A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions

In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii’s fixed point theorem and Banach contraction principle.     

Iodine-catalyzed chemoselective dehydrogenation and aromatization of tetrahydro-β-carbolines: A short synthesis of Kumujian-C,Eudistomin-U,Norharmane, Harmane Harmalan and Isoeudistomine-M

Temperature controlled chemoselective dehydrogenation and aromatization of tetrahydro-β-carbolines, using molecular I₂ and H₂O₂, in DMSO solvent affords a practical access to a series of corresponding 3,4-dihydro-β-carbolines and β-carbolines respectively. This method has been successfully employed in the short synthesis of Kumujian-C, Eudistomin-U, Norharmane Harmane Harmalan and Isoeudistomin-M.     

A concise enantioselective synthesis of (+)-febrifugine

A short enantioselective synthesis of (+)-febrifugine, a potent antimalarial alkaloid, has been described based on the regioselective asymmetric dihydroxylation of a 1,4-dienic ester as the key step. The strategy also involves chemoselective [3,3]-sigmatropic rearrangement of 1,5-hexadiene-3-ol and intramolecular lactamization of azidolactone for the construction of piperidine core.     

Synthesis and Cation Recognition Study of Novel Benzo Crown Ether Functionalized Enamine Derivatives

A novel series of benzo crown ether (dibenzo 18-crown-6 ether, benzo 18-crown-6 ether, and benzo 15-crown-5 ether) functionalized enamines derivatives from amino benzo crown ether (4-amino dibenzo 18-crown-6 ether, 4-amino benzo 18-crown-6 ether, 4-amino benzo 15-crown-5 ether) and substituted 3-(dimethylamino)-1-phenylprop-2-en-1-one compounds have been synthesized. All the synthesized compounds were characterized by infrared, ¹H NMR, ¹³C NMR, distortionless enhancement polarization transfer, and mass and elemental analysis techniques. The cation recognition property for benzo crown ether enamine 8a was studied by absorption and fluorescence spectroscopy.     

Force constants from intensity analysis of molecules CH3Cl and CD3Cl

The secular equation (GF - Eλ)L = 0 contains more force constants than can be calculated from the equations formulated using the frequencies. For a 3 × 3 matrix, there are 6 force constants but only 3 frequencies. Attempts were made by others to estimate all the 6 constants to satisfy the frequencies and Coriolis constants and rotation distortion constants. However, many attempts are not made in these estimations to satisfy the intensities. A full complement of equations is derived to evaluate all the force constants combining the intensity equationsI =L’A withLL’ =G and evaluated the force constants ofA ₁ species of CH₃Cl and CD₃Cl. A simple analysis of a 2 × 2 matrix shows thatF ₁₂/F ₂₂=G ₁₂ ⁻¹ /G ₂₂ ⁻¹ as reported earlier.     

Biodecolorization of Azo Dye Remazol Orange by Pseudomonas aeruginosa BCH and Toxicity (Oxidative Stress) Reduction in Allium cepa Root Cells

In this report a textile azo dye Remazol orange was degraded and detoxified by bacterium Pseudomonas aeruginosa BCH in plain distilled water. This bacterial decolorization performance was found to be pH and temperature dependent with maximum decolorization observed at pH 8 and temperature 30 °C. Bacterium tolerated higher dye concentrations up to 400 mg?l^?1. Effect of initial cell mass showed that higher cell mass concentration can accelerate decolorization process with maximum of 92 % decolorization observed at 2.5 g?l^?1 cell mass within 6.5 h. Effect of various metal ions showed Mn has inducing effect whereas Zn strongly inhibited the decolorization process at 5 mM concentration. Analysis of biodegradation products carried out with UV–vis spectroscopy, HPTLC and FTIR confirmed the decolorization and degradation of Remazol orange. Possible route for the degradation of dye was proposed based on GC-MS analysis. During toxicological scrutiny in Allium cepa root cells, induction in the activities of superoxide dismutase (SOD), guaiacol peroxidase (GPX) and inhibition of catalase (CAT) along with raised levels of lipid peroxidation and protein oxidation in dye treated samples were detected which conclusively indicated the generation of oxidative stress. Less toxic nature of the dye degraded products was observed after bacterial treatment.     

On modelling payments in projects

Projects are often evaluated on financial performance. The net present value (NPV) has long been established as a highly relevant criterion in the management and control of projects. Research in this area has emphasised scheduling of activities in projects to maximise the contractor's NPV assuming that cash flows (both positive and negative) that occur over the duration of the project are known. In practice, however, the contractor usually knows the expenses associated with project activities. He can use this information combined with the knowledge of other project parameters such as activity durations to negotiate the payments received for completed work so that the project achieves the maximum level of financial returns. Extending previous research, this paper examines the problem of simultaneously determining the amount, location and timing of progress payments. We present several models and their solutions for an example problem. Based on the assumptions made, the models are applicable in different project environments. The problem and models presented here can be used by the contractor and client for managing cash flows, setting milestones, and negotiating critical contract parameters, in addition to identifying the location, timing, and amount of progress payments. They also contribute to the body of research on formulating and solving difficult combinatorial optimisation problems.     

Synthesis of Novel 4‐Substituted Coumarins,Docking Studies,and DHODH Inhibitory Activity

Coumarins are the important class of naturally occurring heterocyclic compounds. Activities like antioxidant, antibacterial, anti‐inflammatory, and anticancer have been reported for coumarin derivatives. Present work details the synthesis of substituted coumarin‐4‐pyrrolones as well as coumarin‐4‐acetyl amino acids and their DHODH inhibitory activity, which is a dual target for malaria and cancer. Coumarin‐4‐acetic acids ( 2a – c ) were coupled with different methyl esters of α‐amino acids ( 3 ) giving rise to corresponding coumarin‐4‐acetyl amino acid methyl esters ( 4a – o ), which on hydrolysis under basic condition underwent cyclization forming substituted dihydropyrrole‐2‐ones ( 5a – i ), dihydroindolizine‐3‐ones ( 5j – l ), and dihydropyrrolizin‐3‐one ( 5m – o ). Acidic hydrolysis of the compounds ( 4a – o ) yielded corresponding coumarin‐4‐acetyl amino acids ( 6a – f ). The docking study was performed with the protein 4IGH (obtained from PDB) using Surflex–Dock module. The newly synthesized compounds were tested for DHODH inhibitory activity using Brequinar as the standard. Compound 6b showed remarkable inhibition compared with the standard, and the other compounds with terminal COOH showed moderate inhibition.     

Polymer‐Supported Sulfonic Acid‐Catalyzed Candid Synthesis and Photophysical Properties of 2H‐indazolo[2,1‐b]phthalazinetriones

Polystyrene‐supported sulfonic acid has been found to be an efficient catalyst for the one‐pot, three‐component synthesis of 2H‐indazolo[2,1‐b]phthalazinetriones in greener solvent glycerol. Use of greener solvent glycerol along with a polymer‐supported, low toxic, and inexpensive catalyst renders the method eco‐friendly. High yields, simple product isolation procedure, and fluorescent and electroluminescent natures of the products are the noteworthy aspects of this protocol.