Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: Application to some complicated graphs

A graph theoretical procedure for obtaining eigenvalues of linear chains and cycles having alternant vertex weights (h₁, h₂, h₁, h₂, h₁, h₂, …) and the same edge weight (k) have been developed. The eigenvalues of some complicated graphs, such as graphs of linear polyacenes, methylene‐substituted linear polyacenes and cylindrical polyacene strips, stack graphs, and reciprocal graphs have been shown to be generated in closed analytical forms by this procedure. Many such graphs represent chemically important molecules or radicals. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Conservation of a resource based fishery through optimal taxation

In the present paper, we study a dynamic reaction model in which (i) the predator is provided with an alternative food in addition to the prey species, (ii) the predator is harvested, and (iii) a tax is imposed to regulate the system. The existence of possible steady states along with their local as well as global stability is discussed for both the exploited and unexploited systems. Boundedness of the system is also discussed. It is seen that the system undergoes a Hopf bifurcation by the addition of alternative prey and the criteria for the Hopf-bifurcation is also discussed. Optimal tax policy is discussed using Pontryagin’s maximal principle. Finally, some numerical simulations are given to show the consistency with theoretical analysis.     

A facile microwave assisted synthesis of spiro-1,3-oxazines from N-(2-(cyclohex-1-en-1-yl)ethyl)amides

A mild and efficient methodology has been developed for the synthesis of spiro-1,3-oxazine derivatives by the microwave assisted cyclization of N-2-(1′-cyclohexenyl)ethyl-acetamides/benzamides. The reaction was catalyzed by in situ generated trimethylsilyl iodide and featured by its very short reaction time. The starting materials were easily obtained by the condensation of substituted acetic/benzoic acids with 2-(1′-cyclohexenyl)ethyl amine.     

Conservation of a prey-predator fishery with predator self limitation based on continuous fishing effort

The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.     

A CRITICAL STUDY ON THE INTERACTIONS OF HESPERITIN WITH HUMAN HEMOGLOBIN: FLUORESCENCE SPECTROSCOPIC AND MOLECULAR MODELING APPROACH

Hesperitin, a ubiquitous bioactive flavonoid abundant in citrus fruits is known to possess antioxidant, anti-carcinogenic, hypolipidemic, vasoprotective and other important therapeutic properties. Here we have explored the interactions of hesperitin with normal human hemoglobin (HbA), using steady state and time resolved fluorescence spectroscopy, far UV circular dicroism (CD) spectroscopy, combined with molecular modeling computations. Specific interaction of the flavonoid with HbA is confirmed from flavonoid-induced static quenching which is evident from steady state fluorescence as well as lifetime data. Both temperature dependent fluorescence measurements and molecular docking studies reveal that apart from hydrogen bonding and van der Waals interactions, electrostatic interactions also play crucial role in hesperitin-HbA interactions. Furthermore, electrostatic surface potential calculations indicate that the hesperitin binding site in HbA is intensely positive due to the presence of several lysine and histidine residues.     

Binding of the bioflavonoid robinetin with model membranes and hemoglobin: Inhibition of lipid peroxidation and protein glycosylation

Recent years have witnessed burgeoning interest in plant flavonoids as novel therapeutic drugs targeting cellular membranes and proteins. Motivated by this scenario, we explored the binding of robinetin (3,7,3′,4′,5′-pentahydroxyflavone, a bioflavonoid with remarkable ‘two color’ intrinsic fluorescence properties), with egg yolk phosphatidylcholine (EYPC) liposomes and normal human hemoglobin (HbA), using steady state and time resolved fluorescence spectroscopy. Distinctive fluorescence signatures obtained for robinetin indicate its partitioning (K_p = 8.65 × 10⁴) into the hydrophobic core of the membrane lipid bilayer. HbA–robinetin interaction was examined using both robinetin fluorescence and flavonoid-induced quenching of the protein tryptophan fluorescence. Specific interaction with HbA was confirmed from three lines of evidence: (a) bimolecular quenching constant K_q ? diffusion controlled limit; (b) closely matched values of Stern–Volmer quenching constant and binding constant; (c) τ₀/τ = 1 (where τ₀ and τ are the unquenched and quenched tryptophan fluorescence lifetimes, respectively). Absorption spectrophotometric assays reveal that robinetin inhibits EYPC membrane lipid peroxidation and HbA glycosylation with high efficiency.     

Construction and studies of a new class of reciprocal trees: interknitting of the Pascal's triangle

A method of construction of a new class of trees with reciprocal pairs of eigenvalues (λ, 1/λ) has been developed. They are derived from star graphs and can be symbolized as K _{1, n ?1} + n(p) + mK ₂ (1 ≤ m ≤ n ? 1 except for n = 1). The trees are minimally Kekulenoid and hence contain reciprocal pairs of eigenvalues in their eigenspectra. The characteristic polynomial coefficients of these trees with given values of n and m are shown to be obtainable by appropriate use of the Pascal's triangle. A general formula for this purpose has been developed. An analytical formula for the Wiener indices of such trees in terms of m and n has been derived and some consequences of this formula are presented. The relevance of these trees to real molecular structures is discussed. The trees have been shown to be useful in observing the subspectrallity of two series of IPR fullerenes of formulae C_{50+10 n} and C_{60+12 n} (n is a positive integer).     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.