Averaging Oscillations with Small Fractional Damping and Delayed Terms

We demonstrate the method of averaging for conservative oscillators which may be strongly nonlinear, under small perturbations including delayed and/or fractional derivative terms. The unperturbed systems studied here include a harmonic oscillator, a strongly nonlinear oscillator with a cubic nonlinearity, as well as one with a nonanalytic nonlinearity. For the latter two cases, we use an approximate realization of the asymptotic method of averaging, based on harmonic balance. The averaged dynamics closely match the full numerical solutions in all cases, verifying the validity of the averaging procedure as well as the harmonic balance approximations therein. Moreover, interesting dynamics is uncovered in the strongly nonlinear case with small delayed terms, where arbitrarily many stable and unstable limit cycles can coexist, and infinitely many simultaneous saddle-node bifurcations can occur.     

Current advances in molecularly imprinted polymers and their release mechanisms in drug delivery systems

Molecularly imprinted polymer (MIP) has gained wide interest among researchers due to its unique molecular recognition of the template that is suitable as a drug carrier. Therefore, the preparation and formulation of the MIP are significant to suit the needs of the intended use. Due to its significance in drug delivery, this review aims to highlight various methods in the preparation of MIP, the composition for both controlled and stimuli-responsive drug delivery systems, and the release mechanism of the drugs. In drug delivery systems, MIP should have a sustained release performance as well as flexibility in surface modification for targeted delivery via a range of stimuli-responses, including  external stimuli (magnetic, light) and internal stimuli (pH, temperature, redox, biological). The properties of sustained release and targeted delivery of the MIP can improve the drug's therapeutic efficacy as well as the breakthrough for the tumor targeting application.     

A comparative study on the control of friction-driven oscillations by time-delayed feedback

We perform a detailed study of two linear time-delayed feedback laws for control of friction-driven oscillations. Our comparative study also includes two different mathematical models for the nonlinear dependence of frictional forces on sliding speed. Linear analysis gives stability boundaries in the plane of control parameters. The equilibrium loses stability via a Hopf bifurcation. Dynamics near the bifurcation is studied using the method of multiple scales (MMS). The bifurcation is supercritical for one frictional force model and subcritical for the other, pointing to complications in the true nature of the bifurcation for friction-driven oscillations. The MMS results match very well with numerical solutions. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control effectiveness.     

Ascorbic acid as a new reductant in the thiocyanate method for the spectrophotometric determination of rhenium

Summary A spectrophotometric determination of rhenium is based on its reduction with ascorbic acid in the presence of thiocyanate. The orange-yellow complex is extracted into isoamyl alcohol and the absorbance measured at 430 nm. Various foreign ions do not interfere. Molar absorptivity and Sandell's sensitivity are 31162.79 l/mol/cm and 0.0059 g/cm², respectively.     

Approximations for period-1 rotation of vertically and horizontally excited parametric pendulum

Nonlinear Dynamics - We obtain analytical approximations for period-1 rotations of both vertically and horizontally excited pendulum using Galerkin projections with elliptic functions (GP),...     

Ca<Superscript>+2</Superscript> Concentrations are Key Determinants of Ischemia–Reperfusion-Induced Apoptosis: Significance for the Molecular Mechanism of Bcl-2 Action

The mechanism of action of the anti-apoptotic oncogene Bcl-2 and Ca⁺² regulation in ischemia–reperfusion injury is still obscure. In this present study, we investigated mitochondrial Ca⁺² overloads and mechanism of action of Bcl-2. Eighteen Wistar rats were divided into sham-operated control group (I) (n = 6), ischemia and reperfusion group (II) (n = 6), and amlodipine-treated group (1 mg kg⁻¹ body weight/daily by oral route for 7 days before inducing ischemia–reperfusion maneuver) (III) (n = 6). Rats were subjected to 1 h of hepatic ischemia followed by 3-h reperfusion. Mitochondrial Ca²⁺ content was determined and damage was confirmed by transmission electron microscopy. Decrease of mitochondrial Ca⁺² level is related to reduction of apoptosis and cellular changes, viz. increased Bcl-2 expression followed by reduction in secondary endoplasmic reticulum, whereas ischemia/reperfusion group shows overloading Ca⁺² ions and decrease in Bcl-2 expression as compared to sham-operated rats. Thus, Bcl-2-dependent reduction of Ca⁺² is an important component of the anti-apoptotic program in ischemia–reperfusion injury.     

Mode-locking and improved harmonicity for real strings vibrating in the presence of a curved obstacle

Nonlinear Dynamics - We explore the dominant mechanism leading to mode-locking in real strings used in plucked stringed instruments like sitar and veena which are reported to have large number of...