Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation

In this work we present new results on the convergence of diagonal sequences of certain mixed type Hermite-Padé approximants of a Nikishin system. The study is motivated by a mixed Hermite-Padé approximation scheme used in the construction of solutions of a Degasperis-Procesi peakon problem and germane to the analysis of the inverse spectral problem for the discrete cubic string.This author [G.L.L] was supported by research grant MTM2015-65888-C4-2-P of Ministerio de Economía, Industria y Competitividad. This author [S.M.P.] received support from research grant CONICYT Fondecyt/Postdoctorado/ Proyecto 3170112. [J.S] Partially supported by NSERC

Competition of IL-1 and IL-1ra determines lymphocyte response to delayed stimulation with PHA.

BACKGROUND: Human peripheral blood mononuclear cells (PBMC) left in microcultures for 24h without mitogen do not respond to subsequent stimulation with PHA. They regain reactivity if the native culture medium is absorbed with other party lymphocytes or partially replaced with the medium from a PHA-stimulated culture. The observations suggest that, during the incubation, some inhibitory agent had accumulated in the culture medium. AIM: The study was performed to determine the nature of the observed phenomenon in respect of the possible role of monocytes and their products IL-1 and IL-1 receptor antagonist (IL-1ra), and to test for immunodiagnostic purposes the significance of quantifying the lymphocyte response to delayed stimulation with PHA in patients suffering from inflammatory prosesses. METHODS: Lymphocyte response to delayed stimulation with PHA, calculated as the lymphocyte-monokine interaction (LM) index, was determined in the microcultures of PBMC isolated from the blood of healthy donors or of patients with acute tonsilitis. The values of LM indices were compared with the ratios of IL-1ra/IL-1beta concentration estimated by enzyme-linked immunosorbent assay method in the culture supernatants. The influences of exogenous IL-1beta, IL-1ra, anti-IL1ra antibodies and antibiotic cefaclor on the monokine concentrations and on the values of LM index were tested. RESULTS AND CONCLUSIONS: The results show that the level of lymphocyte response to delayed stimulation with PHA (LM index) is inversely proportional to the ratio of IL-1ra/IL-1beta concentration in the culture. The low LM values at high IL-1ra/IL-1beta ratios in PBMC cultures from healthy donors, reversed proportions found in patients' PBMC (acute tonsilitis), and the cefaclor-induced reduction of LM value with correlated increase of the IL-1ra/IL-1beta ratio suggest that the LM assay may prove to be useful for immunodiagnostic purposes

Characterization of polar organosulfates in secondary organic aerosol from the unsaturated aldehydes 2-E-pentenal, 2-E-hexenal, and 3-Z-hexenal

We show in the present study that the unsaturated aldehydes 2-E-pentenal, 2-E-hexenal, and 3-Z-hexenal are biogenic volatile organic compound (BVOC) precursors for polar organosulfates with molecular weights (MWs) 230 and 214, which are also present in ambient fine aerosol from a forested site, i.e., K-puszta, Hungary. These results complement those obtained in a previous study showing that the green leaf aldehyde 3-Z-hexenal serves as a precursor for MW 226 organosulfates. Thus, in addition to isoprene, the green leaf volatiles (GLVs) 2-E-hexenal and 3-Z-hexenal, emitted due to plant stress (mechanical wounding or insect attack), and 2-E-pentenal, a photolysis product of 3-Z-hexenal, should be taken into account for secondary organic aerosol and organosulfate formation. Polar organosulfates are of climatic relevance because of their hydrophilic properties and cloud effects. Extensive use was made of organic mass spectrometry (MS) and detailed interpretation of MS data (i.e., ion trap MS and accurate mass measurements) to elucidate the chemical structures of the MW 230, 214 and 170 organosulfates formed from 2-E-pentenal and indirectly from 2-E-hexenal and 3-Z-hexenal. In addition, quantum chemical calculations were performed to explain the different mass spectral behavior of 2,3-dihydroxypentanoic acid sulfate derivatives, where only the isomer with the sulfate group at C-3 results in the loss of SO3. The MW 214 organosulfates formed from 2-E-pentenal are explained by epoxidation of the double bond in the gas phase and sulfation of the epoxy group with sulfuric acid in the particle phase through the same pathway as that proposed for 3-sulfooxy-2-hydroxy-2-methylpropanoic acid from the isoprene-related alpha,beta-unsaturated aldehyde methacrolein in previous work (Lin et al., 2013). The MW 230 organosulfates formed from 2-E-pentenal are tentatively explained by a novel pathway, which bears features of the latter pathway but introduces an additional hydroxyl group at the C-4 position. Evidence is also presented that the MW 214 positional isomer, 2-sulfooxy-3-hydroxypentanoic acid, is unstable and decarboxylates, giving rise to 1-sulfooxy-2-hydroxybutane, a MW 170 organosulfate. Furthermore, evidence is obtained that lactic acid sulfate is generated from 2-E-pentenal. This chemistry could be important on a regional and local scale where GLV emissions such as from grasses and cereal crops are substantial

Moment determinants as isomonodromic tau functions

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.Comment: 24 page

A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data

Reactive intermediates revealed in secondary organic aerosol formation from isoprene

Isoprene is a significant source of atmospheric organic aerosol; however, the oxidation pathways that lead to secondary organic aerosol (SOA) have remained elusive. Here, we identify the role of two key reactive intermediates, epoxydiols of isoprene (IEPOX = β-IEPOX + δ-IEPOX) and methacryloylperoxynitrate (MPAN), which are formed during isoprene oxidation under low- and high-NO_x conditions, respectively. Isoprene low-NO_x SOA is enhanced in the presence of acidified sulfate seed aerosol (mass yield 28.6%) over that in the presence of neutral aerosol (mass yield 1.3%). Increased uptake of IEPOX by acid-catalyzed particle-phase reactions is shown to explain this enhancement. Under high-NO_x conditions, isoprene SOA formation occurs through oxidation of its second-generation product, MPAN. The similarity of the composition of SOA formed from the photooxidation of MPAN to that formed from isoprene and methacrolein demonstrates the role of MPAN in the formation of isoprene high-NO_x SOA. Reactions of IEPOX and MPAN in the presence of anthropogenic pollutants (i.e., acidic aerosol produced from the oxidation of SO_2 and NO_2, respectively) could be a substantial source of “missing urban SOA” not included in current atmospheric models

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

The formation, properties and impact of secondary organic aerosol: current and emerging issues

Secondary organic aerosol (SOA) accounts for a significant fraction of ambient tropospheric aerosol and a detailed knowledge of the formation, properties and transformation of SOA is therefore required to evaluate its impact on atmospheric processes, climate and human health. The chemical and physical processes associated with SOA formation are complex and varied, and, despite considerable progress in recent years, a quantitative and predictive understanding of SOA formation does not exist and therefore represents a major research challenge in atmospheric science. This review begins with an update on the current state of knowledge on the global SOA budget and is followed by an overview of the atmospheric degradation mechanisms for SOA precursors, gas-particle partitioning theory and the analytical techniques used to determine the chemical composition of SOA. A survey of recent laboratory, field and modeling studies is also presented. The following topical and emerging issues are highlighted and discussed in detail: molecular characterization of biogenic SOA constituents, condensed phase reactions and oligomerization, the interaction of atmospheric organic components with sulfuric acid, the chemical and photochemical processing of organics in the atmospheric aqueous phase, aerosol formation from real plant emissions, interaction of atmospheric organic components with water, thermodynamics and mixtures in atmospheric models. Finally, the major challenges ahead in laboratory, field and modeling studies of SOA are discussed and recommendations for future research directions are proposed