Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.Nash equilibrium;noncooperative games

Effect of tomato variety, cultivation, climate and processing on Sola l 4, an allergen from Solanum lycopersicum

Tomatoes (Solanum lycopersicum) are one of the most consumed vegetables worldwide. However, tomato allergies in patients suffering from birch pollen allergy occur frequently. Due to highly similar protein structures of the tomato allergen Sola l 4 and the major birch pollen allergen Bet v 1, patients cross-react with allergenic proteins from tomato as well as other fruits or vegetables. The aim of this study was to quantify Sola l 4 in various tomatoes differing in color, size and shape for identification of varieties with a reduced allergen level. Therefore, an indirect competitive ELISA using a specific polyclonal Sola l 4 antibody was developed. In addition, two varieties, both cultivated either conventionally or organically and furthermore dried with different methods, were analyzed to investigate the influence of the cultivation method and processing techniques on Sola l 4 level. Within 23 varieties, Sola l 4 content varied significantly between 0.24 and 1.71 μg Sola l 4/g FW. The tomato cultivars Rugantino and Rhianna showed the significantly lowest level, whereas in cultivars Farbini and Bambello the significantly highest concentration was determined. Drying of tomatoes in the oven and by sun resulted in a significant decrease. The thermal instability was verified for the recombinant Sola l 4 emphasizing the results for the native protein in dried tomato samples. Overall, the Sola l 4 content is cultivar-dependent and no correlation between color and Sola l 4 amount was found. During the drying process of tomatoes Sola l 4 level was significantly reduced due to thermal instability. Growing conditions have a minor effect whereas seasonal effects show a more pronounced impact. These findings could extend the knowledge about the allergen level of different tomato varieties and may help to improve food safety to potentially increase the life quality of patients suffering from birch pollen allergy

Effect of the Strawberry Genotype, Cultivation and Processing on the Fra a 1 Allergen Content

Birch pollen allergic patients show cross-reactivity to vegetables and fruits, including strawberries (Fragaria × ananassa). The objective of this study was to quantify the level of the Fra a 1 protein, a Bet v 1-homologous protein in strawberry fruits by a newly developed ELISA, and determine the effect of genotype, cultivation and food processing on the allergen amount. An indirect competitive ELISA using a specific polyclonal anti-Fra a 1.02 antibody was established and revealed high variability in Fra a 1 levels within 20 different genotypes ranging from 0.67 to 3.97 μg/g fresh weight. Mature fruits of red-, white- and yellow-fruited strawberry cultivars showed similar Fra a 1 concentrations. Compared to fresh strawberries, oven and solar-dried fruits contained slightly lower levels due to thermal treatment during processing. SDS-PAGE and Western blot analysis demonstrated degradation of recombinant Fra a 1.02 after prolonged (>10 min) thermal treatment at 99 ◦ C. In conclusion, the genotype strongly determined the Fra a 1 quantity in strawberries and the color of the mature fruits does not relate to the amount of the PR10-protein. Cultivation conditions (organic and conventional farming) do not affect the Fra a 1 level, and seasonal effects were minor

Approximate fixed point theorems in Banach spaces with applications in game theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games

A New Channel for the Detection of Planetary Systems Through Microlensing: II. Repeating Events

In the companion paper we began the task of systematically studying the detection of planets in wide orbits ($a > 1.5 R_E$) via microlensing surveys. In this paper we continue, focusing on repeating events. We find that, if all planetary systems are similar to our own Solar System, reasonable extensions of the present observing strategies would allow us to detect 3-6 repeating events per year along the direction to the Bulge. Indeed, if planetary systems with multiple planets are common, then future monitoring programs which lead to the discovery of thousands of stellar-lens events will likely discover events in which several different planets within a single system serve as lenses, with light curves exhibiting multiple repetitions. In this paper we discuss observing strategies to maximize the discovery of all wide-orbit planet-lens events. We also compare the likely detection rates of planets in wide orbits to those of planets located in the zone for resonant lensing. We find that, depending on the values of the planet masses and stellar radii of the lensed sources (which determine whether or not finite source size is important), and also on the sensitivity of the photometry used by observers, the detection of planets in wide orbits may be the primary route to the discovery of planets via microlensing. We also discuss how the combination of resonant and wide-orbit events can help us to learn about the distribution of planetary system properties (S 6.1). In addition, by determining the fraction of short-duration events due to planets, we indirectly derive information about the fraction of all short-duration events that may be due to low-mass MACHOs (S 6.2).Comment: 51 pages, 7 figures. To be published in the Astrophysical Journal, 20 February 1999. This completes the introduction to the discovery of planets in wide orbits begun in astro-ph/9808075, also to appear in ApJ on 20 February 199

