Cubic and Quartic Cyclic Homogeneous Inequalities of Three Variables
نویسنده
چکیده
We determine the geometric structures of the families of three variables cubic and quartic cyclic homogeneous inequalities of certain classes. These structures are determined by studying some real algebraic surfaces.
منابع مشابه
Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four
We shall show that the three variable cubic inequality t(a + b + c) + (t − 2t)(ab + bc + ca) ≥ (2t − 1)(ab + bc + ca) + (3t − 6t + 3t − 6t + 3)abc holds for non-negative a, b, c, and for any real number t. We also show some similar three variable cyclic quartic inequalities.
متن کاملCubic-quartic functional equations in fuzzy normed spaces
In this paper, we investigate the generalizedHyers--Ulam stability of the functional equation
متن کاملMinimizing Cubic and Homogeneous Polynomials over Integers in the Plane
We complete the complexity classification by degree of minimizing a polynomial in two variables over the integer points in a polyhedron. Previous work shows that in two variables, optimizing a quadratic polynomial over the integer points in a polyhedral region can be done in polynomial time, while optimizing a quartic polynomial in the same type of region is NP-hard. We close the gap by showing...
متن کاملOn the Cyclic Homogeneous Polynomial Inequalities of Degree Four of Three Nonnegative Real Variables
Let f (x,y,z) is a cyclic homogeneous polynomial of degree four of three nonnegative real variables satisfying the condition f (1,1,1) = 0 . We find necessary and sufficient condition to be true the inequality f (x,y,z) 0 , for this aim we introduce a characteristic polynomial Jf (t) and by its root t0 > 0 we formulate the condition.
متن کاملGeneration of a reduced first - level mixed integer programmimg problem
We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is...
متن کامل