A closed form type reduction method for piecewise linear interval type-2 fuzzy sets

In this study, a new centroid type reduction method is proposed for piecewise linear interval type-2 fuzzy sets based on geometrical approach. The main idea behind the proposed method relies on the assumption that the part of footprint of uncertainty (FOU) of an interval type-2 fuzzy set (IT2FS) has a constant width where the centroid is searched. This constant width assumption provides a way to calculate the centroid of an IT2FS in closed form by using derivative based optimization without any need of iterations. When the related part of FOU is originally constant width, the proposed method finds the accurate centroid of an IT2FS; otherwise, an enhancement can be performed in the algorithm in order to minimize the error between the accurate and the calculated centroids. Moreover, only analytical formulas are used in the proposed method utilizing geometry. This eliminates the need of using discretization of an IT2FS for the type reduction process which in return naturally improves the accuracy and the computation time. The proposed method is compared with Enhanced Karnik–Mendel Iterative Procedure (EKMIP) in terms of the accuracy and the computation time on seven test fuzzy sets. The results show that the proposed method provides more accurate results with shorter computation time than EKMIP.     

Reactivity of mixed organozinc and organocopper reagents. 3. Atom economic electrophilic amination of methyl arylzinc reagents

Reaction of methyl arylzincs with acetone O‐(mesitylenesulfonyl)oxime in THF in the presence of CuCN at room temperature is efficient in selective electrophilic amination of aryl carbanions. This procedure allows for the preparation of arylamines in moderate to good yields and provides an efficient and atom economic alternative to existing amination methods for diarylzincs. Copyright © 2009 John Wiley & Sons, Ltd.     

High Performance Liquid Chromatography for the Determination of Metoclopramide in Pharmaceutical Preparations Using Pre‐column Derivatization with Fluorescamine

A simple, rapid and sensitive high performance liquid chromatography (HPLC) method was developed for the determination of metoclopramide in pharmaceutical preparation. The method is based on the derivatization of metoclopramide with fluorescamine. The separation was achieved on a C₁₈ column using methanol‐water (70:30, V/V) mobile phase. Fluorescence detector was used at the excitation and emission of 403 and 485 nm, respectively. The method was validated for linearity, limit of detection, limit of quantification, precision, accuracy, recovery, robustness and system suitability. The assay was linear over the concentration range of 100–2000 ng/mL. The mean recovery was 100.37%. The proposed method was successfully applied to the assay of metoclopramide in tablet preparation. The preparation was also analyzed with an official method and statistical comparison by t‐ and F‐tests revealed that there was no significant difference between the results of the two methods with respect to mean values and standard deviations at the 95% confidence level.     

Analytical Study of Pair Production Rate from Vacuum in an Elliptic Polarized Field by a Two-Level Transition Technique

Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated.By applying the technique of two level transition amplitude,a routine for obtaining pair production rate is presented,and approximate analytical expressions are given both for the low frequency strong field regime and the high frequency weak field regime.We found that for an elliptically polarized field,the electron-positron pair production rate decrease when the elliptic eccentricity increase in the high frequency weak field regime,however,in the low frequency strong field regime,there is almost the same electron-positron pair production rate as in the constant electric field case.     

Refraction-based photonic crystal diode

A system composed of air holes in a dielectric host to form two square photonic crystals, with the same orientation and lattice constant but different scatterer radii, making an interface along their body diagonals, is numerically demonstrated to facilitate unidirectional light transmission. Band structure computations are carried out via the plane wave expansion method, whereas finite-difference time-domain simulations are carried out to investigate the transient behavior. Unidirectional light transmission is achieved over two adjacent stop bands along the ΓX direction, which are circumvented in the forward direction by scaling down the wave vector and rotating the surface normal. Contrast ratios as high as 0.9 are attained within the lower stop band.     

A rapid and highly sensitive spectrofluorimetric method for the determination of venlafaxine by charge transfer complexation reaction with <Emphasis Type="Italic">p</Emphasis>-bromanil and <Emphasis Type="Italic">p</Emphasis>-chloranil

Simple, rapid and highly sensitive spectrofluorimetric methods were developed for the determination of venlafaxine in pure and pharmaceutical preparations. The proposed methods were based on the reaction of venlafaxine as n-electron donor with π-acceptors namely, p-bromanil and p-chloranil. The method for the determination of venlafaxine over a concentration range of 5–100 and 5–150 ng/mL, for p-bromanil and p-chloranil methods, respectively. The intra- and inter-day precisions were satisfactory, the relative standard deviations did not exceed 1.69%. The proposed method was successfully applied to the determination of venlafaxine in its pharmaceutical preparations with good accuracy; the mean recovery percentages were 99.80%. The results were compared favorably with those of the reference method.     

Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Probabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: \(n \times n^{j+1}\) matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a Hénon–Heiles system is provided.     

Compactly uniform Bochner integrability of random elements

As the concept of uniform integrability has an essential role in the convergence of moments and martingales in the probability theory it is important to study this concept. In the present paper using Bochner integral we define a new type of uniform integrability for sequences of random elements. We give some independent necessary and sufficient conditions for this concept. We also generalize the concepts of strong and statistical convergences to sequences of random elements and we obtain the relationship between these two important concepts of summability theory via this new type of uniform integrability.