Towards an Inverse Scattering theory for non decaying potentials of the heat equation

The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a generic decaying potential is considered. It is shown that these potentials describe $N$ solitons superimposed by Backlund transformations to a generic background. Dressing operators and Jost solutions are constructed by solving a DBAR-problem explicitly in terms of the corresponding objects associated to the original potential. Regularity conditions of the potential in the cases N=1 and N=2 are investigated in details. The singularities of the resolvent for the case N=1 are studied, opening the way to a correct definition of the spectral data for a generically perturbed soliton.Comment: 22 pages, submitted to Inverse Problem

On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed

ОЦІНКА ЕФЕКТИВНОСТІ РЕАБІЛІТАЦІЙНИХ ЗАХОДІВ УЧАСНИКАМ АНТИТЕРОРИСТИЧНОЇ ОПЕРАЦІЇ, ЯКІ ОТРИМАЛИ ЧЕРЕПНО-МОЗКОВУ ТРАВМУ

The article is devoted to the study of the status of patients with the effects of craniocerebral traumas obtained in the ATO zone, at the stages of medical and social rehabilitation.Purpose: determination of the effectiveness of rehabilitation measures taken by ATO participants who have received a craniocerebral trauma, depending on the class of functional disorders.Materials and Methods. We examined 62 patients who were in the clinic of the Research Institute of the Disabled Rehabilitation and had the consequences of mine explosions, close craniocerebral concussion of the brain. Patients were provided with a comprehensive clinical and neuropsychological examination, magnetic resonance imaging or spiral computer tomography, transcranial dopplerography. The severity of neurological disorders was assessed on the NIHSS scale; limitations of life were estimated using the Bartel index.Results. According to the results of the integration assessment of the life limitation of patients we receivedConclusions. The results of the study showed that the factors of the effectiveness of medical and social rehabilitation of patients with a history of craniocerebral injury may be factors such as the dynamics of the reversal of clinical syndromes, the daily life and the ability to work.Стаття присвячена дослідженням визначення стану пацієнтів з наслідками черепно-мозкових травм, отриманих в зоні АТО, на етапах медико-соціальної реабілітації.Мета дослідження. Визначення ефективності реабілітаційних заходів, проведених учасникам АТО, які отримали черепно-мозкову травму, в залежності від класу функціональних розладів.Матеріали та методи. Обстежено 62 пацієнти, які знаходились в клініці Науково-дослідного інституту реабілітації інвалідів (НДІ РІ) і мали наслідки мінно-вибухових травм, ЗЧМТ, струсу головного мозку. Пацієнтам було проведено всебічне клінічне та нейропсихологічне обстеження, МРТ або СКТ, транскраніальну допплерографію. Вираженість неврологічних розладів оцінювали за шкалою NIHSS; обмеження життєдіяльності оцінювали за допомогою індексу Бартеля.Результати. За результатами інтеграційної оцінки обмеження життєдіяльності пацієнтів ми отримали 4 функціональні групи, які відрізнялись між собою за наявністю та ступенем важкості неврологічних ознак хвороби, психологічних розладів та супутніх захворювань, що ускладнюють проведення реабілітаційних заходів.Висновки. Результати дослідження показали, що критеріями ефективності медико-соціальної реабілітації пацієнтів, що мають в анамнезі ЧМТ, можуть бути такі чинники, як динаміка зворотного розвитку клінічних синдромів, повсякденна життєдіяльність та спроможність до трудової діяльності

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

Technologically-Treated Polyclonal Affinity-Purified Antibodies to the Tumor Necrosis Factor-α, Brain Specific S-100 Protein and Histamine in Treatment of Functional Dyspepsia: Results of the Multicenter, Randomized, Double-Blind, Placebo-Controlled Trial

The aim of the study was to evaluate the efficacy and safety of Kolofort® (a complex medicine containing technologically processed forms of antibodies to S-100 protein, tumor necrosis factor-α and histamine) in the management of functional dyspepsia (FD) in outpatient clinical practice.Methods: Outpatients (N = 309) at the age of 18–45 in whom FD was diagnosed according to the Rome IV criteria were enrolled in a multicenter, double-blind, placebo-controlled, randomized clinical trial. Patients were randomized in two groups receiving Kolofort® or placebo 2 tablets tid for 8 weeks. The primary endpoint of the study was a change in the FD symptoms severity score according to the Gastrointestinal symptom score (GIS) at week 8. ITT and [PP] analysis were performed.Results: at week 8 the reduction in GIS sum score was observed in Kolofort® group and placebo group (by 7.2 ± 3.3 [7.2 ± 3.4] and 6.3 ± 4.6 [6.2 ± 4.5], respectively, p = 0.041 [0.039]). The proportion of cases with GIS score reduction by ≥4 was 88,1 % [88.6 %] and 79.1 % [79.6 %] in Kolofort® group and placebo group, respectively (p = 0.046 [p = 0.051]). None of the patients in Kolofort® group had progression of FD symptoms or required additional therapy. There were 29 adverse events (AEs) recorded in 25 patients including 16 cases in 13 (8.6 %) patients in Kolofort® group and 13 AEs in 12 (7.6 %) patients in placebo group.Conclusion: the clinical trial demonstrates the positive effect of Kolofort® in FD with a favorable safety profile

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

We consider the dimensional crossover in the topological matter, which involves the transformation of different types of topologically protected zeroes in the fermionic spectrum. In the considered case, the multiple Dirac (Fermi) point in quasi 2-dimensional system evolves into the flat band on the surface of the 3-dimensional system when the number of atomic layers increases. This is accompanied by formation of the spiral nodal lines in the bulk. We also discuss the topological quantum phase transition at which the surface flat band shrinks and changes its chirality, while the nodal spiral changes its helicity.Comment: 13 pages, 7 figure

Increase of precision of casting blocks by applying acoustical oscillations in gas-impulsive moulding

The present article shows the results of the theoretical and empirical research of the study of the impact made by acoustical oscillations on the working process of a gas-impulsive moulding device with the purpose of increasing the quality of the casting blocks’ seal and decreasing the roughness of the surface of a casting block. It has been shown that acoustical oscillations intensify the working process of the gas-impulsive moulding device. With the increase of frequency and power of oscillations the hardness of a casting block first sharply rises, but then gradually decreases. It has been found out that oscillations may help to adjust the precision of a casting block due to high sensitivity of a gas-impulsive process to the frequency of oscillations. The use of acoustical oscillations broadens technological opportunities of the moulding device

Topological superfluid 3^3He-B: fermion zero modes on interfaces and in the vortex core

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid $^3$He-B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finlan

Two-dimensional rational solitons and their blow-up via the Moutard transformation

By using the Moutard transformation of two-dimensional Schroedinger operators we derive a procedure for constructing explicit examples of such operators with rational fast decaying potentials and degenerate $L_2$-kernels (this construction was sketched in arXiv:0706.3595) and show that if we take some of these potentials as the Cauchy data for the Novikov-Veselov equation (a two-dimensional version of the Korteweg-de Vries equation), then the corresponding solutions blow up in a finite timeComment: 22 pages, PDFLatex, 9 figures. v2: some computations correcte

On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

We study the inverse scattering problem for electric potentials and magnetic fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.Comment: This is a slightly edited version of the previous pape