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.     

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.     

Novel stereoselective control over cis vs trans opening of benzo[c]phenanthrene 3,4-diol 1,2-epoxides by the exocyclic N(2)-amino group of deoxyguanosine in the presence of hexafluoropropan-2-ol

We describe a novel and efficient synthesis (62-84% yields) of the eight possible, diastereomerically pure, cis and trans, R and S O(6)-allyl-protected N(2)-dGuo phosphoramidite building blocks derived through cis and trans opening of (+/-)-3alpha,4beta-dihydroxy-1beta,2beta-epoxy-1,2,3,4-tetrahydrobenzo[c]phenanthrene [BcPh DE-1 (1)] and (+/-)-3alpha,4beta-dihydroxy-1alpha,2alpha-epoxy-1,2,3,4-tetrahydrobenzo[c]phenanthrene [BcPh DE-2 (2)] by hexafluoropropan-2-ol (HFP)-mediated addition of O(6)-allyl-3',5'-di-O-(tert-butyldimethylsilyl)-2'-deoxyguanosine (3) at C-1 of the epoxides. Simply changing the relative amount of HFP used in the reaction mixture can achieve a wide ratio of cis/trans addition products. Thus, the observed cis/trans adduct ratio for the reaction of DE-1 (1) in the presence of 5 equiv of 3 varied from 17/83 to 91/9 over the range of 5-532 equiv of HFP. The corresponding ratios for DE-2 (2) varied from 2/98 to 61/39 under the same set of conditions. When 1 or 2 was fused with a 20-fold excess of 3 at 140 degrees C in the absence of solvent HFP, almost exclusive trans addition (>95%) was observed for the both DEs. Through the use of varying amounts of HFP in the reaction mixture as described above, each of the eight possible phosphoramidite oligonucleotide building blocks (DE-1/DE-2, cis/trans, R/S) of the BcPh DE N(2)-dGuo adducts can be prepared in an efficient fashion. To rationalize the varying cis-to-trans ratio, we propose that the addition of 3 to 1 or 2 in the absence of solvent or in the presence of small amounts of HFP proceeds primarily via an S(N)2 mechanism to produce mainly trans-opened adducts. In contrast, increasing amounts of HFP promote increased participation of an S(N)1 mechanism involving a relatively stable carbocation with two possible conformations. One of these conformations reacts with 3 to give mostly trans adduct, while the other conformation reacts with 3 to give mostly cis adduct.     

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.     

A simple molecular model for N-SmAd-NdRe-N1Re-SmA1 phase sequence in highly polar compounds

Our earlier model of re-entrant liquid crystalline phases exhibited by highly polar compounds, in which the mutual orientation of near-neighbour molecules can change from an antiparallel to a parallel configuration, has been extended to include both nematic and smectic interactions. We show that, as the McMillan parameter alpha is decreased, the SmA_d-SmA₁ line goes over to the SmA_d-N_1Re line, finally becoming the N_dRe-N_1Re transition line, the latter ending in a critical point. This sequence is in agreement with the predictions of Prost's Landau model as well as with an experimental result. The phase sequence N-SmA_d-N_dRe-N_1Re-SmA₁ is obtained on cooling for a range of alpha_A values.     

Ecofriendly synthesis and biological evaluation of 4-(4-nitro-phenyl)-2-phenyl-1,4-dihydro-benzo[4,5]imidazo[1,2-a]pyrimidine-3-carboxylic acid ethyl ester derivatives as an antitubercular agents

An ecofriendly route has been investigated for the synthesis of 4-(4-nitro-phenyl)-2-phenyl-1,4-dihydro-benzo[4,5]imidazo[1,2-a]pyrimidine-3-carboxylic acid ethyl ester derivatives by one-pot, three-component condensation of ethyl benzoylacetate, aromatic aldehydes, and 2-amino benzimidazole using 260?mol% of citric acid as reaction mediator. Citric acid is an inexpensive, nontoxic, and green medium with smoothly activates the rate of reaction. The synthesized compounds were assessed for in vitro antimycobacterial activity against Mycobacterium tuberculosis H₃₇RV strain using the microplate alamar blue assay (MABA). The results indicate that among all the synthesized compound series, P-4 and P-9 compounds illustrate effective activity with a minimum inhibitory concentration of 25?µg/ml.