Existence,Non-existence,and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2

We consider a semilinear heat equation with exponential nonlinearity in ?². We prove that local solutions do not exist for certain data in the Orlicz space exp L ²(?²), even though a small data global existence result holds in the same space exp L ²(?²). Moreover, some suitable subclass of exp L ²(?²) for local existence and uniqueness is proposed.

     

Functional EEG connectivity during competition

Background

Social behavior and interactions pervasively shape and influence our lives and relationships. Competition, in particular, has become a core topic in social neuroscience since it stresses the relevance and salience of social comparison processes between the inter-agents that are involved in a common task. The majority of studies, however, investigated such kind of social interaction via one-person individual paradigms, thus not taking into account relevant information concerning interdependent participants’ behavioral and neural responses. In the present study, dyads of volunteers participated in a hyperscanning paradigm and competed in a computerized attention task while their electrophysiological (EEG) activity and performance were monitored and recorded. Behavioral data and inter-brain coupling measures based on EEG frequency data were then computed and compared across different experimental conditions: a control condition (individual task, t0), a first competitive condition (pre-feedback condition, t1), and a second competitive condition following a positive reinforcing feedback (post-feedback condition, t2).

Results

Results showed that during competitive tasks participants’ performance was improved with respect to control condition (reduced response times and error rates), with a further specific improvement after receiving a reinforcing feedback. Concurrently, we observed a reduction of inter-brain functional connectivity (primarily involving bilateral prefrontal areas) for slower EEG frequency bands (delta and theta). Finally, correlation analyses highlighted a significant association between cognitive performance and inter-brain connectivity measures.

Conclusions

The present results may help identifying specific patterns of behavioral and inter-brain coupling measures associated to competition and processing of social reinforcements.

     

Maize food allergy: lipid-transfer proteins,endochitinases, and alpha-zein precursor are relevant maize allergens in double-blind placebo-controlled maize-challenge-positive patients

Italian patients with maize anaphylaxis have been shown to have IgE toward two major maize allergens: an alpha-amylase inhibitor and a 9-kDa LTP. A complete study on maize food allergens in patients with positive maize double-blind, placebo-controlled food challenge (DBPCFC) is lacking. The objective was to utilize the three maize protein fractions to identify and characterize the most relevant IgE-binding proteins recognized by the sera of Italian and Swiss patients with either a positive maize-DBPCFC or a history of maize-induced anaphylaxis. Osborne’s protein fractions of maize were extracted to obtain water-soluble, total zein, and total protein fractions. Protein IgE-binding capacity was investigated by SDS-PAGE immunoblotting using the sera from DBPCFC-positive patients and from patients with maize-induced anaphylaxis. Purified maize LTP was used to inhibit the IgE immunoblotting of the three protein fractions. IgE immunoblotting demonstrated that the 9-kDa LTP was recognized by all the Italian patients and by none of the Swiss patients. Other allergens were: 14-kDa α-amylase inhibitor, 30-kDa endochitinases A and -B, 19 kDa zein-β precursor, and 26 kDa zein-α precursor; a newly described allergen, the globulin-2 precursor, identified in the total protein fraction. It is noteworthy that maize LTP and endochitinase were cross-reactive with grape LTP and one grape endochitinase. LTP was found to be the only major allergen in Italian patients with either positive maize challenge or a history of maize-induced anaphylaxis. We have identified other maize allergens in subjects with maize food allergy, as grape cross-reactive endochitinase, however, the clinical significance of these proteins needs to be investigated in larger groups of patients with allergy to these food items.     

Synthesis and spectral properties of 5-methylthio-4H-1-(p-substituted-phenyl)-3a-(p-substituted-phenyl)-9-[(m-; and p-substituted)-phenoxy]-3a,4-dihydro[1,2,4]oxadiazolo[4,5-a][1,5]benzodiazepines

The preparation of eight novel substituted [1,2,4]oxadiazolo[4,5-a][1,5]benzodiazepines which have potentially useful pharmacological properties; by 1,3-cycloaddition of benzonitrile oxides, generated in situ from benzohydroxamoyl chloride and triethylamine, to 1,5-benzodiazepine derivatives is described. The structure of all products was corroborated by ir, ¹H-nmr, ¹³C-nmr and ms.     

Multiple solutions for a Hénon-like equation on the annulus

For the equation −Δu=||xα|−2|up−1, 1<|x|<3, we prove the existence of two solutions for α large, and of two additional solutions when p is close to the critical Sobolev exponent ^2∗=2N/(N−2). A symmetry-breaking phenomenon appears, showing that the least-energy solutions cannot be radial functions.     

Non-uniqueness for a critical heat equation in two dimensions with singular data

Nonlinear heat equations in two dimensions with singular initial data are studied. In recent works nonlinearities with exponential growth of Trudinger-Moser type have been shown to manifest critical behavior: well-posedness in the subcritical case and non-existence for certain supercritical data. In this article we propose a specific model nonlinearity with Trudinger-Moser growth for which we obtain surprisingly complete results: a) for initial data strictly below a certain singular threshold function $\stackrel{?}{u}$ the problem is well-posed, b) for initial data above this threshold function $\stackrel{?}{u}$, there exists no solution, c) for the singular initial datum $\stackrel{?}{u}$ there is non-uniqueness. The function $\stackrel{?}{u}$ is a weak stationary singular solution of the problem, and we show that there exists also a regularizing classical solution with the same initial datum $\stackrel{?}{u}$.     

Unambiguous characterization and tissue localization of Pru P 3 peach allergen by electrospray mass spectrometry and MALDI imaging

The lipid transfer protein (LTP), Pru p 3, has been identified as the major allergen present in peach, and its sequence obtained by direct amino acid sequencing has been previously reported. However, several sequences, obtained from c‐DNA and available in databases, show differences among them and from the originally proposed structure. In this paper, we report the fast and unambiguous determination of the structure of Pru p 3 protein, extracted from three different varieties of peach, by electrospray ionization mass spectrometry (ESI‐MS), both coupled to single stage (quadrupole) or advanced (FT‐HRMS) analyzers. The structure was identical to one of the cDNA‐derived sequences and different in two positions from the previously reported structure obtained by amino acid sequencing. Moreover, the exclusive localization of the protein in the outer part of the fruits was assessed by Matrix‐Assisted Laser Desorption Ionization Mass Spectrometry Imaging (MALDI MSI). The results reported here demonstrate the full potential of mass spectrometry for rapidly obtaining high quality structural data of relevant food proteins. Copyright © 2009 John Wiley & Sons, Ltd.