Finite Invariant Sets for a Family of Endomorphisms in Compact Graphs

We prove several results concerning the existence of common invariant finite sets of vertices or of common invariant finite connected subgraphs for some families of endomorphisms of graphs whose ends are all dominated.     

Stable graphs for a family of endomorphisms

We prove several fixed subgraph properties. In particular it is shown that if is a commuting family of contractions of a connected graph G without infinite path and infinite interval, then there exists a nonempty finite subgraph F which is invariant under any element of . In particular this subgraph F is a simplex if G is moreover a strongly dismantlable graph or a ball-Helly graph without infinite block, or if it is chordal. This implies that for any commuting family of contractions of a tree without infinite path, there is a common fixed vertex or a common fixed edge.     

A resolvent operator technique for approximate solving of generalized system mixed variational inequality and fixed point problems

The main aim of this work is to use the resolvent operator technique to find the common solutions for a generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. An example of applying the main result is also given. The results obtained in this work may be viewed as an extension, refinement and improvement of the previously known results.     

Existence and stability of iterative algorithms for the system of nonlinear quasi-mixed equilibrium problems

In this paper, we consider the system of nonlinear quasi-mixed equilibrium problems. The existence theorems of solutions of such problems are provided by considering the limit point of an iterative algorithm. This means, we not only give the conditions for the existence theorems of the presented problems but also provide the algorithm to find such solutions. Moreover, the stability of such an algorithm is also discussed. The results presented in this paper are more general, and may be viewed as an extension, refinement and improvement of the previously known results in the literature.     

Analysis of trace elements in medicinal plants with energy dispersive X-ray fluorescence

Mankind still depend on traditional herbal medicine for the treatment of various diseases and ailments. This paper discusses the elemental composition and concentration of medicinal plants investigated by energy dispersive X-ray fluorescence. The elements present in medicinal plants are P, Cl, K, Ca, S, Al, Ti, V, Rb, Sr, Zr, Nb, Mo, In, Sn, I and Ce. The physical basis of the used analytical method, the experimental set up and the procedure of sample preparation are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Existence and algorithm of solutions for general set-valued Noor variational inequalities with relaxed (μ,ν)-cocoercive operators in Hilbert spaces

The purpose of this paper is to suggest and analyze a number of iterative algorithms for solving the generalized set-valued variational inequalities in the sense of Noor in Hilbert spaces. Moreover, we show some relationships between the generalized set-valued variational inequality problem in the sense of Noor and the generalized set-valued Wiener-Hopf equations involving continuous operator. Consequently, by using the equivalence, we also establish some methods for finding the solutions of generalized set-valued Wiener-Hopf equations involving continuous operator. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory.     

Polymer-Enhanced Ultrafiltration of Fe(III) and Cu(II) Aqueous Solutions Using Poly(Vinyl Alcohol)-Alginic Acid/Cellulose Membranes

This study deals with the removal of Fe(III) and Cu(II) from dilute aqueous solutions using a polymer-enhanced ultrafiltration process. The ultrafiltration studies were carried out in batch stirred cell and the applied pressure was controlled by nitrogen gas. Properties of the composite membranes and its application in metal removal from aqueous solutions were studied. A composite poly(vinyl alcohol)-alginic acid/cellulose membranes were prepared by coating poly(vinyl alcohol)-alginic acid mixture solutions on the filter paper. Poly(vinyl alcohol) and alginic acid were also used as complexing agents to enhance the retention of metal ions. In the filtration of Fe(III) and Cu(II) solutions, the effects of membrane contents, pressure and pH on the retention and the flux were studied. The maximum retention of metals was found as 99% for Fe(III) solution at pressure of 45 psi, pH of 3 in the presence of poly(vinyl alcohol) as complexing agent by using 0.50 (w/v)% [(75 Poly(vinyl alcohol)/25 Alginic acid) (w/w)]/cellulose composite membranes.     

Netlike partial cubes, V: Completion and netlike classes

We define a completion of a netlike partial cube G by replacing each convex 2n-cycle C of G with n≥3 by an n-cube admitting C as an isometric cycle. We prove that a completion of G is a median graph if and only if G has the Median Cycle Property (MCP) (see N. Polat, Netlike partial cubes III. The Median Cycle Property, Discrete Math.). In fact any completion of a netlike partial cube having the MCP is defined by a universal property and turns out to be a minimal median graph containing G as an isometric subgraph. We show that the completions of the netlike partial cubes having the MCP preserves the principal constructions of these graphs, such as: netlike subgraphs, gated amalgams and expansions. Conversely any netlike partial cube having the MCP can be obtained from a median graph by deleting some particular maximal finite hypercubes. We also show that, given a netlike partial cube G having the MCP, the class of all netlike partial cubes having the MCP whose completions are isomorphic to those of G share different properties, such as: depth, lattice dimension, semicube graph and crossing graph.