Time-Cost Trade-Off Analysis in Some Constrained Assignment Problems

Several variations of two-dimensional (workers x jobs) and three-dimensional (workers x jobs x machines) time- as well as cost-minimizing assignment problems, which arise owing to (i) precedence relations of some form among the jobs or (ii) capacity restrictions on workers/machines imposed by the requirement that the surplus resources have to be fully employed, have been considered in the literature. In this paper, an algorithm is presented for time-cost trade-off analysis which is applicable to any general pair of such constrained problems. The algorithm is also illustrated by a numerical example.     

Synthesis and thermal behaviour of salicylaldimine-based liquid crystalline symmetrical dimers

A series of symmetrical dimers consisting of salicylaldimine moieties connected by flexible alkylene central spacer via ether linkages has been synthesized. In order to validate the empirical rule suggested by Date et al. to account for the smectic behaviour of such dimers, the chain length of the terminal alkoxy chain has been kept constant (C₈) while the number of methylene units in the central spacer was varied from C₃ to C₁₁. Another aim of the present investigation was to understand structure-property relationship in these dimers in which the salicylaldimine mesogenic segment has been used for the first time in dimers. The mesomorphic behaviour of these dimers was evaluated using optical microscopy and differential scanning calorimetry and the structure of some of the mesophases has been further investigated with the help of X-ray diffraction. Our studies reveal that the dimers consisting of 3 to 8 methylene units in the flexible spacer show only smectic (smectic C and smectic A) phases. For the dimers containing 4, 6 and 8 methylene units in the central spacer, a unique filament growth pattern has been observed in the smectic A phase while cooling from the isotropic phase. The dimers containing of C₉ to C₁₁ methylene groups exhibit the nematic phase in addition to smectic modifications. This observation indicates that when the terminal chains are shorter than the spacer, the tendency to form smectic phases is not fully extinguished but is perhaps reduced.     

Higher order symplectic RK and RKN methods using perturbed collocation

In this paper, we derive a one-parameter family of symplectic Runge-Kutta-Nyström methods of order 2s-1 and a two-parameter family of symplectic Runge-Kutta methods of order 2s-2.     

Synthesis and solution properties of comblike polymers from octadecyl methacrylate and acrylic acid

Amphiphilic polymers consisting of a statistical distribution of octadecyl methacrylate (ODMA) and acrylic acid in respective molar ratios of 83-22 and 17-78 mol% and in a molecular-weight range of 2.35-4.70᎒⁴ gmol^-1 have been synthesized. The series of polymers consisting of various mole fractions of ODMA and acrylic acid are expected to exhibit unique characteristics resembling ionomer to hydrophobically modified polyelectrolytes. The changes in the I₃/I₁ emission intensity ratios of pyrene, occurring in the presence of tetrahydrofuran (THF) solutions of the polymers have been taken as the main basis for inferring solution structures. The polymers are found to form random-coil to collapsed-coil/aggregated structures in THF solvent depending on the copolymer compositions. The polymer consisting of 83 mol% ODMA and 17 mol% acrylic acid behaves as an ionomer, capable of forming collapsed-coil structures at concentrations of 0.02 gml^-1 and above as shown by a very high I₃/I₁ of 1.20 (I₃/I₁ of pyrene in THF is 0.85). In contrast, the poly(octadecyl methacrylate) homopolymer and the sets of copolymers consisting of a very high proportion of acrylic acid to an extent of 73 mol% and above contribute to almost negligible or very small changes in I₃/I₁ similar to the homopolymer, poly(octadecyl methacrylate), suggesting the formation of random-coil structures.     

A transannular reaction during the base catalysed rearrangement of bicyclo(4.3.0)-2β-hydroxy-2α-vinyl-1β-Methyl-8-oxo-Δ6,7-nonene

Synthesis and rearrangement of bicyclo(4.3.0) - 2β - hydroxy - 2α - vinyl - 1β - methyl - 8 - oxo - Δ⁶ - nonene was observed to yield a transannular reaction product tricycio - (6.3.0.0^1,8) - 2 - methyl - 8α - hydroxy - 4 - oxo - Δ² - undecene 16. Spectral evidence supports the assigned structure.     

