Sentence examples for help of the theory from inspiring English sources

The Banach space valued inhomogeneous Cauchy problem u′(t) = Au(t)+ƒ(t)u(0) = x for a (non-densely defined) linear operator A is treated with the help of the theory of integrated semigroups.

With the help of the theory of Bayesian networks and factor graphs we derive design and organization rules for modular fusion systems which implement exact belief propagation without centralized configuration and fusion control.

In fact, with the help of the theory of inequalities, the existence of extremal solutions and a comparison result were proved by Dhage and Lakshmikantham.

In this paper, we will study the Hopf bifurcation of system (1), the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions with the help of the theory of the normal form and center manifold [23].

With the help of the theory of measure of noncompactness and a fixed point theorem of Darbo type, we establish a new existence theorem of mild solutions for the Cauchy problem above.

So under the assumption that g is continuous with respect to t, some papers, such as [18, 19, 25, 27, 28] have been devoted to Jensen's inequality for g-expectations, with the help of the theory of BSDEs, they have obtained the necessary and sufficient conditions under which Jensen's inequality for g-expectations holds in general.

Firstly, based on stability criterion of linear system, chaotic synchronization is achieved with the help of the active theory, and accordingly, the simulation results are given for verifying the feasibility of the method.

Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory.

With the help of the phenomenological theory of diffusion decay and obtained experimental results, the behavior of induced MT in Cu-Al-Mn alloy was explained and its causes were found out.

The motives for both continuation and discontinuation of oral care can be understood with help of the Motivational Theory of Life Span Development [ 50], in particular the Goal Engagement and Goal Disengagement control strategies [ 51] which form part of this theory.

With the help of set theory, the common and the tissue-specific SAGE tag sequences can be mined by this multi-pool method.