Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear systems had been established to obtain the symmetry structure, namely with 5, 6, 7, 8 and 15 dimensional Lie algebras. For those systems that arise from a scalar complex second-order ordinary differential equation, treated as a pair of real ordinary differential equations, a "reduced optimal canonical form" is obtained. This form yields three of the five equivalence classes of linearizable systems of two dimensions. We show that there exist 6, 7 and 15-dimensional algebras for these systems and illustrate our results with examples

Relationship of Anthropometric Indices of Obesity with Arterial Stiffness and Blood Pressure

To determine the comparison and relationship of anthropometric indices with blood pressure and arterial stiffness index (ASI) in normotensive, prehypertensive and hypertensive male adults.Methods: In this randomized case control study ninety male subjects between 35-55 years of age were selected with each group comprising of thirty normotensive, pre-hypertensive and hypertensive subjects. According to the World Health Organization (WHO) guidelines their height, weight, hip (HC) and waist circumferences (WC) were measured. Waist hip ratio (WHR), body mass index (BMI), conicity index (CI) and waist stature ratio (WSR) were calculated. Blood pressure (BP) was measured by mercury sphygmomanometer with auscultatory method. Photoplethysmography was done by placing velcro scrap on volar surface of middle finger and digital volume pulse (DVP) was recorded with iWorx-214 physiological interface system and ASI was calculated. Statistically, difference amongst the three groups was determined by applying one way ANOVA. Difference between the groups was analyzed by Post Hoc Tukey’s test. Pearson’s correlation coefficient was calculated to study the relationship. p-value<0.05 was considered significant.Results: There was statistically significant difference in WC (0.003), WHR (0.0001) and ASI (0.0001) between the three groups but not BMI (0.223). Amongst the anthropometric measurements, WC and WHR were positively correlated to the systolic and diastolic blood pressure.Conclusions: Central obesity is better predictor of arterial stiffening and hypertension than BMI

Ceria-Water-Reactions Studied by Liquid Cell TEM

Liquid cell TEM is demonstrated to be a highly suitable new technology to study chemical reactions of cerium oxide nanostructures in aqueous environment. Ceria nanoparticles are found to show a diversity of behaviour. At low beam intensity, particle hopping movements and particle attachment, including chain formation is observable. At high intensity, when the water is turned ultra-enriched in ions by radiolysis, we find (in order of observation) particle rounding and shrinkage, followed by complete dissolution, along with formation of new reaction phases, and finally gas bubble formation

Linearization from complex Lie point transformations

Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in $\R^{3}$ of the linearizability criteria in $\R^2$.Comment: 17 Pages, to appear in Journal of Applied Mathematics. arXiv admin note: substantial text overlap with arXiv:1104.383

Magnetic micro-swimmers propelling through bio-rheological liquid bounded within an active channel

The dynamics of a micro-organism swimming through a channel with undulating walls subject to constant transverse applied magnetic field is investigated. The micro-organism is modeled as self-propelling undulating sheet which is out of phase with the channel waves while the electrically conducting biofluid (through which micro-swimmers propel) is characterized by the non-Newtonian shear-rate dependent Carreau fluid model. Creeping flow is mobilized in the channel due to the self-propulsion of the micro-organism and the undulatory motion of narrow gapped walls. Under these conditions the conservation equations are formulated under the long wavelength and low Reynolds number assumptions. The speed of the self-propelling sheet and the rate of work done at higher values of rheological parameters are obtained by using a hybrid numerical technique (MATLAB routine bvp-4c combined with a modified Newton-Raphson method). The results are validated through an alternative hybrid numerical scheme (implicit finite difference method (FDM) in conjunction with a modified Newton-Raphson method). The assisting role of magnetic field and rheological effects of the surrounding biofluid on the swimming mode are shown graphically and interpreted at length. The global behavior of biofluid is also expounded via visualization of the streamlines in both regions (above and below the swimming sheet) for realistic micro-organism speeds. The computations reveal that optimal swimming conditions for the micro-organism (i.e., greater speed with lower energy losses) are achievable in magnetohydrodynamic (MHD) environments including magnetic field-assisted cervical treatments. Keywords: Micro-organism; peristaltic (active) channel; Carreau fluid; Swimming speed; biomagnetohydrodynamics (bioMHD); Rate of work done; Hybrid numerical method, Newton-Raphson method; Cervical magnetic therap

Effect of Cyclodextrin Derivatization on Solubility and Efficacy of Drugs

Cyclodextrins (CDs) possess cyclic structure having (α-1,4)-linked glucopyranose units making them less vulnerable to enzymatic degradation as than the linear dextrins. Commonly used natural CDs are α-CD, β-CD, and ɣ-CD with truncated cone-like appearance having lipophilic central cavity and hydrophilic exterior surface. The problem of low aqueous solubility of natural CDs can be addressed by reacting them with various reagents to produce water-soluble derivatives. CD derivatives can be categorized in many ways depending upon their substituents, biological activity, polarity, and size. The derivatization of natural CDs produces noncrystalline and amorphous forms with higher water solubility that are physically and microbiologically stable for prolonged time period. Variety of methods can be used to determine average degree of substitution for a modified CD. Dissociation by dilution is considered as major release mechanism of drugs from complex. It is essential to optimize the amount of CDs for a given preparation because they can either retard or promote drug delivery through biological membrane