Solving nonlinear ordinary differential equations using the NDM

In this research paper, we examine a novel method called the Natural Decomposition Method (NDM). We use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, we successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.     

Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation

The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments,such as the ionosphere plasma.     

Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Microscopic Spin–Orbit Potential for Proton + $${}^{9}$$ Be Scattering

Physics of Atomic Nuclei - The elastic scattering differential cross-section ( $$d\sigma/d\Omega$$ ) and the vector analyzing power ( $$A_{y}$$ ) are reanalyzed simultaneously for the $$p+^{9}$$ Be...     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

On the homotopy type of (<Emphasis Type="Italic">n</Emphasis>-1)-connected (3<Emphasis Type="Italic">n</Emphasis>+1)-dimensional free chain Lie algebra

Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ?Q, then p=∞. Denote by DGL _n ^np , n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL _n ^np . In this work we intend to answer the following two questions: Given an object (L(V), ?) in DGL _n ³ⁿ⁺² and denote by S(L(V), ?) the class of objects homotopy equivalent to (L(V), ?). How we can characterize a free dgl to belong to S(L(V), ?)? Fix an object (L(V), ?) in DGL _n ³ⁿ⁺² . How many homotopy equivalence classes of objects (L(W), δ) in DGL _n ³ⁿ⁺² such that H _* (W, d′)?H _* (V, d) are there? Note that DGL _n ³ⁿ⁺² is a subcategory of DGL _n ^np when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl.     

A glassy carbon immunoelectrode modified with vanadium oxide nanobelts for ultrasensitive voltammetric determination of the core antigen of hepatitis C virus

Microchimica Acta - The authors describe a voltammetric immunoassay for the hepatitis C virus core antigen. It is based on the use of vanadium oxide nanobelts that were used to modify a glassy...     

A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period

Nonlinear Dynamics - We investigate tunneling behavior between two bright solitons in a Bose–Einstein condensate with attractive contact interactions between atoms. The explicit tunneling...     

Determination of the transplacental transfer of paclitaxel and antipyrine by high performance liquid chromatography coupled with photodiode array detector

Ex vivo placental perfusion experiments are important in understanding the quantity and mechanisms of xenobiotic transport to the fetus during pregnancy. Our study demonstrates that paclitaxel and antipyrine concentrations in placental perfusion medium containing physiological concentrations of human serum albumin during pregnancy (30?mg/mL) can be quantified by RP-HPLC and UV detection. A liquid-liquid extraction method was developed for the quantification of paclitaxel and celecoxib (internal standard) from perfusion medium. Antipyrine, which is a necessary marker in placental perfusions for determining the validity of experiments and calculating the clearance index of xenobiotics, was also analyzed by HPLC and UV detection. Antipyrine concentrations were determined by HPLC after precipitating the perfusion medium in acetonitrile and separating the precipitated proteins by centrifugation. Concentrations were fitted to linear regressions with R² values approaching 1. Lower limits of detection for paclitaxel and antipyrine were 100?ng/mL and 200?ng/mL, respectively. Both methods demonstrated high intra-day and inter-day precision and trueness. Additionally, the use of these methods was demonstrated in a placental perfusion experiment using Taxol^® (paclitaxel dissolved in Cremophor-EL). The fetal transfer rate of Taxol was 6.6% after 1 hour.     

Synthesis,characterization, density functional theory,X‐ray study,thermal stability,and biological and MOE relevance of metal complexes of griseofulvin

Metal(II) and metal(III) coordination compounds of griseofulvin (GFV) drug were synthesized. The structure of the ligand was determined on the basis of elemental analyses, infrared and ¹H NMR spectroscopies and thermal studies. GFV behaved as a neutral tridentate chelating agent and coordinated to metal ions through three oxygen atoms: two methoxy groups and oxygen atom of furan ring. Metal complexes were characterized by means of elemental analyses and molar conductance, spectral (infrared, electron spin resonance) and thermal studies. All the complexes showed molar conductance behaviour corresponding to an electrolytic nature. All the complexes showed octahedral geometry, except [Zn(GFV)Cl]Cl that showed tetrahedral geometry. Density functional theory (DFT) calculations were employed to understand and estimate the contribution of each interaction in the formation of the assembly using several theoretical models. The computed parameters from DFT calculations for structure optimizations and vibrational frequencies were in good agreement with the experimental data. Newly synthesized metal complexes in addition to GFV were examined against opportunistic pathogens. The biological applications of complexes were studied with two Gram‐positive bacteria (Bacillus subtilis and Staphylococcus aureus) and two Gram‐negative bacteria (Escherichia coli and Neisseria gonorrhoeae) as well as their antifungal activity against Candida albicans. Results suggested that metal complexes were more biologically sensitive than free ligand. The complexes showed a moderate inhibition of MCF7 breast cancer cell line growth. Molecular docking studies further helped in understanding the mode of action of the compounds through their various interactions with the crystal structures of: human serum albumin (PDB: 5FUO), Staphylococcus aureus nucleoside (PDB: 3Q8U), human acetylcholinesterase (PDB: 1B41) and the human DNA–Topo I complex (PDB: 1SC7).