This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

and Applied Analysis 3 4 strictly η-monotone if 〈 u − v, ηx, y > 0, ∀x, y ∈ H, x / y, u ∈ M x , v ∈ M ( y ) ; 2.5 5 strongly monotone if there exists a constant r > 0 satisfying 〈 u − v, x − y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.6 6 strongly η-monotone if there exists a constant r > 0 satisfying 〈 u − v, ηx, y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.7 7 maximal monotone resp., maxim...

Shape constrained densities are encountered in many nonparametric estimation problems. The classes of monotone or convex (and monotone) densities can be viewed as special cases of the classes of k−monotone densities. A density g is said to be k−monotone if (−1)g is nonnegative, nonincreasing and convex for l = 0, . . . , k−2 if k ≥ 2, and g is simply nonincreasing if k = 1. These classes of sha...

We consider the size of monotone circuits for quadratic boolean functions, that is, disjunctions of length-2 monomials. Our motivation is that a good (linear in the number of variables) lower bound on the monotone circuit size for a certain type of quadratic function would imply a good (even exponential) lower bound on the general non-monotone circuit size. To get more insight into the structur...

In this paper, we present a new hybrid extragradient algorithm for finding common element of the fixed point problem demicontractive mapping and split equilibrium pseudomonotone Lipschitz-type continuous bifunction. By using technique choosing step size proposed method, our algorithms do not need any prior information operator norm. fact, propose an inertial type in order to accelerate its conv...

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from signed network structure, associated to purely stoichiometric information and ignoring fluxes. In particular, monotone systems respond in a predictable fashion ...