A new efficient technique for solving two-point boundary value problems for integro-differential equations

In this paper, we propose a new efficient method based on a combination of Adomian decomposition method (ADM) and Green’s function for solving second-order boundary value problems (BVPs) for integro-differential equations (IDEs). The proposed method depends on constructing Green’s function before establishing the recursive scheme for the solution components. Unlike the ADM or modified ADM , the proposed method avoids solving a sequence of difficult nonlinear equations (transcendental equations) for the unknown parameters. The proposed method provides a direct recursive scheme for obtaining the series solution with easily calculable components. We also provide a sufficient condition that guarantees a unique solution to the second-order BVPs for IDEs. Convergence and error analysis of the proposed method are also discussed. Convergence analysis is reliable enough to estimate the error bound of the series solution. Some numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed approach. The numerical results reveal that the proposed method is very effective and simple.     

In Vitro Propagation and Assessment of the Genetic Fidelity of Musa acuminata (AAA) cv. Vaibalhla Derived from Immature Male Flowers

An efficient in vitro propagation method has been developed for the first time for Musa acuminata (AAA) cv. Vaibalhla, an economically important banana cultivar of Mizoram, India. Immature male flowers were used as explants. Murashige and Skoog’s (MS) medium supplemented with plant growth regulators (PGRs) were used for the regeneration process. Out of different PGR combinations, MS medium supplemented with 2 mg L^?1 6-benzylaminopurine (BAP) + 0.5 mg L^?1 α-naphthalene acetic acid (NAA) was optimal for production of white bud-like structures (WBLS). On this medium, explants produced the highest number of buds per explant (4.30). The highest percentage (77.77) and number (3.51) of shoot formation from each explants was observed in MS medium supplemented with 2 mg L^?1 kinetin + 0.5 mg L^?1 NAA. While MS medium supplemented with a combination of 2 mg L^?1 BAP + 0.5 mg L^?1 NAA showed the maximum shoot length (14.44 cm). Rooting efficiency of the shoots was highest in the MS basal medium without any PGRs. The plantlets were hardened successfully in the greenhouse with 96 % survival rate. Random amplified polymorphic DNA (RAPD) and inter-simple sequence repeat (ISSR) markers were employed to assess the genetic stability of in vitro regenerated plantlets of M. acuminata (AAA) cv. Vaibalhla. Eight RAPD and 8 ISSR primers were successfully used for the analysis from the 40 RAPD and 30 ISSR primers screened initially. The amplified products were monomorphic across all the regenerated plants and were similar to the mother plant. The present standardised protocol will find application in mass production, conservation and genetic transformation studies of this commercially important banana.     

Sodium alginate/HPMC/liquid paraffin emulsified (o/w) gel beads,by factorial design approach; and in vitro analysis

The present study involved development of a novel sodium alginate (SA)/HPMC/light liquid paraffin emulsified (o/w) gel beads containing Diclofenac sodium (DS) as an active pharmaceutical ingredient and its site specific delivery by using hard gelatin capsule fabricated by enteric coated Eudragit L-100 polymer. Emulsified gel beads were formulated by 3-level factorial design, ionic gelatin method. The obtained beads were characterized by Fourier transform infrared, X-ray diffraction and Field emission scanning electron microscope analysis. The variables such as SA (X₁), HPMC (X₂), were optimized for drug loading and in vitro drug release with the help of response surface methodology (RSM). The RSM analysis predicted that SA was significant for both drug loading (p = 0.0005) and drug release (p = 0.0041). HPMC was only significant for drug release (p = 0.0154). The cross-product contribution (2FI) and quadratic model were found to be adequate and statistically accurate with correlation value (R²) of 0.9054 and 0.9450 to predict the drug loading and drug release respectively. An increase in concentration of HPMC and SA decreases the drug loading as well as the drug release. The obtained optimum values of drug loading and DS released were 7.43 % and 85.54 % respectively, which were well in agreement with the predicted value by RSM.     

Distribution patterns of gamma radiation dose rate in the high background radiation area of Odisha,India

Journal of Radioanalytical and Nuclear Chemistry - Absorbed dose rates in air for 20 residential areas in Odisha were measured using a vehicle-mounted NaI(Tl) scintillation spectrometer. The...     

