Quantum annealing for systems of polynomial equations

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

Solving Systems of Polynomial Equations

Canonical representation for approximating solution of fuzzy polynomial equations

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness. 

coupled systems of equations with entire and polynomial functions

we consider the coupled system$f(x,y)=g(x,y)=0$,where$$f(x, y)=bs 0 {m_1}   a_k(y)x^{m_1-k}mbox{ and } g(x, y)=bs 0 {m_2} b_k(y)x^{m_2-k}$$with entire functions $a_k(y), b_k(y)$.we    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

Classical equations for quantum systems.

The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that decohere, w...