More on limit theorems for iterates of probability measures on semigroups and groups

Summary In this paper, we continue earlier works of one of the authors on vague convergence of the sequence _k,n= _k+1 *...* _n, where _n is a sequence of probability measures on semigroups or groups. Typical results in this paper are: Theorem. Let S be a locally compact noncompact second countable group such that being the support of a probability measure on S. Suppose there exists an open set V with compact closure such that x ^–1 Vx=V for every xS. Then for all compact sets K, sup{ ⁿ (Kx): xS0 as n. Theorem. Let S be an at most countable discrete group. Let _n be a sequence of probability measures on S. Then for all nonnegative integers k, the sequence _k,n converges vaguely to some probability measure if and only if there exists a finite subgroup G such that the series and for any proper subgroup G of G and any choice of elements g_n in S, the series . A sufficient condition for the vague convergence of the sequence _k,n to a probability measure is that (i) there exists a finite subgroup G such that and (ii) _n(e)>s>0 for all n, e being the identity.The author was supported by NSF grant MCS77-03639     

Classification of Polish Natural Bee Honeys Based on Their Chemical Composition

The targeted quantitative NMR (qNMR) approach is a powerful analytical tool, which can be applied to classify and/or determine the authenticity of honey samples. In our study, this technique was used to determine the chemical profiles of different types of Polish honey samples, featured by variable contents of main sugars, free amino acids, and 5-(hydroxymethyl)furfural. One-way analysis of variance (ANOVA) was performed on concentrations of selected compounds to determine significant differences in their levels between all types of honey. For pattern recognition, principal component analysis (PCA) was conducted and good separations between all honey samples were obtained. The results of present studies allow the differentiation of honey samples based on the content of sucrose, glucose, and fructose, as well as amino acids such as tyrosine, phenylalanine, proline, and alanine. Our results indicated that the combination of qNMR with chemometric analysis may serve as a supplementary tool in specifying honeys.     

The Small Molecule PPARγ Agonist GL516 Induces Feeding-Stimulatory Effects in Hypothalamus Cells Hypo-E22 and Isolated Hypothalami

PPARγ agonists are implicated in the regulation of diabetes and metabolic syndrome and have therapeutic potential in brain disorders. PPARγ modulates appetite through its central effects, especially on the hypothalamic arcuate nucleus (ARC). Previous studies demonstrated that the small molecule GL516 is a PPARγ agonist able to reduce oxidative stress and apoptosis with a potential neuroprotective role. Herein, we investigated the effects of GL516, in vitro and ex vivo, on the levels of hypothalamic dopamine (DA) and serotonin (5-HT). The gene expressions of neuropeptide Y, CART, AgRP, and POMC, which play master roles in the neuroendocrine regulation of feeding behavior and energy balance, were also evaluated. HypoE22 cells were treated with H₂O₂ (300 μM) for 2 h e 30’ and with different concentrations of GL516 (1 nM-100 µM). The cell viability was evaluated after 24 and 48 h of culturing using the MTT test. DA and 5-HT levels in the HypoE22 cell supernatants were analyzed through HPLC; an ex vivo study on isolated hypothalamic specimens challenged with scalar concentrations of GL516 (1–100 µM) and with pioglitazone (10 µM) was carried out. The gene expressions of CART, NPY, AgRP, and POMC were also determined by a quantitative real-time PCR. The results obtained showed that GL516 was able to reduce DA and 5-HT turnover; moreover, it was effective in stimulating NPY and AgRP gene expressions with a concomitant reduction in CART and POMC gene expressions. These results highlight the capability of GL516 to modulate neuropeptide pathways deeply involved in appetite control suggesting an orexigenic effect. These findings emphasize the potential use of GL516 as a promising candidate for therapeutical applications in neurodegenerative diseases associated with the reduction in food intake and stimulation of catabolic pathways.     

Photo-Induced Reactions between Glyoxal and Hydroxylamine in Cryogenic Matrices

In this paper, the photochemistry of glyoxal–hydroxylamine (Gly–HA) complexes is studied using FTIR matrix isolation spectroscopy and ab initio calculations. The irradiation of the Gly–HA complexes with the filtered output of a mercury lamp (λ > 370 nm) leads to their photoconversion to hydroxyketene–hydroxylamine complexes and the formation of hydroxy(hydroxyamino)acetaldehyde with a hemiaminal structure. The first product is the result of a double hydrogen exchange reaction between the aldehyde group of Gly and the amino or hydroxyl group of HA. The second product is formed as a result of the addition of the nitrogen atom of HA to the carbon atom of one aldehyde group of Gly, followed by the migration of the hydrogen atom from the amino group of hydroxylamine to the oxygen atom of the carbonyl group of glyoxal. The identification of the products is confirmed by deuterium substitution and by MP2 calculations of the structures and vibrational spectra of the identified species.     

Aerosol retrievals from channel-1 and -2 AVHRR radiances: Long-term trends updated and revisited

The nominal Global Aerosol Climatology Project (GACP) record of aerosol optical thickness (AOT) and Ångström exponent (AE) over the oceans is extended by 6 months to cover the period from August 1981 through December 2005. The most recent 4-year segment reveals no significant short-term tendencies in globally and hemispherically averaged AOTs and AEs. This finding is consistent with contemporaneous MODIS and MISR results and the accumulating evidence of a gradual transition from global brightening to global dimming. We also analyze the retrieval implications of allowing the imaginary part of the aerosols refractive index Im(m) to change over the duration of the GACP record. Our sensitivity study shows that increasing Im(m) from 0.003 during the 4-year pre-Pinatubo period up to 0.007 during the most recent 4-year segment of GACP data eliminates the previously identified long-term decreasing AOT trend. Should this long-term trend in Im(m) be real then it would cause the global absorption AOT over the oceans to more than double and the global single-scattering albedo to decrease from ～0.95 to ～0.88. Such changes could make tropospheric aerosols significant contributors to the recent surface temperature increase.     

Synthesis and Tuberculostatic Activity of 1,3-Thiazacycloalkyl[3,2-b]-1,2,4-triazoles

The 4-hydroxyalkyl-1,2,4-triazole-3-thiones cyclization allowed us to work out the effective method of 1,3-thiazacycloalkyl[3,2-b]-1,2,4-triazoles synthesis. Some of the compounds that were obtained were tested for their tuberculostatic activity.