Sentence examples for basic properties on the from inspiring English sources

For more basic properties on the sphere, we refer to [16].

The basic properties on the positivity and boundedness of solutions and the existence of the virus-free equilibrium, the no-immune equilibrium and the infected equilibrium are established.

The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established.

For slow system (7), the basic properties on the existence of disease-free equilibrium (P_{0}), unique endemic equilibrium (P^) and two positive equilibria (P_{1}) and (P_{2}), and the positivity and ultimate boundedness of the solutions with positive initial values are established.

For whole coupled systems (3)–(4), the basic properties on the existence of infection- and disease-free equilibrium (D_{0}), viral infection and disease-free equilibrium (D_{1}), unique endemic equilibrium (D^) and two endemic equilibria (D_{2}) and (D_{3}), and the local stability of equilibria (D_{0}) and (D_{1}) are established, respectively.

This paper first summarizes the recent results on basic properties of the parameter set (αi, τ) and shows a scheme to construct a target characteristic polynomial that meets a desired transient response characteristic.

On the basic properties of the space W1,p(x) we refer to [7, 28 30].

This section is dedicated to presenting an overview on some basic properties of the classical Jacobi polynomials which are useful in the sequel.

Based on the basic properties of the reciprocal symmetrical matrix, a method is proposed, which permits us to factorize the transfer matrix of the mode converter into a product of reciprocal symmetrical matrices.

These may be molecular or dissociative, depending on the acidic and basic properties of the molecules in gas phase and of the nature of the surface oxide.

Based on the analysis above, in Section 2, we present some new Gronwall-type inequalities, based on which and some basic properties of the modified Riemann-Liouville fractional derivative, we derive explicit bounds for the unknown functions concerned in these inequalities.