Solving of second order nonlinear PDE problems by using artificial controls with controlled error

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region inR ². We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error inL ₁ is controlled.     

HPLC and GC Methods for Determination of Lubricants and Their Evaluation in Analysis of Real Samples of Polyethylene

High performance liquid chromatography (HPLC) and gas chromatography (GC) are introduced for analysis of polymer lubricants (stearamide, oleamide and erucamide). In the HPLC method, a reverse phase octadecylsilane (ODS) column along with acetonitrile/methanol (60:40) as a mobile phase were used. Detection of analytes was performed by a UV detector at 202 nm. The analysis time was less than 8 min. In the GC method, polar capillary column and flame ionization detector (FID) were used for separations and detection, respectively. The analysis time by GC was longer than HPLC and was about 30 min. Limits of detection, linear range and repeatability of both methods are similar, but determination of oleamide in real samples by HPLC method is difficult due to complexity of the initial part of HPLC chromatogram in polyethylene samples. That problem is not observed in the GC method. Detection limits in both methods for all analytes are lower than 0.003% which are much lower than the amount of lubricants in commercial polymers (0.05–0.2%).     

Adsorption Studies of Radionuclides and Toxic Metal Ions on a Modified Mesoporous Lanthanum(III) Silicate

A new adsorbent, modified mesoporous lanthanum(III) silicate, has been prepared with various molar ratios of Si/La (10, 20, 40, 80) and cethyltrimethylammonium bromide (CTAB) as structure directing agent. XRD, nitrogen sorption, SEM, IR, thermogravimetry and sorption of radionuclides and toxic metal ions have been studied. The results show that adsorption amount of some element such as Pb(II) and Th(IV) has been increased significantly by incorporation of lanthanum ions in the framework of adsorbent. Separation of Co(II)‐Th(IV), Co(II)‐U(VI) and Mo(VI)‐U(VI) has been developed on columns of this adsorbent.     

Description of Closed Maximal Ideals in Topological Algebras of Continuous Vector-Valued Functions

Let X be a completely regular Hausdorff space, A be a unital locally convex algebra with jointly continuous multiplication and C(X,A) be the algebra of all continuous A-valued functions on X equipped with the topology of \({\mathcal{K}(X)}\) -convergence. Moreover, let \({\mathfrak{M}_{\ell}(A)}\) and \({\mathfrak{M}(A)}\) denote the set of all closed maximal left and two-sided ideals in A, respectively. In this note, we describe all closed maximal left and two-sided ideals in C(X,A) and show that there exist bijections from \({\mathfrak{M}_{\ell}(C(X, A))}\) onto \({X \times \mathfrak{M}_{\ell}(A)}\) and \({\mathfrak{M}(C(X, A))}\) onto \({X \times \mathfrak{M}(A)}\) . We also present new characterizations of closed maximal ideals in C(X, A) when A is a unital commutative locally convex Gelfand–Mazur algebra with jointly continuous multiplication.     

PQWs in complex plane: Application to Fredholm integral equations

In this paper, we use a numerical procedure for solving Fredholm integral equations of the second kind in complex plane. The periodic quasi-wavelets (PQWs) constructed on [0,2π]$[0\text{,}2\pi ]$ are utilized as a basis in collocation method to reduce the solution of linear integral equations to a system of algebraic equations. Convergence analysis is derived and we used some numerical examples to illustrate the accuracy and the implementation of the method.     

Guanidine Hydrochloride: A Highly Efficient Organocatalyst for the Synthesis of 12‐Aryl‐8,9,10,12‐tetrahydrobenzo[a]xanthene‐11‐ones Under Solvent‐Free Conditions

A new green protocol has been developed for the synthesis of 12‐aryl‐8,9,10,12‐tetrahydrobenzo[a]xanthen‐11‐ones using guanidine hydrochloride as an organocatalyst under solvent‐free conditions. Operational simplicity, mild reaction conditions, enhanced rates, high isolated yields of the pure products, and purification of products by nonchromatographic methods are significant advantages of the protocol presented here.     

Voltammetric sensor for simultaneous determination of ascorbic acid,acetaminophen, and tryptophan in pharmaceutical products

A novel carbon paste electrode modified with carbon nanotubes and 5-amino-2′-ethyl -biphenyl-2-ol was fabricated. The electrochemical study of the modified electrode, as well as its efficiency for electrocatalytic oxidation of ascorbic acid (AA), is described. The electrode was employed to study the electrocatalytic oxidation of AA, using cyclic voltammetry, chronoamperometry, and square-wave voltammetry (SWV) as diagnostic techniques. It has been found that the oxidation of AA at the surface of modified electrode occurs at a potential of about 250 mV less positive than that of an unmodified carbon paste electrode. SWV exhibits a linear dynamic range from 2.0?×?10^?7 to 5.0?×?10^?4 M and a detection limit of 1.0?×?10^?7 M for AA. In addition, this modified electrode was used for simultaneous determination of AA, acetaminophen (AC), and tryptophan (TRP). Finally, the modified electrode was used for determination of AA, AC, and TRP in pharmaceutical products.     

Existence,uniqueness and stability of solutions for a class of nonlinear integral equations under generalized Lipschitz condition

In this paper, we prove the existence, uniqueness and the stability of solutions for some nonlinear functional-integral equations by using generalized Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aims in Banach space X:= C([a, b],R). As application we study some Volterra integral equations with linear, nonlinear and singular kernel.     

A new approach for solving the Stokes problem

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate the velocity functions by piecewise linear functions. Then, the approximate values of pressure are obtained by a finite difference scheme.     

Purification of L-Lysine in Simulated Moving Bed and Fixed-Bed Chromatography

 L-Lysine was produced by a microbial process utilizing a Corynebacterium glutamicum (ATCC 21799) strain. L-Lysine was purified from the cultivated medium by fixed-bed and simulated moving bed （SMB） chromatography. The separation conditions including pH, eluent concentration and Lys+ and Lys2+ adsorption isotherms were studied in batch adsorption. The column capacity, eluent flow rate and eluent concentration have been studied in fixed-bed chromatography. Maximum purification rate of lysine was obtained as 0.066 g/(g·h) (per gram resin and per hour) at an eluent flow rate of 10 mL/min in fixed-bed chromatography. The results obtained from SMB were 0.11 g/(g·h) for L-lysine purification rate and 96% for L-lysine recovery.