Sentence examples for depending on the free from inspiring English sources

It turns out that these are infinite amount of polar orthotropic circular plates that solve the posed semi-inverse problem, depending on the free parameter represented by one of the coefficients in variation of flexural rigidities.

It is thought that these can form a variety of bonds with reactants depending on the free lattice electrons and the holes in the catalyst lattice.

Phenols, phosphites, or amine compounds are used as antioxidants depending on the free radicals expected to form.

These interactions can be attractive (hydrophobic attraction) or repulsive (hydrophilic repulsion), depending on the free energy of hydrophobic interaction [37,38].

This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points.

Stimuli-sensitive hydrogels, e.g., many poly acrylamide) representatives, can be in a critical swelling equilibrium depending on the free enthalpy of mixing polymer network and water as a swelling agent and the elasticity of polymer chains.

The vibrancy of our globalized economy depends on the free movement of people, goods and ideas.

Any economist will tell you that prosperity depends on the free flow of goods and people.

"Our nation's progress depends on the free flow of information," he conceded.

He insists the future prosperity of Latin America depends on the free flow of commerce and labor between the United States and countries to the south.

The freedom of innocent men and the security of the remaining Iranian Jewish community depend on the free world's perseverance.