Stability of multiobjective NLP problems with fuzzy parameters in the objectives and constraints functions

This paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the objectives and constraints functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first kind and of the second kind) in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of α-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding α-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.     

Structure and experimental consequences of chiral SU3 × SU3 breaking

Chiral SU₂ × SU₂ breaking, Cabibbo angle, non-electromagnetic isospin breaking, η → 3π decay rate, and pion and kaon mass differences are related to one another in a nonlinear Lagrangian model of broken chiral SU₃ × SU₃ symmetry. The agreement with experiment is very good.     

The aging effect on the dispersion of the refractive index of lithium fluoride in the wavelength range of 460–1000 nm

Transmittance measurements were carried out for LiF thin films directly after preparation, then one day, one week, four weeks and six weeks later. The aging effect on the optical properties of the film was thus studied. This showed that the aged LiF films have refractive indices larger than those of fresh films.     

Gelation and Swelling Behavior of Semi-Interpenetrating Polymer Network Hydrogels Based on Polyacrylamide and Poly(vinyl alcohol)

Novel semi-Interpenetrating Polymer Network (semi-IPN) hydrogels based on partially Hydrolyzed Polyacrylamide (HPAM) and Poly(Vinyl Alcohol) (PVA) were prepared by solution crosslinking using chromium triacetate. Effects of PVA content on the gelation process and swelling behavior in tap water and different electrolyte solutions were investigated. Study of the gelation behavior using dynamic rheometery showed that the limiting storage modulus of the semi-IPN gels decreased with increasing PVA content. It was also found that increasing the PVA content increases the loss factor, indicating that the viscous properties of this gelling system increase more strongly than the elastic properties. The swelling ratio of the semi-IPN gels in tap water decreased as the concentration of the PVA increased. However, the semi-IPN gels showed lower salt sensitivity factor in synthetic oil reservoir water as compared with HPAM gels. Therefore, they are potentially good candidates for enhanced oil recovery applications.     

On FC-Purity and I-Purity of Modules and Köthe Rings

In this article, several characterizations of certain classes of rings via FC-purity and I-purity are considered. Among others results, it is shown that every I-pure injective left R-module is projective if and only if every FC-pure projective left R-module is injective, if and only if, R is a semisimple ring. In particular, the structures of FC-pure projective and I-pure projective modules over a left Artinian ring are completely described. Also, it is shown that every left R-module is FC-pure projective if and only if every indecomposable left R-module is a finitely presented cyclic R-module, if and only if, R is a left Köthe ring. Finally, we introduce FC-pure flatness and I-pure flatness of modules and several characterizations of these notions are given. In particular, we show that a commutative ring R is quasi-Frobenius if and only if R is an Artinian ring and I-pure injective, if and only if, R is an Artinian ring and the injective envelope E(R) is an FC-pure projective R-module.     

Nil-Armendariz Rings Relative to a Monoid

For a monoid M, we introduce nil-Armendariz rings relative to M, which are a generalization of nil-Armendariz and M-Armendariz rings, and investigate their properties. First we show that semicommutative rings are nil-Armendariz relative to every unique product monoid M. Also it is shown that for a strictly totally ordered monoid M and an ideal I of R, if I is a semicommutative subrng of R and R/I nil-Armendariz relative to M, then R is nil-Armendariz relative to M. Then we show that if R is a semicommutative ring and nil-Armendariz relative to M, then R is nil-Armendariz relative to M × N, where N is a unique product monoid. As corollaries we obtain some results of [2] and [10].     

A simple route for the synthesis of novel N-alkyl-2-(alkylthio)-1H-imidazole derivatives

Novel $N$ -alkyl-2-(alkylthio)-1 $H$ -imidazole derivatives were synthesized in a single step by an efficient and simple method in high yields. Readily available starting materials, mild reaction conditions, operational simplicity and novelty are the key advantages of this method. Besides their novel structures, these compounds may have important biological activities and industrial applications.     

Chaos and reproduction in sea level

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: optimal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.