| Judul | Abstract | Halaman |
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| Locating-Chromatic Number of Amalgamation of Stars | Let G be a connected graph and c a proper coloring of G . For i ƒ¬1,2,ƒ»,k define the color class i C as the set of vertices receiving color i . The color code c (v) „¨ of a vertex v in G is the ordered k -tuple 1 ( ( , ), , ( , )) k d v C ƒ» 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 amalgamation of stars k ,m S . k ,m S is obtained from k copies of star 1,m K by identifying a leaf from each star. We also determine a sufficient condition for a connected subgraph k ,m H „~ S satisfying , ( ) ( ) L L k m ƒÓ H „T ƒÓ. | 1-8 |
| Doping Calcia and Yttria into Zirconia Obtained from by Product of Tin Concentrator to Improve its Ionic Conductivity | 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 „aC 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 X-ray diffraction method. Ionic conductivity was measured by complex impedance spectroscopy. The results show that doping of Yttria into Zirconia (YSZ) and Calcia-Yttria into Zirconia (CYZ) allows phase transformation of Zirconia from tetragonal with space group P42/nmc into cubic Fm3m and enhance the ionic conductivity. However, the prepared materials are porous and have not met the requirement for the electrolyte material yet. | 9-18 |
| On Tight Euclidean 6-Designs: An Experimental Result | 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:
∑_(i=1)^p▒(w (X_i ))/|S_i | ∫_(s_i)▒〖f(x) 〖dσ〗_(i ) (x)=∑_xϵX▒w(x) 〗 f(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] constructed tight Euclidean t-designs in the plane (n=2) for arbitrary t and p . In this paper we show that for case t=6 and p=2 , tight Euclidean 6-designs constructed by Bajnok is the unique configuration in ℝn, for 2 ≤ n ≤ 8. | 19-42 |
| Demethylation of Quinine Using Anhydrous Aluminium Trichloride | 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 trichloride of 1 to 4 in dried methylene chloride under nitrogen atmosphere. The reaction was firstly carried out at 0°C for 4 h and after the reaction mixture reached room temperature, the reaction was continued up to 24 h. | 43-50 |
| Existence and Uniqueness Results for Difference Φ-Laplacian Boundary Value Problems | 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. | 51-58 |
| Hierarchically Porous ZSM-5 Synthesized by Nonionic- and Cationic-Templating Routes and Their Catalytic Activity in Liquid-Phase Esterification | 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 type IV isotherms with narrow distribution of mesopore diameters. The catalytic activity of these mesoporous ZSM-5 was tested in liquid-phase esterification of benzyl alcohol with hexanoic acid. The conversion of benzyl alcohol on mesoporous ZSM-5 prepared via cationic-templating route was almost 100%, being much higher than on mesoporous ZSM-5 prepared with silylated nonionic surfactant as well as on conventional ZSM-5 with no mesopores. The presence of Brønsted acid sites, together with the mesopores, was responsible for this catalytic conversion, as confirmed by pyridine adsorption monitored by in situ infrared and 27Al magic angle spinning nuclear magnetic resonance spectroscopy. | 59-72 |
