Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation

Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for multipeakon solutions of Novikov's cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation.Comment: 41 pages, LaTeX + AMS packages + pstrick

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

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

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

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works

Terpenylic acid and related compounds: precursors for dimers in secondary organic aerosol from the ozonolysis of α- and β-pinene

In the present study, we have characterized the structure of a higher-molecular weight (MW) 358 α- and β-pinene dimeric secondary organic aerosol (SOA) product that received ample attention in previous molecular characterization studies and has been elusive. Based on mass spectrometric evidence for deprotonated molecules formed by electrospray ionization in the negative ion mode and chemical considerations, it is suggested that diaterpenylic acid is a key monomeric intermediate for dimers of the ester type. It is proposed that cis-pinic acid is esterified with the hydroxyl-containing diaterpenylic acid, which can be explained through acid-catalyzed hydrolysis of the recently elucidated lactone-containing terpenylic acid and/or diaterpenylic acid acetate, both first-generation oxidation products. To a minor extent, higher-MW 358 and 344 diester products are formed containing other terpenoic acids as monomeric units, i.e., diaterpenylic acid instead of cis-pinic acid, and diaterebic acid instead of diaterpenylic acid. It is shown that the MW 358 diester and related MW 344 compounds, which can be regarded as processed SOA products, also occur in ambient fine (PM2.5) rural aerosol collected at night during the warm period of the 2006 summer field campaign conducted at K-puszta, Hungary, a rural site with coniferous vegetation. This indicates that, under ambient conditions, the higher-MW diesters are formed in the particle phase over a longer time-scale than that required for gas-to-particle partitioning of their monomeric precursors in laboratory α-/β-pinene ozonolysis experiments

Terpenylic Acid and Related Compounds from the Oxidation of α-Pinene: Implications for New Particle Formation and Growth above Forests

Novel secondary organic aerosol (SOA) products from the monoterpene α-pinene with unique dimer-forming properties have been identified as lactone-containing terpenoic acids, i.e., terpenylic and 2-hydroxyterpenylic acid, and diaterpenylic acid acetate. The structural characterizations were based on the synthesis of reference compounds and detailed interpretation of mass spectral data. Terpenylic acid and diaterpenylic acid acetate are early oxidation products generated upon both photooxidation and ozonolysis, while 2-hydroxyterpenylic acid is an abundant SOA tracer in ambient fine aerosol that can be explained by further oxidation of terpenylic acid. Quantum chemical calculations support that noncovalent dimer formation involving double hydrogen bonding interactions between carboxyl groups of the monomers is energetically favorable. The molecular properties allow us to explain initial particle formation in laboratory chamber experiments and are suggested to play a role in new particle formation and growth above forests, a natural phenomenon that has fascinated scientists for more than a century

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