A parameter-uniform scheme for singularly perturbed partial differential equations with a time lag

A numerical scheme for a class of singularly perturbed delay parabolic partial differential equations which has wide applications in the various branches of science and engineering is suggested. The solution of these problems exhibits a parabolic boundary layer on the lateral side of the rectangular domain which continuously depends on the perturbation parameter. For the small perturbation parameter, the standard numerical schemes for the solution of these problems fail to resolve the boundary layer(s) and the oscillations occur near the boundary layer. Thus, in this paper to resolve the boundary layer the extended cubic B-spline basis functions consisting of a free parameter λ are used on a fitted-mesh. The extended B-splines are the extension of classical B-splines. To find the best value of λ the optimization technique is adopted. The extended cubic B-splines are an advantage over the classical B-splines as for some optimized value of λ the solution obtained by the extended B-splines is better than the solution obtained by classical B-splines. The method is shown to be first-order accurate in t and almost the second-order accurate in x. It is also shown that this method is better than some existing methods. Several test problems are encountered to validate the theoretical results.     

Ant colony approach to constrained redundancy optimization in binary systems

This paper presents an ant colony optimization algorithm to address the constrained redundancy allocation problem in order to maximize system reliability for complex binary systems. The constraints involved, though separable, are both linear and non-linear. We couple an adaptive penalty function with the basic ant colony approach to handle highly constrained problems and embed a local search technique to find still better locally optimal solutions. The proposed algorithm has been tested on a large number of problems, containing even up to 500 subsystems, with both fixed and randomly generated parameters. Experimental results demonstrate the advantage of the proposed algorithm to solve similar types of problems.     

Quantification of Flavonoids,Phenols and Antioxidant Potential from Dropped Citrus reticulata Blanco Fruits Influenced by Drying Techniques

Physiologically dropped immature Citrus reticulata Blanco fruits are regarded as waste and discarded in the citrus orchard but are a good source of bioactive compounds including flavonoids, antioxidants and total phenols. A study was undertaken to identify and quantify these bioactive compounds and to investigate the influence of different drying techniques, namely freeze drying and hot air oven drying, on flavonoids namely flavanone glycosides, antioxidant potential and total phenol content in immature dropped fruits of Citrus reticulata Blanco. Flavonoids were quantified in high-performance liquid chromatography (HPLC). The antioxidant activity were investigated with three assays azino-bis [3-ethylbenzthiazoline-6-sulfonic acid]) (ABTS), 2,2-diphenyl-1-picrylhydrazyl radical (DPPH), Ferric Reducing Ability of Plasma (FRAP) and total phenol content was determined. Freeze dried samples of 12 and 14 mm size retained maximum hesperidin flavonoid content (27.03% and 27.20%) as compared to the hot air dried samples (17.99%) and retained higher phenolic content ranged from 50.54–54.19 mg GAEL⁻¹. The antioxidant activity in freeze dried fruits was from 12.21–13.55 mM L⁻¹ Trolox and 15.27–16.72 mM L⁻¹ Trolox with ABTS, DPPH assay and FRAP values ranging from 7.31–9.07 mM L⁻¹ Trolox. Significant positive correlation was found between the flavonoid hesperidin with antioxidant assays and total phenolic content (TPC). The results showed that waste citrus fruits can act as potential source of bioflavonoids, especially hesperidin, and antioxidants for pharmaceutical as well as nutraceutical industry.     

Orientational order parameter estimated from molecular polarizabilities – an optical study

An optical study of N-(p-n-alkyloxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds with the alkoxy chain number n?=?1, 3, 6, 7, and 10 has been carried out by measuring the refractive indices using modified spectrometer and direct measurement of birefringence employing the Newton's rings method. Further, the molecular polarizability anisotropies are evaluated using Lippincott δ-function model, the molecular vibration method, Haller's extrapolation method, and scaling factor method. The molecular polarizabilities α _e and α ₀ are calculated using Vuk's isotropic and Neugebauer anisotropic local field models. The order parameter S is estimated by employing the molecular polarizability values determined from experimental refractive indices and density data and the polarizability anisotropy values. Further, the order parameter S is also obtained directly from the birefringence data. A comparison has been carried out among the order parameter obtained from different ways and the results are compared with the body of the data available in the literature.     

