The circle as an attractor of an iterated function system on the plane

We give an iterated function system (IFS) on the plane with the circle as attractor. In doing this, we also give a sufficient condition for radially contracting functions on the plane (or on Rn) to be a contraction. A counterexample shows that radial contractiveness is not enough to be a contraction.     

Derivation of Korteweg-de Vries flow equations from the regularized long-wave (RLW) equation

We perform a multiple-time scales analysis and compatibility condition to the regularized long-wave (RLW) equation. We derive Korteweg-de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation.     

A new Taylor collocation method for nonlinear Fredholm‐Volterra integro‐differential equations

The aim of this article is to present an efficient numerical procedure for solving nonlinear integro‐differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro‐differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unkown Taylor coefficients. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer program written in Maple10. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

The impact of human activity patterns on asymptomatic infectious processes in complex networks

The study of the impact of human activity patterns on network dynamics has attracted a lot of attention in recent years. However, individuals’ knowledge of their own physical states has rarely been incorporated into modeling processes. In real life, for certain infectious processes, infected agents may not have any visible or physical signs and symptoms; therefore, they may believe that they are uninfected even when they have been infected asymptomatically. This infection awareness factor is covered neither in the classical epidemic models such as SIS nor in network propagation studies. In this article, we propose a novel infectious process model that differentiates between the infection awareness states and the physical states of individuals and extend the SIS model to deal with both asymptomatic infection characteristics and human activity patterns. With regards to the latter, we focus particularly on individuals’ testing action, which is to determine whether an individual is infected by an epidemic. The simulation results show that less effort is required in controlling the disease when the transmission probability is either very small or large enough and that Poisson activity patterns are more effective than heavy-tailed patterns in controlling and eliminating asymptomatic infectious diseases due to the long-tail characteristic.     

Legendre polynomial solutions of high-order linear Fredholm integro-differential equations

In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.     

Renal-related perinephric fluid collections: MRI findings

We retrospectively reviewed MR studies on 10 patients with renal-related perinephric fluid collections who underwent MRI in three institutions between January 2001 and August 2004. All patients underwent MRI of the abdomen and T1-weighted, T2-weighted and serial contrast-enhanced images, including delayed-phase contrast-enhanced images 10-12 min after contrast injection, were obtained. Perinephric fluid collections in 5 patients revealed MRI findings of simple fluid content (i.e., hypointense on T1-weighted images and hyperintense on T2-weighted images). In another 5 patients, a complex perinephric fluid content (i.e., mixed hyper/hypointense on T1-weighted images and mixed hypo/hyperintense on T2-weighted images compatible with blood breakdown products and pus) was observed. In 5 patients, contrast extravasation on late-phase images that was compatible with urine leak was demonstrated. Our results suggest that MRI may determine the content of perinephric fluid collections on noncontrast T1-weighted and T2-weighted images and that contrast extravasation on late-phase images is associated with urine extravasation from renal collecting systems.     

On Semi-Slant $${\varvec{\xi ^\perp }}$$-Riemannian Submersions

The aim of the present paper is to define and study semi-slant \(\xi ^\perp \)-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant \(\xi ^\perp \)-Riemannian submersions, semi-invariant \(\xi ^\perp \)-Riemannian submersions and slant Riemannian submersions. We obtain characterizations, investigate the geometry of foliations which arise from the definition of this new submersion. After we investigate the geometry of foliations, we obtain necessary and sufficient condition for base manifold to be a locally product manifold and proving new conditions to be totally umbilical and totally geodesicness, respectively. Moreover, some examples of such submersions are mentioned.     

Structural characterization of disperse black 9 based Cu (II) complex and investigation of its some properties

We obtained the azo‐imine ligand (2,2′‐[4‐(5‐methoxy salicylidene‐4‐iminophenylazo)phenylimino]diethanol) (HL) and its Cu (II) complex (CuL) from the ethanol solution. The complex Cu(L)₂ was obtained as single crystals from the CH₃OH solution and structurally characterized. The electronic and photoluminescence properties of the ligand and its Cu (II) complex were investigated both in DMF solution and solid state. The oxidation and reduction behaviours of the compounds were studied in the solution and found that the redox processes are irreversible. Thermal studies show that the ligand has higher thermal stability than the CuL complex. Single crystals of the complex were obtained from slow evaporation of a DMF solution of the complex. Crystals of the complex showed a diffraction pattern; however, the structure of the complex was able to be solved.     

Corrosion prevention of mild steel in acidic medium by 2-Pyrrolidin-1-yl-1,3-thiazole-5-carboxylic acid: Theoretical and experimental approach

The inhibition efficiency of 2-Pyrrolidin-1-yl-1,3-thiazole-5-carboxylic acid (PTCA) against mild steel (MS) corrosion was investigated in acidic solution by using quantum chemical calculations based on Density Functional Theory (DFT) method and electrochemical measurements. The electrochemical impedance spectroscopy (EIS), potentiodynamic, potential zero charge (pzc) analysis and electrochemical noise (EN) measurements at various concentrations (from 0.1 to 10 mM) and immersion times were utilized in experimental part. The surface analysis was achieved scanning electron microscope (SEM) and contact angle measurements in the absence and presence of 10 mM PTCA. According to DFT results, PTCA exhibited 3.737 eV band gap and 8.130 Debye dipole moment which were a signal of potentially convenient corrosion inhibitor properties. PTCA has a remarkable corrosion inhibition capability to mild steel, which inhibited both anodic and cathodic corrosion rates, relying on it's physically adsorption on the metal solution interface and protection ability was increased with increasing PTCA concentration. The obtained adsorption equilibrium constant was 11.11 × 10³ M^-1 and calculated standard free energy of adsorption was ?33.03 kJ mol^?1. The determined activation energy values were 55.58 kJ mol^?1 and 96.86 kJ mol^?1 in 0.5 M HCl in the absence and presence of 10 mM PTCA, respectively. PTCA demonstrated a strong inhibition efficiency of 98.3%, after 168 h immersion, according to the EIS results. As a consequently, we recommend that PTCA is a convenient inhibitor in 0.1 M HCl for mild steel protection against corrosion.     

Quantification of methyldopa in pharmaceuticals using a glassy carbon electrode modified with carbon nanotubes

The quantification of methyldopa in pharmaceuticals has been carried out using a glassy carbon electrode(GCE) modified with multi-walled carbon nanotubes(MWCNTs). Methyldopa exhibited a quasi-reversible response with a peak potential separation of 473 m V on a bare GCE. However, the cyclic voltammetric behaviour of methyldopa was improved with the increase of the amount of MWCNTs. It was also shown that the electrocatalytic activity of the electrode towards the response of methyldopa was higher with larger amount of film on the surface. The results showed that the peak current was proportional to the concentration of methyldopa with a linear dynamic range of 0.005–0.388 mmol/L and a detection limit of 1.0 nmol/L was obtained using square wave voltammetry. The experimental data showed that the detection limit of methyldopa and peak separation from interfering compounds such as ascorbic acid(AA) and uric acid(UA) were improved using the proposed procedure. The method was successfully applied for the determination of methyldopa in pharmaceuticals.