Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

Rotating flow of a third grade fluid in a porous space with Hall current

This study investigates the rotating magnetohydrodynamic (MHD) flow of a third-grade fluid in a porous space. Modified Darcy's law has been utilized for the flow modeling. The Hall effects are taken into consideration. The basic equations governing the flow are reduced to a highly nonlinear ordinary differential equation. This equation has been solved analytically by employing the homotopy analysis method (HAM). The effects of the various interesting parameters on the velocity distribution have been discussed.     

On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.     

Urease inhibition and anti-leishmanial assay of substituted benzoylguanidines and their copper(II) complexes

A series of N,N',N'-trisubstituted guanidines (1-6) and their copper(II) complexes, [κ(2)(O,N)-C(6)H(5)CONHC(NHC(6)H(4)Cl)NR](2)Cu(ii) (R = iso-propyl (1a), n-butyl (2a), sec-butyl (3a), tert-butyl (4a), benzyl (5a), and para-tolyl (6a)) were synthesized and characterized using elemental analysis, FTIR and NMR spectroscopy. DFT studies were used to assess the location of the protons in the free ligands. However, calculations have shown that, in all cases, hydrogen bonding from either N-H group gives conformations that are very similar in energy. Single crystal XRD studies were used to characterize ligands 1 and 4 and the related complexes 1a and 4a. The structures reveal that these complexes are mononuclear in the solid state and that copper adopts a regular square planar geometry. In both metallic species, the N, N', N'-trisubstituted guanidine ligands chelate the Cu(II) atom using the oxygen and one nitrogen. The synthesized compounds were investigated for urease inhibition using thiourea as a standard drug. Most complexes exhibit a better activity than the respective guanidines and compound 1a was found to be the most active with IC(50) = 9.83 ± 0.07 μM (the IC(50) for thiourea is 21.0 ± 0.1 μM). The species were also screened for their anti-leishmanial activity. However, all of the compounds were devoid of any significant activity.     

Power law fluid model for blood flow through a tapered artery with a stenosis

In the present paper, blood flow through a tapered artery with a stenosis is analyzed, assuming the flow is steady and blood is treated as non-Newtonian power law fluid model. Exact solution has been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Some special cases of the problem are also presented.     

微极流体在两个伸展平面之间的不稳定轴对称MHD流动

研究在两个径向伸展的平面之间,微极流体作随时间变化的磁流体动力学(MHD)流动.考虑了高浓度微元(n=0)和低浓度微元(n=0.5)两种情况.使用恰当的变换,将偏微分方程转换为常微分方程.用同伦分析法(HAM),对变换后的方程求解.给出不同参数下,角速度、表面摩擦因数和面应力偶系数的图形结果.     

Structure and dynamics of highly PEG-ylated sterically stabilized micelles in aqueous media

Molecular assemblies of highly PEG-ylated phospholipids are important in many biomedical applications. We have studied sterically stabilized micelles (SSMs) of self-assembled DSPE–PEG2000 in pure water and isotonic HEPES-buffered saline solution. The observed SSM sizes of 2–15 nm largely depend on the solvent and the lipid concentration used. The critical micelle concentration of DSPE–PEG2000 is 10 times higher in water than in buffer, and the viscosity of the dispersion dramatically increases with the lipid concentration. To explain the experimentally observed results, we performed atomistic molecular dynamics simulations of solvated SSMs. Our modeling revealed that the observed assemblies have very different aggregation numbers (N(agg) ≈ 90 in saline solution and N(agg) < 8 in water) because of very different screening of their charged PO4(–) groups. We also demonstrate that the micelle cores can inflate and their coronas can fluctuate strongly, thus allowing storage and delivery of molecules with different chemistries.     

Development of an efficient protein phosphatase-based colorimetric test for okadaic acid detection

Okadaic acid (OA), responsible for gastrointestinal problems, inhibits protein phosphatase 2A (PP2A). Therefore, the inhibition exerted by the toxin on PP2A could be used to detect the presence of OA in aqueous solution and in shellfish sample.In this work, two commercial PP2As (from ZEU Immunotec and Millipore) and one produced by molecular engineering (from GTP Technology) were tested. Enzymes were used in solution and also immobilized within a polymeric gel. In solution, best performances were obtained using PP2A purchased from ZEU Immunotec (Spain). OA was detected in aqueous solution in concentration as low as 0.0124 μg L⁻¹ using the enzyme from ZEU Immunotec whereas the detection limits were 0.47 μg L⁻¹ and 0.123 μg L⁻¹ with PP2As from Millipore and GTP Technology, respectively. Considering that the immobilization step contributes to stabilize the PP2A activity, enzymes were entrapped within a photopolymer and an agarose gel. These different polymeric matrices were optimized, tested and compared. Agarose gel seems to be a good alternative to the photopolymer largely used in our group. For instance, the IC₅₀ value obtained with the test based on PP2A from ZEU Immunotec immobilized within an agarose gel was 1.98 μg L⁻¹. This value was 1.8-fold lower than those obtained with the photopolymer test using the same enzyme. The proposed test is sensitive, fast and does not require expensive equipment. To evaluate the efficiency of the assay, PP inhibition tests based on PP2A from ZEU Immunotec in solution or immobilized within a gel were used for OA detection in contaminated shellfish.     

Poiseuille Flow of a Third Grade Fluid in a Porous Medium

Effects of porous medium have been investigated on the steady flow of a third grade fluid between two stationary porous plates. The continuity and momentum equations along with modified Darcy??s law are used for the development of mathematical problem. The governing nonlinear problem is solved by a homotopy analysis method. The dimensionless velocity and shear stresses at the plates are analyzed.     

Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

This article studies the three-dimensional boundary layer flow of an elasticoviscous fluid over a stretching surface. Velocity of the stretching sheet is assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction is further considered. Computations are made by the homptopy analysis method (HAM). Convergence of the obtained series solutions is explicitly analyzed. Variations of embedding parameters on the velocity and concentration are graphically discussed. Numerical computations of surface mass transfer are reported. Comparison of the present results with the numerical solutions is also given.