Perturbation determinants for singular perturbations

Let A be a densely defined symmetric operator and let {Ã′, Ã} be an ordered pair of proper extensions of A such that their resolvent difference is of trace class. We study the perturbation determinant Δ_Ã′/Ã(·) of the singular pair {Ã′, Ã} by using the boundary triplet approach. We show that, under additional mild assumptions on {Ã′, Ã, the perturbation determinant Δ_Ã′/Ã(·) is the ratio of two ordinary determinants involving the Weyl function and boundary operators. In particular, if the deficiency indices of A are finite, then we obtain Δ_Ã′/Ã(z) = det (B′ - M(z))/det (B - M (z)), z ∈ ρ(Ã), where M(·) stands for the Weyl function and B′ and B for the boundary operators corresponding to Ã′ and à with respect to a chosen boundary triplet Π. The results are applied to ordinary differential operators and to second-order elliptic operators.     

Regularization and convergence for singular perturbations

We present an abstract result on removing regularization for singular perturbations in the operator theory. Our main result concerns singular perturbations which are not (formally) semibounded from below.     

Weakly singular perturbations of a discrete spectrum

We consider weakly singular perturbations ¦x¦^–(0<<2) of an even restoring potential. We compute the matrix elements of the perturbation together with the additional point potential associated with the perturbation. It is shown that even for unperturbed wave functions, the matrix elements exist when 0 < < 3/2. The series for the Rayleigh-Schrödinger coefficients converge in all orders for the same interval in , regardless of the form of the restoring potential. For odd states, the matrix elements of the perturbation exist when 0 < < 3, while estimates for the Rayleigh-Schrödinger coefficients give the boundary = 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 14–18, June, 1989.     

Large metric perturbations from rescattering

We study numerically evolution of metric perturbations during reheating in a model with two fields and a strong parametric resonance. Our calculation is fully nonlinear and includes gravity but is restricted to spherical symmetry. In this model, super-Hubble metric perturbations can grow during reheating only due to effects nonlinear in fluctuations of the fields. We find that they indeed grow and, soon after the growth begins, dominate variances of the metric functions. Thus, the metric functions become smooth but varying significantly over large scales. Their profiles at late times are interpreted as signaling a gravitational instability and formation of a black hole.     

辐射图像脉冲去噪方法

为去除辐射图像中的脉冲噪音,建立了一种先进行脉冲噪音检测再进行噪音数据修复的联合去噪音方法.首先采用测地膨胀方法从减灰度图像出发对原图像进行形态学灰度重构,再采用灰度阈值法从原图像与重构图像的差值图像中分割检测出脉冲噪音,然后采用改进非本地均值方法对噪音数据进行修复.改进非本地均值方法对相似像素的选择范围进行了限制,从原理上避免了传统非本地均值方法用于去除辐射图像脉冲噪音时易发生的以错纠错问题,本文对其进行了数学表述.实验证明,该方法对不同类型辐射图像的脉冲噪音均具有较好滤除效果,表现出良好的噪音数据修复和图像细节保护能力.     

辐射图像脉冲去噪方法

为去除辐射图像中的脉冲噪音,建立了一种先进行脉冲噪音检测再进行噪音数据修复的联合去噪音方法.首先采用测地膨胀方法从减灰度图像出发对原图像进行形态学灰度重构,再采用灰度阈值法从原图像与重构图像的差值图像中分割检测出脉冲噪音,然后采用改进非本地均值方法对噪音数据进行修复.改进非本地均值方法对相似像素的选择范围进行了限制,从原理上避免了传统非本地均值方法用于去除辐射图像脉冲噪音时易发生的以错纠错问题,本文对其进行了数学表述.实验证明,该方法对不同类型辐射图像的脉冲噪音均具有较好滤除效果,表现出良好的噪音数据修复和图像细节保护能力.     

Control of dynamical systems behavior by parametric perturbations: An analytic approach

The problem of parametric suppression of deterministic chaos is considered. It is proved that certain parametric perturbations of a one-dimensional map with chaotic dynamics can lead to a transition of that map into a regime of regular behavior.     

Magnetic field generation from cosmological perturbations

In this Letter, we discuss the generation of magnetic field from cosmological perturbations. We consider the evolution of three component plasma (electron, proton, and photon) evaluating the collision term between electrons and photons up to the second order. The collision term is shown to induce electric current, which then generates magnetic field. There are three contributions, two of which can be evaluated from the first-order quantities, while the other one is fluid vorticity, which is purely second order. We estimate the magnitudes of the former contributions and show that the amplitude of the produced magnetic field is about approximately 10(-19) G at 10 Mpc comoving scale at the decoupling. Compared to astrophysical and inflationary mechanisms for seed-field generation, our study suffers from much less ambiguities concerning unknown physics and/or processes.     

Viscous entrainment from a nozzle: singular liquid spouts

We analyze a long-wavelength model of viscous entrainment from a nozzle and show that, when appropriate large-scale boundary conditions are imposed, the entrainment transition can become continuous. As the entrainment threshold is approached from above, the entrained steady-state spout becomes vanishingly thin compared to the nozzle radius and takes the form of a thin tendril emerging from a base profile whose tip is perfectly conical.     

An exact result for bimetallic interface energies

An exact result is derived for the interface energy of a jellium interface. An approximate model of the bimetallic interface is then used to find approximate values of the adhesive energies of jellium interfaces and specific metal pairs.     

An existence result for super Lie groups

An analogue of the classical global third Lie theorem is proved to hold for super Lie groups whose ground Banach—Grassmann algebra is (possibly) infinite-dimensional, provided that this algebra has an ordered basis. It is also proved that the superanalytic structure of a connected super Lie group having a prescribed Lie module is unique, although in a weaker sense than in the case of ordinary Lie groups.Work partly supported by the National Group for Mathematical Physics (GNFM) of the Italian National Research Council (CNR), and by the Italian Ministry of Education through the research project Geometry and Physics.     

NOR gate response in a double quantum ring: An exact result

NOR gate response in a double quantum ring, where each ring is threaded by a magnetic flux , is investigated. The double quantum ring is sandwiched symmetrically between two semi-infinite one-dimensional metallic electrodes, and two gate voltages, namely, V_a and V_b, are applied, respectively, in lower arms of the two rings those are treated as the two inputs of the NOR gate. A simple tight-binding model is used to describe the system, and all the calculations are done through the Green’s function formalism. Here we calculate exactly the conductance–energy and current–voltage characteristics as functions of the ring-to-electrode coupling strengths, magnetic flux and gate voltages. Our numerical study predicts that, for a typical value of the magnetic flux =₀/2 (₀=ch/e, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the inputs to the gate are low (0), while if one or both are high (1), a low output current (0) results. It clearly demonstrates the NOR gate behavior, and this aspect may be utilized in designing an electronic logic gate.     

Probing integrable perturbations of conformal theories using singular vectors (II). N = 1 superconformal theories

In this work we pursue the singular-vector analysis of the integrable perturbations of conformal theories that was initiated in our earlier paper [Nucl. Phys. B 475 (1996) 361]. Here we consider the detailed study of the N = 1 superconformal theory and show that all integrable perturbations can be identified from a simple singular-vector argument. We identify these perturbations as theories based on affine Lie superalgebras and show that the results we obtain relating two perturbations can be understood by the extension of affine Toda duality to these theories with fermions. We also discuss how this duality is broken in specific cases.