A constructive approach to cubic Hermite Fractal Interpolation Function and its constrained aspects

The theory of splines is a well studied topic, but the kinship of splines with fractals is novel. We introduce a simple explicit construction for a -cubic Hermite Fractal Interpolation Function (FIF). Under some suitable hypotheses on the original function, we establish a priori estimates (with respect to the L _p -norm, 1≤p≤∞) for the interpolation error of the -cubic Hermite FIF and its first derivative. Treating the first derivatives at the knots as free parameters, we derive suitable values for these parameters so that the resulting cubic FIF enjoys global smoothness. Consequently, our method offers an alternative to the standard moment construction of -cubic spline FIFs. Furthermore, we identify appropriate values for the scaling factors in each subinterval and the derivatives at the knots so that the graph of the resulting -cubic FIF lies within a prescribed rectangle. These parameters include, in particular, conditions for the positivity of the cubic FIF. Thus, in the current article, we initiate the study of the shape preserving aspects of fractal interpolation polynomials. We also provide numerical examples to corroborate our results.     

Impact of yttria stabilized zirconia coating on diesel engine performance and emission characteristics fuelled by lemon grass oil biofuel

Journal of Thermal Analysis and Calorimetry - The aim of present work is to improve the efficiency and reduce the harmful exhaust emissions from diesel engines. Neat lemongrass oil was selected as...     

Bimetallic Co–Ni/TiO<Subscript>2</Subscript> catalysts for selective hydrogenation of cinnamaldehyde

Bimetallic Co–Ni catalysts in the composition range Co_(1?x)Ni_x with x?=?0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1.0, with total metal loading of 15% w/w and supported on TiO₂-P25, have been prepared by chemical reduction of the metal acetates by glucose in aqueous alkaline medium and characterized by XRD, TEM, TPR, XPS and H₂-TPD techniques. Selective hydrogenation of cinnamaldhyde (CAL) to hydrocinnamaldehyde (HCAL), cinnamyl alcohol (COL) and hydrocinnamyl alcohol (HCOL) has been investigated at 20 bar pressure, in the temperature range 120–140 °C. Co/Ni crystallite sizes in the range 6.0?±?1 nm are observed by TEM. TPR and XPS results indicate the formation of nanoscale Co–Ni alloys, which tend to weaken M–H bond strength, as revealed by H₂-TPD measurements. Ni/TiO₂ displays very high conversion of CAL (86.9%) with high selectivity (78.7%) towards HCAL formation at 140 °C. Co/TiO₂, on the other hand, exhibits relatively lower CAL conversion (55%) and higher selectivity (61.3%) for COL formation at the same temperature. However, bi-metallic Co–Ni catalysts in the composition range x?=?0.3–0.6 display very high conversion (>?98%) due to alloy formation and weakening of M–H bonds. Bimetallic Co_0.7Ni_0.3 catalyst displays high conversion of CAL (98.1%) and high selectivity (82.9%) towards HCOL. Overall CAL hydrogenation activity at 140 °C, when expressed as TOF, displays a maximum value at the composition Co_0.5Ni_0.5. Activity and selectivity patterns have been rationalized based on the reaction pathways observed on the catalysts and the influence of Co–Ni alloy formation and M–H bond strength. Thus, a synergetic effect, originating from an appropriate composition of base metal catalysts and reaction conditions, could result in hydrogenation activity comparable with noble metal based catalysts.     

An approach towards the oxidation of 2-amino-4H-chromenes to 2-imino-2H-chromenes

A novel method for the synthesis of 2-imino-2H-benzo[h]chromenes via the sequential addition of N-chlorosuccinimide and triethylamine to 2-amino-4H-benzo[h]chromenes has been established. This reaction protocol represents an efficient synthetic strategy to form iminochromene derivatives under mild reaction conditions, which utilizes readily accessible aminochromenes as starting materials and tolerates a wide range of substrates.     

Phytochemical constituents from dietary plant Citrus hystrix

Chemical investigation of the fruit peel of dietary plant Citrus hystrix offered two new flavones 5,6,4′-trihydroxypyranoflavone I and 5,4′-dimethyl-6-prenylpyranoflavone XIII besides 11 known compounds. The structures of all compounds were elucidated with the aid of suitable analytical methods like 1D, 2D-NMR, mass and single crystal X-ray analysis. An X-ray crystal study of compound II was done for the first time and the compounds I–VI, XI and XII are hitherto not reported from this plant. Biological studies revealed that compound I found to have a good antidiabetic and antiacetylcholinesterase activities meanwhile compounds II, III and V showed a significant free radical scavenging ability as well as antioxidant capacity. In addition, compounds I, IV, V and VI showed cytotoxicity against U87, A549 and MCF-7 cells. Overall, the new compound I showed valuable bioactive properties. Due to insufficient quantity of compound XIII, biological studies were not done.     