Type Ia supernova Hubble diagram with near-infrared and optical observations

We main goal of this paper is to test whether the NIR peak magnitudes of SNe Ia could be accurately estimated with only a single observation obtained close to maximum light, provided the time of B band maximum and the optical stretch parameter are known. We obtained multi-epoch UBVRI and single-epoch J and H photometric observations of 16 SNe Ia in the redshift range z=0.037-0.183, doubling the leverage of the current SN Ia NIR Hubble diagram and the number of SNe beyond redshift 0.04. This sample was analyzed together with 102 NIR and 458 optical light curves (LCs) of normal SNe Ia from the literature. The analysis of 45 well-sampled NIR LCs shows that a single template accurately describes them if its time axis is stretched with the optical stretch parameter. This allows us to estimate the NIR peak magnitudes even with one observation obtained within 10 days from B-band maximum. We find that the NIR Hubble residuals show weak correlation with DM_15 and E(B-V), and for the first time we report a possible dependence on the J_max-H_max color. The intrinsic NIR luminosity scatter of SNe Ia is estimated to be around 0.10 mag, which is smaller than what can be derived for a similarly heterogeneous sample at optical wavelengths. In conclusion, we find that SNe Ia are at least as good standard candles in the NIR as in the optical. We showed that it is feasible to extended the NIR SN Ia Hubble diagram to z=0.2 with very modest sampling of the NIR LCs, if complemented by well-sampled optical LCs. Our results suggest that the most efficient way to extend the NIR Hubble diagram to high redshift would be to obtain a single observation close to the NIR maximum. (abridged)Comment: 39 pages, 15 figures, accepted by A&

A New Channel for the Detection of Planetary Systems Through Microlensing: I. Isolated Events Due to Planet Lenses

We propose and evaluate the feasibility of a new strategy to search for planets via microlensing. This new strategy is designed to detect planets in "wide" orbits, i.e., with orbital separation, $a$ greater than $\sim 1.5 R_E$. Planets in wide orbits may provide the dominant channel for the microlensing discovery of planets, particularly low-mass (e.g., Earth-mass) planets. This paper concentrates on events in which a single planet serves as a lens, leading to an isolated event of short duration. We point out that a distribution of events due to lensing by stars with wide-orbit planets is necessarily accompanied by a distribution of shorter- duration events. The fraction of events in the latter distribution is proportional to the average value of $\sqrt{q}$, where $q$ is the ratio between \pl and stellar masses. The position of the peak or peaks also provides a measure of the mass ratios typical of planetary systems. We study detection strategies that can optimize our ability to discover isolated short-duration events due to lensing by planets, and find that monitoring employing sensitive photometry is particularly useful. If planetary systems similar to our own are common, even modest changes in detection strategy should lead to the discovery of a few isolated events of short duration every year. We therefore also address the issue of the contamination due to stellar populations of any microlensing signal due to low-mass MACHOs. We describe how, even for isolated events of short duration, it will be possible to test the hypothesis that the lens was a planet instead of a low-mass MACHO, if the central star of the planetary system contributes a measurable fraction of the baseline flux.Comment: 37 pages, 6 figure. To be published in the Astrophysical Journal. This is part one of a series of papers on microlensing by planetary systems containing wide-orbit planets; the series represents a reorganization and extension of astro-ph/971101

Potential of delphinidin-3-rutinoside extracted from Solanum melongena L. as promoter of osteoblastic MC3T3-E1 function and antagonist of oxidative damage

Purpose: Increasing evidence suggests the potential use of natural antioxidant compounds in the prevention/treatment of osteoporosis. This study was undertaken to investigate the effects of purified delphinidin-3-rutinoside (D3R), isolated from Solanum melongena L., on osteoblast viability and differentiation in basal conditions and its ability to protect MC3T3-E1 cells against oxidative damage induced by tert-butyl hydroperoxide (t-BHP). Methods: MC3T3-E1 osteoblastic cells were treated with D3R (10 1211\u201310 125 M for 24 h), followed by treatment with t-BHP (250 \ub5M for 3 h). To test cell viability, MTT test was performed. Apoptotic cells were stained with Hoechst-33258 dye. Cytoskeleton rearrangement was stained with FICT-labelled phalloidin. Intracellular ROS production was measured using dichlorofluorescein CM-DCFA. The reduced glutathione to oxidized glutathione ratio (GSH/GSSG) contents was measured according to the OPT fluorimetric assay. Results: D3R (10 129 M) significantly increases viability of MC3T3-E1 cells and promotes osteoblast differentiation by increasing the expression of type I collagen, alkaline phosphatase and osteocalcin. Pre-treatment with D3R (10 129 M) significantly prevented t-BHP-induced osteoblastic dysfunction and changes in the cytoskeleton organization by decreasing intracellular ROS and preventing the reduction in GSH/GSSG. D3R did not significantly modify the expression of Osteoprotegerin/RANKL system activated by t-BHP suggesting a lack of effect of D3R on osteoblast/osteoclast crosstalk. D3R protective effects against t-BHP-induced osteoblastic dysfunction were mediated by the PI3K/Akt pathway since they were completely prevented by LY294002, a PI3K/Akt specific inhibitor. Conclusions: These findings indicate that D3R protects MC3T3-E1 cells from oxidative damage and suggest the potential utility of dietary D3R supplement to prevent osteoblast dysfunction in age-related osteoporosis