Abstract: The 3-SAT problem is one of the most important and interesting NP-complete problems with many applications in different areas. In several previous papers we showed the use of ternary vectors and set-theoretic considerations as well as binary codings and bit-parallel vector operations in order to solve this problem. Lists of orthogonal ternary vectors have been the main data structure,...

 In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.

In this paper, the relations among T-invariants, repetitive vectors and siphons are investigated and new methods for computing repetitive vectors and siphons are suggested based on them. The transition-added net of a net is defined and a relation is shown that there always exists a T-invariant of the transition-added net corresponding to a repetitive vector of the original net, and vice versa. ...

We introduce a new method for the analysis of singularities in the unstable problem ∆u = −χ{u>0}, which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of “supercharacteristic” growth of the solution, i.e. points at which the solution grows faster than the characteristic/invariant scaling of the equation would suggest. At such points the ...

We present a technique to compute over-approximations of the time trajectories of an affine hybrid system using template polyhedra. Such polyhedra are obtained by conjoining a set of inequality templates with varying constant coefficients. Given a set of template expressions, we show the existence of a smallest template polyhedron that is a positive invariant w.r.t to the dynamics of the contin...

We present a technique to compute over-approximations of the time trajectories of an affine hybrid system using template polyhedra. Such polyhedra are obtained by conjoining a set of inequality templates with varying constant coefficients. Given a set of template expressions, we show the existence of a smallest template polyhedron that is a positive invariant w.r.t to the dynamics of the contin...

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend variou...

Hyper-sensitivity to unknown boundary conditions plagues indirect methods of solving optimal control problems as a Hamiltonian boundary-value problem for both state and costate. Yet the hyper-sensitivity may imply manifold structure in the Hamiltonian flow, knowledge of which would yield insight regarding the optimal solutions and suggest a solution approximation strategy that circumvents the h...

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated. Keywords—Lorentzian 5-space; Frenet-Serret Invariants; Nonnull Curves.