Structural and electrical properties of lanthanum-substituted lead titanate ceramics

The effect of lanthanum substitution on the structural, dielectric and piezoelectric properties of lead calcium titanate (PCT) ceramics is studied. Samples with compositional formula Pb_{0.76? x} La _x Ca_0.24Ti_0.98Mn_0.02O₃ (PLCT) (x?=?0–0.08, in steps of 0.02) were prepared by the conventional dry ceramic technique. Phase and structural analysis was carried out using XRD and SEM respectively. X-ray analysis confirmed the formation of single-phase compound with tetragonal crystal structure. Dielectric properties were studied in detail as a function of frequency and temperature. The Curie temperature (T _C) and tetragonality (c/a) was found to decrease with increase in lanthanum content. The Curie temperature was also confirmed from the thermal-expansion behaviour of the sintered samples. Piezoelectric coefficients (d ₃₃, d ₃₁, g ₃₃, g ₃₁, g _h, d _h, k _t and k _p) were measured at room temperature. From this study it is found that La³⁺ substitution helps in the improvement of electro-mechanical anisotropy.     

An analysis of phase-modulated heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance

The design of variants of the swept-frequency two-pulse phase modulation sequence for heteronuclear dipolar decoupling in solid-state NMR is reported, their performance evaluated, and compared with other established sequences like TPPM and SPINAL. Simulations performed to probe the role of the homonuclear (1)H-(1)H bath show that the robustness of the decoupling schemes improves with the size of the bath. In addition, these simulations reveal that the homonuclear (1)H-(1)H bath also leads to broad baselines at high MAS rates. Results from a study of the SPINAL decoupling scheme indicate that optimisation of the starting phase and phase increment improves its performance and efficiency at high MAS rates. Additionally, experiments performed on a liquid crystal display the role of the initial phase in SPINAL-64 and sequences in the SW(f)-TPPM family.     

Study of crystalline perfection and thermal analysis of zinc cadmium thiocyanate single crystals grown in silica gel

Zinc cadmium thiocyanate ZnCd(SCN)₄ abbreviated as ZCTC is a bimetallic thiocyanate complex that exhibits excellent nonlinear optical property. Single crystals of ZCTC have been grown in silica gel by the process of diffusion. Colorless transparent crystals of size 12 mm x 2 mm x 1.3 mm have been obtained. High resolution X‐ray diffraction study was carried out to investigate the crystalline perfection of the grown crystal and the quality of the crystal was found to be quite good. Thermal stability of the grown crystal was investigated by thermogravimetric and differential thermal analyses. Fourier Transform Infrared spectrum was recorded to confirm the functional groups. Microhardness of the crystal is also studied. Being a nonlinear optical material, a comparative study of its second harmonic generation efficiency with urea has been made. (© 2007 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pyrazole‐4‐carboxylic Acids from Vanadium‐catalyzed Chemical Transformation of Pyrazole‐4‐carbaldehydes

The conversion of aldehydes into carboxylic acids using oxidizing agents is a common protocol in transformation chemistry. An efficient oxidation strategy of transformation of pyrazole‐4‐aldehydes to the corresponding acids using vanadium catalysts in the presence of 30% H₂O₂ as an oxidant is described. The catalytic technology was successfully applied to a range of various 4‐formylpyrazoles, and plausible mechanism is also discussed.     

Synthesis of Dihydropyridine Derivatives under Eco‐friendly Approach and Investigation of Cytotoxic Activity

In an effort for development of innovative biologically active agents, a sequence of 1,4‐dihydropyridine analogues was synthesized through the green synthetic method. In addition, all compounds were evaluated for their cytotoxic activities against three human cancer cell lines and mouse melanoma and figured out the most active compounds. Besides, promoter reusability, easy handling of the chemical reagent, simple reaction process, time minimization, ethanol–water solvent compatibility, and cost reduction reagent are key tools for this fruitful path. Thus, these examinations recommended that dihydropyridine and their derivatives are motivating moieties for the discovery of new anticancer drugs.     

An alternative synthetic strategy for (3R),(5R)-5-hydroxy-de-O-methyllasiodiplodin and its epimer

A concise total synthesis of (3R),(5R)-5-hydroxy-de-O-methyllasiodiplodin and its epimer have been synthesized from commercially available (R)-propylene oxide and Orsellinic acid as starting materials. The key steps involved in the synthesis are Wittig reaction, epoxide ring opening with 1,3-dithiane intermediate and Yamaguchi macrolactonization.