Plumbagin Alleviates Intracerebroventricular-Quinolinic Acid Induced Depression-like Behavior and Memory Deficits in Wistar Rats

Plumbagin, a hydroxy-1,4-naphthoquinone, confers neuroprotection via antioxidant and anti-inflammatory properties. The present study aimed to assess the effect of plumbagin on behavioral and memory deficits induced by intrahippocampal administration of Quinolinic acid (QA) in male Wistar rats and reveal the associated mechanisms. QA (300 nM/4 μL in Normal saline) was administered i.c.v. in the hippocampus. QA administration caused depression-like behavior (forced swim test and tail suspension tests), anxiety-like behavior (open field test and elevated plus maze), and elevated anhedonia behavior (sucrose preference test). Furthermore, oxidative–nitrosative stress (increased nitrite content and lipid peroxidation with reduction of GSH), inflammation (increased IL-1β), cholinergic dysfunction, and mitochondrial complex (I, II, and IV) dysfunction were observed in the hippocampus region of QA-treated rats as compared to normal controls. Plumbagin (10 and 20 mg/kg; p.o.) treatment for 21 days significantly ameliorated behavioral and memory deficits in QA-administered rats. Moreover, plumbagin treatment restored the GSH level and reduced the MDA and nitrite level in the hippocampus. Furthermore, QA-induced cholinergic dysfunction and mitochondrial impairment were found to be ameliorated by plumbagin treatment. In conclusion, our results suggested that plumbagin offers a neuroprotective potential that could serve as a promising pharmacological approach to mitigate neurobehavioral changes associated with neurodegeneration.     

Controlling the optical and catalytic properties of artificial metalloenzyme photocatalysts using chemogenetic engineering

Visible light photocatalysis enables a broad range of organic transformations that proceed via single electron or energy transfer. Metal polypyridyl complexes are among the most commonly employed visible light photocatalysts. The photophysical properties of these complexes have been extensively studied and can be tuned by modifying the substituents on the pyridine ligands. On the other hand, ligand modifications that enable substrate binding to control reaction selectivity remain rare. Given the exquisite control that enzymes exert over electron and energy transfer processes in nature, we envisioned that artificial metalloenzymes (ArMs) created by incorporating Ru(ii) polypyridyl complexes into a suitable protein scaffold could provide a means to control photocatalyst properties. This study describes approaches to create covalent and non-covalent ArMs from a variety of Ru(ii) polypyridyl cofactors and a prolyl oligopeptidase scaffold. A panel of ArMs with enhanced photophysical properties were engineered, and the nature of the scaffold/cofactor interactions in these systems was investigated. These ArMs provided higher yields and rates than Ru(Bpy)₃²⁺ for the reductive cyclization of dienones and the [2 + 2] photocycloaddition between C-cinnamoyl imidazole and 4-methoxystyrene, suggesting that protein scaffolds could provide a means to improve the efficiency of visible light photocatalysts.

Artificial metalloenzyme visible light photocatalysts possess enhanced optical properties and are competent towards single electron and energy transfer organic transformations.     

Nonlinear dynamics of a viscoelastic beam traveling with pulsating speed,variable axial tension under two-frequency parametric excitations and internal resonance

This paper investigates nonlinear combined parametric transverse vibrations of a traveling viscoelastic beam. The combined parametric excitations originate from the time dependency of axial velocity as well as axial tension. Two parametric excitations are enforced into the system amid the internal resonance. Two-frequency parametric resonance is assumed to be comprised of combination parametric resonance of first two modes due to the time dependency of axial velocity, and the principal parametric resonance of first mode due to the variable tension in the axial direction in the presence of internal resonance for viscoelastic beam is considered for the first time. The higher-order integro-partial differential equation of motion is solved through direct method of multiple scales. Continuation algorithm is employed to explore the stability and various bifurcations of the nonlinear dynamic system. Focus has been made to study the effect of variations of fluctuating tension component, fluctuating velocity component independently and when combined, internal and parametric frequency detuning parameters and damping on the system response. Frequency response equilibrium curves are complex and unique in shapes which are embodied with various bifurcations. Such steady-state behavior is not seen in the existent literature. With variation in fluctuating velocity component, the number of steady-state nontrivial equilibrium curves increases to three and with variation in fluctuating axial tension, they become four. In this process, significant changes in stability, number and position of various bifurcations like supercritical and subcritical pitchfork, Hopf and saddle node are observed. Unlike the previous study, the shape, stability and bifurcations of equilibrium curves under the combined effect of axial velocity and tension closely match with the case of fluctuating axial tension component. The effect of variation in internal and parametric frequency detuning parameter is more realized for second mode compared to first mode. A comparison of the present work with a previous one where axial tension is variable reveals many qualitative and quantitative similarities and dissimilarities. But when compared with earlier work where axial velocity is constant, significant dissimilarities are surfaced. The system displays a wide ranging dynamic behavior including stable periodic, quasiperiodic and unstable chaotic behavior. The numerical computation depicts various nonlinear characteristics and oscillatory behaviors which are not found so far in the existent literature.     

Energy conditions of the f(T,B) gravity dark energy model with the validity of thermodynamics

In this article, the analysis of Tsallis holographic dark energy(which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f(T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=αT~m+βB~n, made possible by the fact that the model is purely accelerating,corresponds to q=-0.54(Mamon and Das 2017 Eur. Phys.J.C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe.With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter,whereas it appears when the model is in the quintessence dominated era.     

Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non‐Abelian point group. Here, we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z‐component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half‐filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non‐Abelian point group. The C₆₀ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012