Perfect r-domination in the Kronecker product of two cycles, with an application to diagonal/toroidal mesh

If r?1, and m and n are each a multiple of (r+1)²+r², then each isomorphic component of C_m×C_n admits of a vertex partition into (r+1)²+r² perfect r-dominating sets. The result induces a dense packing of C_m×C_n by means of vertex-disjoint subgraphs, each isomorphic to a diagonal array. Areas of applications include efficient resource placement in a diagonal mesh and error-correcting codes.     

A comment on “The domination number of exchanged hypercubes”

This note presents a technical improvement to an upper bound in “The domination number of exchanged hypercubes” [Inf. Process. Lett. 114 (4) (2014) 159–162] by Klav?ar and Ma.     

Orthogonal drawings and crossing numbers of the Kronecker product of two cycles

An orthogonal drawing of a graph is an embedding of the graph in the plane such that each edge is representable as a chain of alternately horizontal and vertical line segments. This style of drawing finds applications in areas such as optoelectronic systems, information visualization and VLSI circuits. We present orthogonal drawings of the Kronecker product of two cycles around vertex partitions of the graph into grids. In the process, we derive upper bounds on the crossing number of the graph. The resulting upper bounds are within a constant multiple of the lower bounds. Unlike the Cartesian product that is amenable to an inductive treatment, the Kronecker product entails a case-to-case analysis since the results depend heavily on the parameters corresponding to the lengths of the two cycles.     

Experimental investigation on engine parameters variation in common rail direct injection engine fueled with biodiesel

Clean Technologies and Environmental Policy - Biodiesel is an alternative sustainable energy source and can be utilized in the compression ignition engine without any changes in the engine design....     

Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables

A hierarchical and computationally efficient mathematical model was developed to explain the polymerization of high-density polyethylene (HDPE) in an isothermal, industrial, continuous stirred tank slurry reactor (CSTR). A modified polymeric multi-grain model (PMGM) was used. Steady-state macroscopic mass balance equations were derived for all species (namely, monomer, solvent, catalyst and polymer) to obtain the final particle size and the required monomer and solvent input rates for a given catalyst input and the reactor residence time. The interphase mass transfer coefficients were calculated for the industrial CSTR using the operating data on the reactor. The present model was tuned with some data on an isothermal industrial reactor and the simulation results were compared with data on another set of industrial reactor. The comparison revealed that the present tuned model is capable of predicting the productivity and the polymer yield at various catalyst feed rates and the mean residence times. The effects of variation of two operating variables (catalyst feed rate and mean residence time) on the productivity, the polymer yield, the polydispersity index (PDI) and the operational safety were analyzed. The present study indicated that an optimal value of the reactor residence time (for maximum productivity per catalyst particle) exists at any catalyst feed rate.