On Soliton-type Solutions of Equations Associated with N-component Systems

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure

シンサイ ニツイテ タイワスル コドモ ノ テツガク ノ カノウセイ

International audienc

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page

Folic acid deficiency optic neuropathy: A case report

<p>Abstract</p> <p>Introduction</p> <p>Nutritional optic neuropathies are uncommon and can be associated with gradual visual loss and optic atrophy or sudden vision loss and optic disc swelling.</p> <p>Case presentation</p> <p>A 44-year-old woman presented with a 4-week history of progressive visual loss and was noted to have bilateral retrobulbar optic neuropathy. No other clinical abnormality was noted. Investigations revealed severe folate deficiency with normal vitamin B12 levels. Her alcohol and tobacco consumption was moderate and subsequent correction of folate levels with oral supplementation has led to improvement in her visual acuity.</p> <p>Conclusion</p> <p>This case highlights an unusual presentation of folic acid deficiency that may present to the general physician.</p

Local atomic order, electronic structure and electron transport properties of Cu-Zr metallic glasses

We studied atomic and electronic structures of binary Cu-Zr metallic glasses (MGs) using combined experimental and computational methods including X-ray absorption fine structure spectroscopy, electrical resistivity, thermoelectric power (TEP) measurements, molecular dynamics (MD) simulations, and ab-initio calculations. The results of MD simulations and extended X-ray absorption fine structure analysis indicate that atomic order of Cu-Zr MGs and can be described in terms of interpenetrating icosahedral-like clusters involving five-fold symmetry. MD configurations were used as an input for calculations of theoretical electronic density of states (DOS) functions which exhibits good agreement with the experimental X-ray absorption near-edge spectra. We found no indication of minimum of DOS at Fermi energy predicted by Mott's nearly free electron (NFE) model for glass-forming alloys. The theoretical DOS was subsequently used to test Mott's model describing the temperature variation of electrical resistivity and thermoelectric power of transition metal-based MGs. We demonstrate that the measured temperature variations of electrical resistivity and TEP remain in a contradiction with this model. On the other hand, the experimental temperature dependence of electrical resistivity can be explained by incipient localization of conduction electrons. It is shown that weak localization model works up to relatively high temperatures when localization is destroyed by phonons. Our results indicate that electron transport properties of Cu-Zr MGs are dominated by localization effects rather than by electronic structure. We suggest that NFE model fails to explain a relatively high glass-forming ability of binary Cu-Zr alloy

De novo lipogenesis alters the phospholipidome of esophageal adenocarcinoma

The incidence of esophageal adenocarcinoma is rising, survival remains poor, and new tools to improve early diagnosis and precise treatment are needed. Cancer phospholipidomes quantified with mass spectrometry imaging can support objective diagnosis in minutes using a routine frozen tissue section. However, whether mass spectrometry imaging can objectively identify primary esophageal adenocarcinoma is currently unknown and represents a significant challenge, as this microenvironment is complex with phenotypically similar tissue-types. Here we used desorption electrospray ionisation mass spectrometry imaging (DESI-MSI) and bespoke chemometrics to assess the phospholipidomes of esophageal adenocarcinoma and relevant control tissues. Multivariable models derived from phospholipid profiles of 117 patients were highly discriminant for esophageal adenocarcinoma both in discovery (area-under-curve = 0.97) and validation cohorts (AUC = 1). Among many other changes, esophageal adenocarcinoma samples were markedly enriched for polyunsaturated phosphatidylglycerols with longer acyl chains, with stepwise enrichment in pre-malignant tissues. Expression of fatty acid and glycerophospholipid synthesis genes was significantly upregulated, and characteristics of fatty acid acyls matched glycerophospholipid acyls. Mechanistically, silencing the carbon switch ACLY in esophageal adenocarcinoma cells shortened GPL chains, linking de novo lipogenesis to the phospholipidome. Thus, DESI-MSI can objectively identify invasive esophageal adenocarcinoma from a number of pre-malignant tissues and unveils mechanisms of phospholipidomic reprogramming. These results call for accelerated diagnosis studies using DESI-MSI in the upper gastrointestinal endoscopy suite as well as functional studies to determine how polyunsaturated phosphatidylglycerols contribute to esophageal carcinogenesis

Imaging of esophageal lymph node metastases by desorption electrospray ionization mass spectrometry

Histopathological assessment of lymph node metastases (LNM) depends on subjective analysis of cellular morphology with inter-/intra-observer variability. In this study, LNM from esophageal adenocarcinoma was objectively detected using desorption electrospray ionization-mass spectrometry imaging (DESI-MSI). Ninety lymph nodes and their primary tumor biopsies from 11 esophago-gastrectomy specimens were examined and analyzed by DESI-MSI. Images from mass spectrometry and corresponding histology were co-registered and analyzed using multivariate statistical tools. The MSIs revealed consistent lipidomic profiles of individual tissue types found within lymph nodes. Spatial mapping of the profiles showed identical distribution patterns as per the tissue types in matched immunohistochemistry images. Lipidomic profile comparisons of LNM versus the primary tumor revealed a close association in contrast to benign lymph node tissue types. This similarity was used for the objective prediction of LNM in mass spectrometry images utilizing the average lipidomic profile of esophageal adenocarcinoma. The multivariate statistical algorithm developed for LNM identification demonstrated a sensitivity, specificity, positive predictive value and negative predictive value of 89.5, 100, 100 and 97.2 per-cent, respectively, when compared to gold-standard immunohistochemistry. DESI-MSI has the potential to be a diagnostic tool for peri-operative identification of LNM and compares favorably with techniques currently used by histopathology experts

A new extended q-deformed KP hierarchy

A method is proposed in this paper to construct a new extended q-deformed KP ($q$-KP) hiearchy and its Lax representation. This new extended $q$-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when $q$ goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations.Comment: 17 pages, no figur