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.     

Sensitive and rapid spectrophotometric methods for determination of anticancer drugs

Sensitive, rapid, and simple spectrophotometric methods were developed for determination of the anticancer drugs vinblastine sulfate (VBS) and vincristine sulfate (VCS), which belong to the class of vinca alkaloids. The first method is based on the reaction of VBS and VCS with diazotized dapsone, forming yellow azo products with absorption maxima at 430 nm. The colored species obey Beer's law in the concentration range of 0.5-24 microg/mL for VBS and 0.5-12 microg/mL for VCS. The second method describes the reaction of VBS and VCS with iron(III) and subsequent reaction with ferricyanide in hydrochloric acid medium to yield blue products with absorption maxima at 750 nm. The Beer's law range for this method is 0.1-4 microg/mL for VBS and 0.5-10 microg/mL for VCS. With both methods, colored species were stable for 1 h. The methods are simple and reproducible and are applied for determination of VBS and VCS in pharmaceutical formulations. Commonly encountered pharmaceuticals added as excipients do not interfere in the analysis and the results obtained in the analysis of dosage forms agree well with the labeled contents.     

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.     

Synthesis, Characterization, and X-Ray Diffraction Analysis of Triethylenetetraammonium Tetrathiomolybdate

The reaction of gaseous H₂S with aqueous ammonium heptamolybdate in the presence of triethylenetetramine (trien) gave a red complex. The complex was recrystallized in hot water and characterized by element analysis and UV, visible, IR, and ¹H NMR spectroscopy. PMR has revealed accidental magnetic equivalence, resulting from the proximity of [MoS₄]^2- species in one complex molecule to the open triethylenetetramine ligand of another molecule. (TrienH₂)[MoS₄] crystallizes in the orthorhombic crystal system, space group Pca2₁, a=13.045(2), b=16.461(3), c=13.754(2) , =90, =90, =90°, V=2953.5(9) ³, Z=8, R₁=0.0323, wR₂=0.0730. The structure consists of the tetrahedral tetrathiomolybdate anions, forming an extended 3D framework in solids due to the interactions with triene cations via Mo-S...H-N hydrogen bonds.     

A new,sensitive, and rapid spectrophotometric method for the determination of sulfa drugs

A sensitive, rapid, and simple spectrophotometric method is described for the determination of sulfa drugs. The method is based on the formation of a red-colored product by the diazotization of sulfonamides such as sulfathiazole (SFT), sulfadiazine (SFD), sulfacetamide (SFA), sulfamethoxazole (SFMx), sulfamerazine (SFMr), sulfaguanidine (SFG), and sulfamethazine (SFMt), followed by complexation with dopamine in the presence of molybdate ions in (1 + 1) H2SO4 medium. Absorbance of the resulting red product is measured at 490-510 nm, and the product is stable for 2 days at 27 degrees C. Beer's law is obeyed in the concentration range of 0.04-8.0 microg/mL at the wavelength of maximum absorption. The method was used successfully for the determination of some sulfonamides in tablets and eye drops. Common excipients used as additives in pharmaceuticals do not interfere in the proposed method. The method offers the advantages of simplicity, rapidity, and sensitivity without the need for extraction or heating. The limits of detection and quantitation were calculated for SFT, SFD, SFA, SFMx, SFMr, SFG, and SFMt.     

Proton‐bifurcated C—H⋯(O,O) hydrogen bonds in 2,3‐dichloro‐6‐nitro­benzyl­aminium chloride

In the crystal structure of the title salt, C₇H₇Cl₂N₂O₂⁺·Cl⁻, the chloride anions participate in extensive hydrogen bonding with the aminium cations and indirectly link the mol­ecules through multiple N⁺—H⋯Cl⁻ salt bridges. There are two independent mol­ecules in the asymmetric unit, related by a pseudo‐inversion center. The direct inter­molecular coupling is established by C—H⋯O, C—H⋯Cl and C—Cl⋯Cl⁻ inter­actions. A rare three‐center (donor bifurcated) C—H⋯(O,O) hydrogen bond is observed between the methyl­ene and nitro groups, with a side‐on intra­molecular component of closed‐ring type and a head‐on inter­molecular component.