Comparative study of Metallocene catalyst propylene polymerization with different iteration rates

This paper proposed a mathematical model corresponding to metallocene catalyzed propylene polymerization that uses the Me2Si [Ind]2ZrCL2 and Et [Ind]2ZrCL2. Comprehensive kinetic models consisting of mass and population balance equations, are developed based on elementary reactions proposed in the reaction mechanism. The result from the above indicates that metallocene catalysts in the presence of ethylene zirconium dichloride and methylene zirconium dichloride shows modularity and new peaks are obtained. The temperature variation from 25 to 75 also increase the rate and reason for the same could be chain shuttling polymerization. The model is presented through simulative study. Initially genetic approach is used but convergence rate is poor. To achieve best possible result, particle swarm optimization is used. The optimization approach with particle swarm optimization is implemented. The local and global solutions are comparable entities and replace each other in case value of local variable is not optimized. From the simulative study it is discovered that Et [Ind]2ZrCL2 produce best possible polymers both at 25 and 750C.

Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses

<abstract><p>The main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear functional analysis are the major tools to demonstrate our results. In last, an example is given to illustrate these analytical results.</p></abstract>

Breaking supersymmetry with pure spinors

For several classes of BPS vacua, we find a procedure to modify the PDEs that imply preserved supersymmetry and the equations of motion so that they still imply the latter but not the former. In each case we trace back this supersymmetry-breaking deformation to a distinct modification of the pure spinor equations that provide a geometrical interpretation of supersymmetry. We give some concrete examples: first we generalize the Imamura class of Mink6 solutions by removing a symmetry requirement, and then derive some local and global solutions both before and after breaking supersymmetry.

Local and global solutions for a hyperbolic–elliptic model of chemotaxis on a network

In this paper, we study a hyperbolic–elliptic system on a network which arises in biological models involving chemotaxis. We also consider suitable transmission conditions at internal points of the graph which on one hand allow discontinuous density functions at nodes, and on the other guarantee the continuity of the fluxes at each node. Finally, we prove local and global existence of non-negative solutions — the latter in the case of small (in the [Formula: see text]-norm) initial data — as well as their uniqueness.