Some new extragradient iterative methods for variational inequalities

In this paper, we suggest and analyze some new extragradient iterative methods for finding the common element of the fixed points of a nonexpansive mapping and the solution set of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We also consider the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Results proved in this paper may be viewed as improvement and refinement of the previously known results.     

Modified Householder iterative method for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We show that this new two-step method is a sixth-order convergent method. Several examples are given to illustrate the efficiency of this new method and its comparison with other sixth-order methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

An improved approximation to the microstrip line capacitance

A new empirical formula is presented for the normalised capacitance of microstrip lines. The formula uses a single equation to represent the microstrip line capacitance over the useful range of the aspect ratio. The maximum error of the new formula is contained within 0.8 percent and the relative root-mean-square error is contained within 0.55 percent. The new formula can be easily implemented in computeraided design and analysis as well as in hand calculations using pocket calculators.     

Common fixed points of two maps in cone metric spaces

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.      

Unique representation domains, II

Given a star operation ∗ of finite type, we call a domain R a ∗-unique representation domain (∗-URD) if each ∗-invertible ∗-ideal of R can be uniquely expressed as a ∗-product of pairwise ∗-comaximal ideals with prime radical. When ∗ is the t-operation we call the ∗-URD simply a URD. Any unique factorization domain is a URD. Generalizing and unifying results due to Zafrullah [M. Zafrullah, On unique representation domains, J. Nat. Sci. Math. 18 (1978) 19-29] and Brewer-Heinzer [J.W. Brewer, W.J. Heinzer, On decomposing ideals into products of comaximal ideals, Comm. Algebra 30 (2002) 5999-6010], we give conditions for a ∗-ideal to be a unique ∗-product of pairwise ∗-comaximal ideals with prime radical and characterize ∗-URD’s. We show that the class of URD’s includes rings of Krull type, the generalized Krull domains introduced by El Baghdadi and weakly Matlis domains whose t-spectrum is treed. We also study when the property of being a URD extends to some classes of overrings, such as polynomial extensions, rings of fractions and rings obtained by the D+XD_S[X] construction.     

Oxovanadium(IV) complexes of non-steroidal anti-inflammatory drugs: Synthesis,spectroscopy, and antimicrobial activity

Oxovanadium(IV) complexes with four different non-steroidal anti-inflammatory drugs have been synthesized. These complexes were characterized by different analytical techniques such as CHN, IR, UV-Vis spectroscopy, and mass spectrometry. The IR data show the bidentate nature of the ligands and reveal hexacoordinate geometry in the solid state. The complexes were tested for their biological activity against six different bacterial strains and plant pathogens, and all complexes showed good biological activity with few exceptions The text was submitted by the authors in English.     

Synthesis of 1-azaxanthones by condensation of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with 3-(cyano)benzopyrylium triflates and subsequent domino ‘retro-Michael/nitrile-addition/heterocyclization’ reaction

Functionalized 1-azaxanthones (5-oxo-5H-[1]-benzopyrano[2,3-b]pyridines) were prepared by TMSOTf-mediated condensation of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with 3-cyanochromones and subsequent base-mediated domino ‘retro-Michael/nitrile-addition/heterocyclization’ reaction.