Duality in inexact fractional programming with set-inclusive constraints

This paper extends the fractional programming problem with set-inclusive constraints studied earlier by replacing every coefficient vector in the objective function with a convex set. A dual is formulated, and well-known duality results are established. A numerical example illustrates the dual strategy to obtain the value of the initial problem.The research of the first author was conducted while he was on sabbatical at the Department of Operations Research, Stanford University, Stanford, California. The financial assistance of the International Council for Exchange of Scholars is gratefully acknowledged. The author is grateful to the Department of Operations Research at Stanford for the use of its research facilities.     

Forced Degradation Study on Gliclazide and Application of Validated Stability-Indicating HPLC-UV Method in Stability Testing of Gliclazide Tablets

Forced degradation study on gliclazide was conducted under the conditions of hydrolysis, oxidation, dry heat and photolysis and an isocratic stability-indicating HPLC-UV method was developed and validated. All the seven degradation products (I–VII) formed under different conditions were optimally resolved on a C₁₈ column with mobile phase composed of 40% acetonitrile and 60% ammonium acetate solution (0.025 M, pH 3.5) at a flow rate of 0.25 mL min^?1 using 235 nm as detection wavelength. The method was linear between 5–500 μg mL^?1 drug concentrations. The %RSD of intra- and inter-day precision studies was <1 and <2% respectively. Excellent recoveries (99.81–100.97%) proved the method sufficiently accurate. Each peak resolved always with a resolution of >1.90 indicating the method to be rugged enough. The method was used to study the drug degradation behaviour under the forced conditions. Four degradation products (I–IV) were formed in 0.1 N HCl and water whereas only I and III were formed in 3% H₂O₂. Two new products V and VI in addition to I, III and IV were formed in 0.1 N NaOH. The drug was stable to thermal and photolytic decomposition. The degradation behaviour in water and 0.1 N NaOH was similar under dark and light conditions but a new product VII was formed in 0.01 N HCl in light. In general, the rate of degradation was accelerated by the light. The method was applied successfully in stability testing of gliclazide tablets.     

Anion receptor functions of lanthanide tris(beta-diketonate) complexes: naked eye detection and ion-selective electrode determination of Cl- anion

Lanthanide tris(fluorinated beta-diketonates) acted as effective receptors of Cl- anion in luminescence sensing and ion-selective electrode systems via highly coordinated complexation.     

1D and 2D NMR studies of N-vinylcarbazole/butyl methacrylate copolymers

Copolymers containing N-vinylcarbazole (V) and butyl methacrylate (B) units of different compositions were synthesized and their compositions were determined from quantitative ¹³C{¹H} NMR spectroscopy. The reactivity ratios of the comonomers were estimated using the Kelen-Tudos and non-linear error in variable methods. The complete spectral assignment in terms of compositional and configurational sequences of the overlapping ¹H and ¹³C{¹H} spectra of the copolymers were done with the help of distortionless enhancement by polarization transfer, 2D heteronuclear single quantum correlation and total correlated spectroscopy experiments.     

Mössbauer effect studies on sodium hexa/carboxylato/ ferrates/III/

Mössbauer spectra of a series of the complexes of the type Na₃[Fe/RCOO/₆]xH₂O /R=H, CH₃, C₂H₅, C₆H₅/ has been recorded at 298±2 K. All display a quadrupole doublet with isomer shift and quadrupole splitting values in agreement with high spin iron/III/ octahedral geometry. The quadrupole splitting show an increasing trend with increasing polarizability of the substituent anion /RCOO^–/. A linear correlation between quadrupole splitting values and the /Fe–O/ stretching frequencies has also been observed.     

Gas chromatographic determination of 1,4-dioxane at low parts-per-million levels in glycols

1,4-Dioxane is a flammable liquid and tends to form explosive peroxides. Its formation in glycols (low parts-per-million levels), which are used as dehumidifying agents in refineries, may take place by condensation. 1,4-Dioxane thus formed gets distilled over with benzene in the refinery process. Therefore, it is necessary to identify and determine the levels of 1,4-dioxane in glycols as well as benzene. Gas chromatography (GC) is probably the best technique for this purpose. GC analysis may be carried out using a flame ionization detector. Results show that 1,4-dioxane can be comfortably determined down to 2 ppm in glycols and benzene.     

Synthetic Ionophores. 13. Pyridine-Diamide-Diester Receptors: Remarkable Effect of Amide Substituents on Molecular Organization and Ag(+) Selectivity

The N(Py).HN(amide) hydrogen bonding within the macrocyclic cavities in 9, 10, and 13 invokes their symmetrical electron-deficient structures ((1)H NMR) and consequently bind with water. This results in their poor ionophore characters. The steric requirement of methyl/benzyl substituents on amide N in 11 and 12 takes the substituents out of the cavity and thus positions the amide O toward the cavity ((1)H, (13)C NMR and X-ray analysis). This arrangement of two pyridine N and two amide O ((13)C NMR, IR) binding sites provides an appropriate environment for selective binding toward Ag(+) over Pb(2+), Tl(+), alkali, and alkaline earth cations. The increased spacer length in 14 leads to a lop-sided twist of pyridine rings (X-ray) and disturbs the above arrangement and leads to its poor binding character.     

Cu-assisted C–N bond formations in six-membered N-heterocycle synthesis

Abstract

One of the highly emerging and important aspect of organic chemistry is the metal-catalyzed synthesis of the heterocycles. The methodologies used earlier for its synthesis were less approachable to the organic chemist because of their high cost, highly specified instrumentation and inconvenient methods. For both the stereoselective and regioselective synthesis of six-membered nitrogen-containing heterocycles, cyclic reactions that are Cu-catalyzed have known to be very efficient. The presented review covers the varied applications of Cu as a catalyst and its importance in the formation of six-membered nitrogen-containing heterocycles. The fascinating research that has been done in this area is also enclosed in this review.     

Solid state photodecomposition of alkaline earth tris/malonato/ferrates/III/

Solid state photolysis of alkaline earth tris/malonato/ferrates/III/, i.e., M₃[Fe(CH₂C₂O₄)₃]₂.xH₂O /M=Mg, Ca, Sr, Ba/ has been investigated employing Mössbauer, infrared and reflectance spectroscopic techniques. The complexes were irradiated for 400 h using a medium pressure mercury vapour lamp of 250 Watts. Photoreduction led to the formation of M[Fe^II(CH₂C₂O₄)₂(H₂O)₂]. The extent of photoreduction showed the following order: Ca>Sr>Mg>Ba. The results have been compared with those of analogous alkaline earth tris/oxalato/ferrates/III/.     

Thermal analysis of lithium tris (malonato) ferrate(III) tetrahydrate

Thermal decomposition of lithium tris (malonato) ferrate (III) tetrahydrate i.e. Li₃[Fe(CH₂C₂O₄)₃].4H₂O has been studied in the temperature range of 353–873 K in static air atmosphere using Mössbauer, infrared spectroscopy and nonisothermal techniques (TG-DTG-DTA). The anhydrous complex decomposed into ferric oxide of varying particle sizes and alkali metal malonates/carbonates in succesive stages. Fimally a solid state reaction between -Fe₂O₃ and alkali metal carbonate gives fine particles of lithium ferrite (LiFeO₂) at a temperature lower than for oxalate precursor and for ceramic method.