Then by applying the properties (continuity, explicit boundedness, monotonicity, and nonnegativity) of (A_{alpha,beta}(w)), (alpha,betain 0,1)), for (w<0) and fixed point theorems, we can deduce some interesting existence results for a nonlinear problem.
By applying the results of fractional calculus an explicit equation is derived to express non-integer moments as a function of any arbitrary number of integer moments.
We propose to fight this problem by applying the idea of bounding the examined state space in explicit model checking.
Auto-calibration algorithms require a minimal constraint to define the network datum, which can be done by applying the minimum constraint, free-network adjustment, or through an explicit minimal control point (Remondino and Fraser 2006).
By applying the "freezing" technique to the control system (1.1 - 1.2 1.1 - 1.2ve explicit stabilizability conditions, provided that the coefficients are slowey varying.
The explicit expressions for the seven displacement parameters are then presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations.
Xuan et al.[2] derived the explicit formula for the extremal functions of the best embedding constant by applying the Bliss lemma [3].
We present an explicit solution to an optimal stopping problem of the stochastic Gilpin-Ayala population model by applying the smooth pasting technique (Dixit in The Art of Smooth Pasting, 1993 and Dixit and Pindyck in Investment under Uncertainty, 1994).
Explicit local and global stability conditions for the unique non-trivial equilibrium were obtained by applying the method of delays in differential inequalities and linear stability theory of non-linear delay differential equations.
Then, the explicit characterizations of the observer/controller gains are obtained by means of certain nonlinear matrix inequalities that can be effectively solved by applying the cone complementary linearization algorithm.
