On the Achromatic Number of Silicate Networks

Abstract

The silicates are the largest, the most interesting and the most complicated class of minerals by far. The basic chemical unit of silicates is the (SiO 4 ) tetrahedron. A silicate sheet is a ring of tetrahedrons which are linked by shared oxygen nodes to other rings in a two dimensional plane that produces a sheet-like structure. We consider the silicate sheet as a fixed interconnection parallel architecture and call it a silicate network. The achromatic number for a graph G= (V, E) is the largest integer m such that there is a partition of V into disjoint independent sets (V 1 , ..., V m ) satisfying the condition that for each pair of distinct sets V i , V j , V i ∪ V j is not an independent set in G. In this paper, we determine an approximation algorithm for the achromatic number of Silicate Network which is N P complete even for trees.

Excess Acoustical Properties and Molecular Interactions in Ternary Liquid Mixtures of 3(Meta)Methoxy Phenol, 1 Propanol and n- Hexane at 303 K, 308 K & 313 K using Ultrasonic Techniques

“…The excess ultrasonic velocity shows negative values which reveals a strong interactions are possessed by the system and these values (magnitude) decrease while the temperatures increases irrespective of all the concentrations that may be attributed to the thermal agitations. And at particular temperature the excess ultrasonic velocities increase with increase in concentration which also support the existence of strong interactions among the molecules (the corresponding plot is given in Fig 5).Similar conclusions were also arrived byG.Arulet.al [12].…”

“…where u and ρ denote the ultrasonic velocity and density for the mixture, u 1 u 2 and u 3 and ρ 1 ρ 2 and ρ 3 denote the ultrasonic velocities and densities for the pure components. k is Jacobson's constant The values of , Z E , and for each mixture has been fitted to the Redlich-Kister polynomial equation (12) The values of the coefficients a i were calculated by the method of least squares along with the standard deviation σ(Y E ). The coefficient i is an adjustable parameter for the best fit of the excess functions.…”

Intermolecular interactions in mixtures of ethyl formate with methanol, ethanol, and 1-propanol on density, viscosity, and ultrasonic data

“…The adiabatic compressibility (β) decreased with increasing the concentration of ethyl formate as listed in Table 2. The decreasing values elucidate that the addition of ethyl formate breaks the molecular clustering of the liquid mixture and releasing more number of dipoles for the interactions [17]. The reverse trend has been observed in the acoustic imped ance.…”

Thermodynamic Interactions of P-Chlorotoluene with P-Xylene at 303.15 K, 308.15 K, 313.15 K and 318.15 K

“…The decrease in density and viscosity with temperature indicates that decrease in intermolecular forces due to increase in thermal energy of the system, which cause increase in volume expansion and hence increase in free length. Viscosity increases with concentration of P-chlorotoluene confirms that increase of cohesive forces because of strong interaction [12][13][14] . The internal pressure decreases with increasing mole fraction of P-Chlorotoluene.…”