The problem of quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by function RealTriangularize in Maple15, the theory of complete discrimination systems and the so-called Criterions on Equality of Symmetric Inequalities method. The equivalent simple quantifier-free formula is proposed, which is difficult to obtain automat...

<p style='text-indent:20px;'>We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals driven by Caputo derivative. Several novel criterions are examined showing positive-definiteness associated kernel functions. deduce strict energy-dissipation number non-local energy fu...

We recover the cases of solutions in shape bright, dark and singular optical solitons for self-phase modulation effect, which belongs to type N. A. Kudryashov's sextic power-law nonlinearity refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme addendum common method. All enlisted criterions their existence ment...

this paper deals with the problem of forbidden states in discrete event systems modeled by petri net. to avoid the forbidden states, some constraints which are called generalized mutual exclusion constraints can be assigned to them. enforcing these constraints on the system can be performed using control places. however, when the number of these constraints is large, a large number of control p...

we design a two-stage scheme to consider trajectory planning problem of two mobile manipulators for cooperative transportation of a rigid body in presence of static obstacles. within the first stage, regarding the static obstacles we develop a method that searches the workspace for the shortest possible path between start and goal configurations by constructing a graph on a portion of the confi...

the redundancy allocation problem can be described as selecting the components and system configuration in order to optimize some objective function(s) without violating the system constraints. operating conditions are not constant in many advanced engineering systems. mostly, in the engineering applications selection, the number of redundancy components must be balanced among the constraints (...