Photoactive Titania Float for Disinfection of Water; Evaluation of Cell Damage by Bioanalytical Techniques

A photoactive float was fabricated with the modified titania to cause a feasible disinfection of water, contaminated with E. coli. The commercially available titania was doped with neodymium by pulverization technique to enhance its activity in sunlight and a multiapproach technique was used to evaluate the extended efficiency of the doped sample. X‐ray diffraction patterns depicted the retention of anatase phase on doping and the existence of neodymium was confirmed by the energy dispersive atomic X‐ray analysis and the X‐ray photoelectron spectroscopy. Transmission electron microscopy and Bruner–Emmett–Teller analysis depicted a marginal increase in the particle size and a decrease in the surface area, respectively. Doping induces semiconductor behavior with lower band energy that could respond to visible light and exhibit better disinfection activity. The “f” and “d” transitions of the lanthanide in doped sample caused new electronic behavior of trapping/detrapping effect together with bandgap narrowing. The amount of malondialdehyde, protein, DNA and RNA released on destruction of E. coli was observed to be 0.915 × 10^?3 μg mL^?1, 859.912 μg mL^?1, 20.173 μg mL^?1 and 1146.073 μg mL^?1, respectively. The above analytical methods along with standard plate count method substantiated the enhanced disinfection efficiency of the doped sample in sunlight.     

Influence of Hydrogen Bond on Thermal and Phase Transitions of Binary Complex Liquid Crystals

A novel supramolecular liquid crystal (LC) is synthesized from the binary complex of 4-decyloxy benzoic acid and cholesteryl acetate. Fourier transform infrared (FTIR) spectroscopic study confirms the formation of intermolecular hydrogen bond between the mesogens. Various mesophases and corresponding textural changes in the complex are observed by comparing with its constituents through polarizing optical microscopic (POM) studies. The thermal stability factor of smectic phase for present complex is calculated. An interesting observation of present work is that investigation of extended thermal span of mesomorphic phases, decreased enthalpy, a nematic phase with a high clearing point and a low melting point. This is due to an arrangement of molecular reorientations and the development of new associations by hydrogen bonding. Optical tilt angle for smectic C phase is determined and the same is fitted to a power law.     

Biological and catalytic evaluation of Ru(II)‐p‐cymene complexes of Schiff base ligands: Impact of ligand appended moiety on photo‐induced DNA and protein cleavage,cytotoxicity and C‐H activation

Two organometallic Ru(II)‐p‐cymene complexes of the type [Ru(η⁶‐p‐cymene)(L)Cl]PF₆ 1 and 2 , where L is N,N‐bis(4‐isopropylbenzylidene)ethane‐1,2‐diamine (bien, L1 ) or N,N‐bis (pyren‐2‐ylmethylene)ethane‐1,2‐diamine (bpen, L2 ) have been prepared and characterized well. Because of appended pyrenyl groups in coordinated bpen ligand, the complex 2 exhibits higher DNA and protein binding than complex 1 in which isopropylbenzyl groups are incorporated. Interestingly, the luminescent characteristic complex 2 is unique in displaying DNA cleavage after light activation by UVA light at 365 nm through oxygen dependent mechanism. AFM analysis attests the photo‐induced DNA fragmentation ability of complex 2 . Also, the complex 2 cleaves the protein after light exposure in a non‐specific manner suggesting that it can act as a protein photo cleaving agent. In contrast to the trend of DNA and protein interaction of complexes, the complex 1 exhibits cytotoxic activity against human breast carcinoma ( MCF‐7 ) and liver carcinoma ( HepG2 ) with potency higher than that of complex 2 due to enhanced hydrophobicity of isopropyl groups present in p‐cymene and bien ligands. Indeed, complex 2 is inactive against MCF‐7 and HepG2 cancer cell lines even up to 200 μM concentration. The AO/EB staining assay reveals that the complex 1 is able to induce late apoptotic mode of cell death in breast cancer cells, which is further confirmed by inter‐nucleosomal DNA cleavage. Furthermore, the complexes 1 and 2 are evaluated for their catalytic activities and found to be working well for the β‐carboline directed C–H arylation to afford the desired products in good yield (40–47%).