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On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs
Das, Kinkar Ch.,Aouchiche, Mustapha,Hansen, Pierre Elsevier 2018 Discrete Applied Mathematics Vol.243 No.-
<P><B>Abstract</B></P> <P>Let G be a graph of order n . The energy E ( G ) of a simple graph G is the sum of absolute values of the eigenvalues of its adjacency matrix. The Laplacian energy, the signless Laplacian energy and the distance energy of graph G are denoted by L E ( G ) , S L E ( G ) and D E ( G ) , respectively. In this paper we introduce a distance Laplacian energy D L E and distance signless Laplacian energy D S L E of a connected graph. We present Nordhaus–Gaddum type bounds on Laplacian energy L E ( G ) and signless Laplacian energy S L E ( G ) in terms of order n of graph G and characterize graphs for which these bounds are best possible. The complete graph and the star give the smallest distance signless Laplacian energy D S L E among all the graphs and trees of order n , respectively. We give lower bounds on distance Laplacian energy D L E in terms of n for graphs and trees, and characterize the extremal graphs. Also we obtain some relations between D E , D S L E and D L E of graph G . Moreover, we give several open problems in this paper.</P>
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Study of leaching of a 2M-Zirconolite (Ca0,83Ce0,17ZrTi1,66Al0.34O7) in acidic and basic media
R. Souag,N. Kamel,M. Hammadi,Z. Kamel,D. Moudir,F. Aouchiche,Y. Mouheb,S. Kamariz 한양대학교 세라믹연구소 2015 Journal of Ceramic Processing Research Vol.16 No.1
Zirconolite is a mineral intended for actinides elements confinement and is known for its good chemical durability. In this work, 2M-zirconolite, with the chemical formula: Ca0,83Ce0,17ZrTi1,66Al0.34O7 have been synthesized at 1400 o C by the metallurgical route at a laboratory scale. This stoechiometry corresponds to a CeO2 loading of 8.61 m.%. Ce is employed as an actinide surrogate. The effect of both pH and temperature on the chemical durability of this mineral has been studied. Phase identification and micrography observations have been done by X-ray diffraction, scanning electronic microscopy, and Fourrier transform infra-red spectroscopy. The end-product has a monophasic structure of 2M-zirconolite. Its density is about 4.013 g/cm3 , and its relative density is of 96 %TD. It has a microhardeness of 370 MPa. The Ce behavior in leaching media of extreme pH values: acidic medium (pH = 2) and basic medium (pH = 12), at 23 o C and 70 o C, shows that the Ce dissolution speeds are faster at 70 o C compared with those obtained at 23 o C. The 2M-zirconolite matrice presently studied appears to have a good chemical durability.
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