An exponentially fitted special second-order finite difference method for solving singular perturbation problems

An exponentially fitted special second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a tri-diagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. To demonstrate the applicability of the method, we have solved several linear and non-linear problems. From the results, it is observed that the present method approximates the exact solution very well.     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.     

Heavy metal ion uptake properties of polystyrene-supported chelating polymer resins

Metal ion uptake properties of polystyrene-supported chelating polymer resins functionalized with (i) glycine, (ii) hydroxy benzoic acid, (iii) Schiff base and (iv) diethanol amine have been investigated. The effects of pH, time and initial concentration on the uptake of metal ions have been studied. The uptake of metal ion depends on pH. The resins are more selective at pH 10 for Pb(II) and Hg(II), whereas at pH 6 they are found to be Cd(II) and Cr(VI) selective. Metal ion uptake properties of resins follow Freundlich’s equation. The resins are recyclable and are therefore employed for the removal of heavy metal pollutants from industrial waste water.     

新型菲涅尔线聚焦聚光太阳电池组件研究

以聚甲基丙烯酸甲脂为材料,采用热压成型工艺加工成型线聚焦菲涅尔聚光透镜(8×),可用于空间、地面光伏系统太阳电池组件的聚光系统,并对在其聚光条件下,太阳电池的电流电压特性进行测试,结果表明,该菲涅尔线聚焦棱镜能有效提高太阳电池的单位输出功率.模具的机械加工精度和光学抛光精度低,是造成其部分聚光率损失的原因.     

Baseline studies of radon/thoron concentration levels in and around the Lambapur and Peddagattu areas in Nalgonda district, Andhra Pradesh, India

Studies conducted by Atomic Minerals Directorate of Exploration and Research (AMD) of Hyderabad, India had established the presence of higher concentrations of uranium in Lambapur and Peddagattu areas of Nalgonda district, AP, India and it was estimated that it could be a viable source for commercial extraction. The envisaged extraction process involves dispersion of radioactive particulate matter into atmosphere. Environmental radioactive studies in and around proposed mining areas at this point of time will be extremely useful for establishing base line data before a large scale uranium extraction process comes into existence. To this end, Solid State Nuclear Track Detectors were installed to evaluate indoor radon and thoron concentration levels in the dwellings of the area. The geometric means of radon and thoron concentration levels were found to be (7.1±0.2)×10¹ and (6.7±0.3)×10¹ Bq/m³, respectively. Simultaneously, natural background radiation measurements were also made and these levels are found to vary from 770 to 3995 μGy/y in the spatial distribution.     

Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.