The diminishing segment process

Let Ξ₀=[−1,1], and define the segments Ξ_n recursively in the following manner: for every n=0,1,…, let Ξ_n+1=Ξ_n∩[a_n+1−1,a_n+1+1], where the point a_n+1 is chosen randomly on the segment Ξ_n with uniform distribution. For the radius ρ_n of Ξ_n, we prove that n(ρ_n−1/2) converges in distribution to an exponential law, and we show that the centre of the limiting unit interval has arcsine distribution.     

Isolation and Characterization of Novel Capsorubin‐Like Carotenoids from the Red Mamey (Pouteria sapota)

From the ripe fruits of red mamey (Pouteria sapota), two new carotenoids, 3′‐deoxycapsorubin and 3,3′‐dideoxycapsorubin, were isolated and identified based on their UV/VIS, CD, ¹H‐NMR, and mass spectral data.     

Location tracking in mobile ad hoc networks using particle filters

Mobile ad hoc networks (MANETs) are dynamic networks formed on-the-fly as mobile nodes move in and out of each others' transmission ranges. In general, the mobile ad hoc networking model makes no assumption that nodes know their own locations. However, recent research shows that location-awareness can be beneficial to fundamental tasks such as routing and energy-conservation. On the other hand, the cost and limited energy resources associated with common, low-cost mobile nodes prohibits them from carrying relatively expensive and power-hungry location-sensing devices such as GPS. This paper proposes a mechanism that allows non-GPS-equipped nodes in the network to derive their approximated locations from a limited number of GPS-equipped nodes. In our method, all nodes periodically broadcast their estimated location, in terms of a compressed particle filter distribution. Non-GPS nodes estimate the distance to their neighbors by measuring the received signal strength of incoming messages. A particle filter is then used to estimate the approximated location, along with a measure of confidence, from the sequence of distance estimates. Simulation studies show that our solution is capable of producing good estimates equal or better than the existing localization methods such as APS-Euclidean for the more difficult scenario when the network connectivity is low.     

Product integration for volterra integral equations of the second kind with weakly singular kernels

We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.

     

A environmentally friendly reversed-phase liquid chromatography method for phthalates determination in nail cosmetics

A simple and rapid analytical method was developed for the determination of phthalates, usually employed in nail cosmetic products. The method is based on an ultrasonic extraction of the sample with ethanol-water (90:10, v/v) followed by HPLC separation and quantitation. HPLC was carried out using a C18 column and spectrophotometric detection at 254 nm. A linear gradient elution was performed with ethanol-water starting from 50 to 95% ethanol in 30 min. Standard calibration curves were linear for all the analytes over the concentration range 5-200 μg ml⁻¹ with LOD values of about 0.5 μg ml⁻¹.The proposed green analytical method has been successfully applied for the analysis of commercial samples in order to check the presence of phthalates and to determine their concentration.     

On finite pseudorandom sequences of k symbols

In earlier papers C. Mauduit and A. Sárközy have introduced and studied the measures of pseudorandomness for finite binary sequences. In [8] they extend this theory to sequences of k symbols: they give the definitions and also construct a “good” pseudorandom sequence of k symbols. In this paper these measures are studied for a “truely random” sequence.     

Use of capillary electrophoresis to monitor wheat maturation

Summary The maturation of wheat varieties with different harvest times has been examined by high-performance capillary electrophoresis. The unique proteins of the albumin, gliadin and glutenin fractions of Hungarian winter wheat cultivars Bánkúti 1201 (early harvest time), Martonvásári 23 (medium harvest time), and Martonvásári 15 (semi-late harvest time) were analysed. An acidic phosphate buffer containing a polymeric additive and organic modifiers was used in capillary zone electrophoresis mode. Formation of albumin followed the same time scale, and the patterns were quite similar, for all three cultivars. For gliadins and glutenins the time scale and patterns were different and some correlation was observed between harvest time and gliadin formation. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001     

Development of a tandem thin-layer chromatography-high-performance liquid chromatography method for the identification and determination of corticosteroids in cosmetic products

A solid-phase extraction clean-up and and a liquid chromatographic method with ultraviolet detection were developed for the analysis of 51 corticosteroids in cosmetic samples in order to screen commercial samples for the presence of undeclared synthetic corticosteroids. A thin-layer chromatographic analysis was carried out on silica gel plates, using different eluants and detection reagents. When such a preliminary chromatographic separation gave some indications about the presence of steroid compounds, the methanol extracts from real samples were applied to a solid-phase extraction C₁₈ cartridge, and the analytes eluted with ethyl ether. The high-performance liquid chromatographic separation was then carried out for the identification and determination of the analytes using a Purospher RP-18 column, an isocratic or a gradient elution with a mixture acetonitrile-water and a photodiode-array detector. The accuracy of the method was determined by spiking experiments on home-made cosmetic samples. The analytical recoveries were satisfactory.