaction strength.Comment: 6 pages, 5 figures, extended version from the conference TIDS1

Uncertainty constants and quasispline wavelets

In 1996 Chui and Wang proved that the uncertainty constants of scaling and wavelet functions tend to infinity as smoothness of the wavelets grows for a broad class of wavelets such as Daubechies wavelets and spline wavelets. We construct a class of new families of wavelets (quasispline wavelets) whose uncertainty constants tend to those of the Meyer wavelet function used in construction.Comment: 27 page

Global stability for the multi-channel Gel'fand-Calder\'on inverse problem in two dimensions

We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$

Hahn decomposition and Radon-Nikodym theorem with a parameter

The paper contains a simple proof of the classical Hahn decomposition theorem for charges and, as a corollary, an explicit measurable in parameter construction of a Radon-Nikodym derivative of one measure by another

New instantons in the double-well potential

A new instanton solution is found in the quantum-mechanical double-well potential with a four-fermion term. The solution has finite action and depends on four fermionic collective coordinates. We explain why in general the instanton action can depend on collective coordinates.Comment: 10 pages, clarifications and references adde

Modulational stability of cellular flows

We present here the homogenization of the equations for the initial modulational (large-scale) perturbations of stationary solutions of the two-dimensional Navier–Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function phi = sinx1/epsilonsinx2/epsilon+δ cosx1/epsiloncosx2/epsilon, 0 ≤ δ ≤ 1. Two results are given here. For any Reynolds number we prove the homogenization of the linearized equations. For small Reynolds number we prove the homogenization for the fully nonlinear problem. These results show that the modulational stability of cellular flows is determined by the stability of the effective (homogenized) equations