Vol. 43 No. 1 (2011)

Let G be a connected graph and c a proper coloring of G. For i Æ’­1,2,Æ’»,k define the color class i C as the set of vertices receiving color i. The color code c (v) "ž¨ of a vertex v in G is the ordered k -tuple 1 ( (, ),, (, )) k d v C Æ’» d v C where (, ) i d v C is the distance of v to i C. If all distinct vertices of G have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number of graph G, denoted by ( ) L ƒÓ G is the smallest k such that G has a locating coloring with k colors. In this paper we discuss the locating-chromatic number of…

A finite set n X ⊆ ℝn with a weight function w: X → ℝ > 0 is called Euclidean t-design in ℝ > 0 (supported by p concentric spheres) if the following condition holds:           1 i p i i i S x X w X f d w f S      x x  x x for any polynomial f(x) ∈ Polℝ > 0 of degree at most t. Here Si ℝn is a sphere of radius ri ≥ 0, Xi=X ∩ S, and σi(x) is an O(n) -invariant measure on Si such that |Si|=rin-1|Sn-1>|, with |Si| is the surface area of Si and |Sn-1|is a surface area of the unit sphere in ℝn. Recently, Bajnok [1]…

Quinine is a natural alkaloid having a methoxy group bound to quinoline ring and an allyl group bound to quinuclidine ring. Demethylation of quinine applying strong acid such as HBr or HI at high temperature was unsuccessful. The aim of this research was to obtain demethylated quinine by means of mild and selective demethylation procedure to prevent the addition reaction of allyl group. Selective demethylation of quinine has been carried out using anhydrous aluminium trichloride as reagent. The demethylation product was achieved in 68.12% yield by mole ratio of quinine to anhydrous aluminium…

This paper is devoted to study the existence and uniqueness of solutions to nonlinear difference Φ-Laplacian boundary value problems with mixed and Dirichlet boundary conditions.

Hierarchically porous MFI zeolites (ZSM-5) have been synthesized by hydrothermal treatment in the presence of trialkoxysilylated-derivatives of nonionic poly(oxyethylene) alkyl ether or alkyl quaternary ammonium cation as mesopore-generating agent, along with tetrapropylammonium cation as zeolite structure-directing agent. Powder X-ray diffraction revealed that zeolites have been crystallized, and scanning electron microscopy showed rugged surface morphology that was quite different from conventional ZSM-5. The mesoporosity was confirmed by nitrogen adsorption-desorption measurement showing…

Zirconia has been prepared from Zircon concentrate by caustic fusion methods. Zircon is a by product from tin ore concentration plant at Bangka island of Indonesia. Yttria Stabilized-Zirconia (YSZ) was prepared by introducing the 8 % mol yttrium oxide into zirconia and sintered at 1500 "žaC for 5 hours. In order to obtain constant oxygen vacancy of 8 % mol in Zirconia, an appropriate amount of Yttria and Calcia were introduced into Zirconia and the mixtures were heated at 1350 oC for 5 hours. Elemental composition was determined by SEM/EDX and XRF and lattice parameters were determined using…