Deviations from uniform power law scaling in nonstationary time series

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.     

Enhanced fluoride sorption using La(III) incorporated carboxylated chitosan beads

The carboxylated chitosan beads (CCB), which have a defluoridation capacity (DC) of 1385 mg F(-)/kg, have been further chemically modified by incorporating La(3+) ion (La-CCB) and its DC was found to be 4711 mg F(-)/kg whereas the raw chitosan beads (CB) possess only 52 mg F(-)/kg. The fluoride removal by La-CCB is governed by both adsorption and complexation mechanism. The functional groups present in beads were identified by FTIR analysis. The surface condition and existence of fluoride on the beads was confirmed by SEM with EDAX analysis. The experimental data have been analyzed using Freundlich and Langmuir isotherm models. Thermodynamic parameters such as DeltaG(o), DeltaH(o) and DeltaS(o) were calculated to predict the nature of sorption. The kinetic studies were investigated with reaction-based and diffusion-based models. A field trial was carried out with fluoride water collected from a nearby fluoride-endemic village.     

Effect of metal ion loaded in a resin towards fluoride retention

Indion FR 10 is a commercially available ion exchange resin with sulphonic acid functionality named as H⁺ form, has appreciable defluoridation capacity (DC). It has been chemically modified to La³⁺, Fe³⁺, Ce³⁺ and Zr⁴⁺ forms by incorporating respective metal ions into the resin in order to know their fluoride selectivity by measuring the DC of the respective resin. The maximum DC of these chemically modified ion exchange resins namely La³⁺, Fe³⁺, Ce³⁺ and Zr⁴⁺ forms were found to be 469.7, 467.5, 456.3 and 470.9 mg F⁻/kg respectively suggests their higher selectivity towards fluoride than H⁺ form which has the DC of only 275 mg F⁻/kg at 11 mg/L initial fluoride concentration. The higher DC of the modified resins was explained by electrostatic adsorption and complexation whereas H⁺ form retains fluoride by hydrogen bond. The functional groups present in the sorbents were identified by FTIR and the existence of fluoride onto the resins was confirmed by EDAX analysis. The experimental data was fitted with both Freundlich and Langmuir isotherms. Thermodynamic parameters such as ΔG°, ΔH° and ΔS° indicate that the nature of sorption is spontaneous and endothermic. The applicability of reaction-based and diffusion-based kinetic models was investigated. A field trial was carried out with fluoride water collected from a nearby fluoride-endemic village to test the suitability of these sorbents at field conditions.     

Free radical-mediated aryl amination: convergent two- and three-component couplings to chiral 2,3-disubstituted indolines

5-exo-trig Cyclization of an aryl radical to the nitrogen of an azomethine is used as the key annulating step in a modular preparation of 2,3-cis- and trans-disubstituted indolines. The precursors are readily prepared by phase-transfer-catalyzed Michael addition of a glycine Schiff base to a variety of acceptors. When the more reactive alkylidene malonate Michael acceptors are implemented, a one-pot three-component coupling is possible. The net result is a convergent [3 + 2] coupling strategy for the construction of highly functionalized indolines, a substructure occurring in numerous biologically active natural products.     

meso-meso-Linked corrole dimers with modified cores: synthesis, characterization, and properties

The synthesis and characterization of the first examples of core-modified corrole dimers linked through the meso positions are described. The dimers are obtained by a simple Ag(I)- or Fe(III)-catalyzed coupling reaction in near-quantitative yields. The corroles obtained are metalated with metal ions, such as Cu(II) and Ni(II). The electronic-absorption spectral studies reveal weak electronic interaction between the two subunits and the exciton coupling observed for the free-base corrole dimer (1717 cm(-1)) is lower than that for the corresponding protonated derivative (4081 cm(-1)). The solution-state structure derived from (1)H and two-dimensional NMR spectral studies reveals a noncoplanar arrangement of two corrole units. Geometry optimization at the B3LYP-631G level also confirms the noncoplanar arrangement of corroles with a dihedral angle of 64.8 degrees between two corrole planes. The electron paramagnetic resonance (EPR) and magnetic characterization studies on the paramagnetic copper-metalated dimer indicate that both copper ions behave as independent spins without any noticeable interaction. Results of fluorescence studies reveal a bathochromic shift of about 60 nm upon dimerization. The first hyperpolarizability (beta) measured by using the hyper Rayleigh scattering (HRS) method reveals doubling of the beta values on progressing from monomer to dimer, attributed to enhanced pi conjugation. The use of copper dimers in the photocleavage of DNA is also explored. It is shown that the bimetallic copper dimer selectively cleaves the nucleic acids without affecting the proteins, suggesting a possible application of the copper complex in the removal of nucleic acid contaminants from protein extracts through a simple photolytic pathway.