Sentence examples for modeled by initial from inspiring English sources

It is well known that many physically significant problems can be modeled by initial value problems (IVP) of the following form: x ′ ( t ) + A x ( t ) = 0, x ( 0 ) = x 0, (1.1).

It is known that many physically significant problems can be modeled by initial value problems of the form x ′ ( t ) + A x ( t ) = 0, x ( 0 ) = x 0, (1.1).

It is well known that many physically significant problems can be modeled by initial value problems of the following form: (x'(t)+Ax t)=0), (x 0)=x_{0}) where A is an accretive operator in an appropriate Banach space.

It is well known that many physically significant problems can be modeled by initial value problems of the form x ′ ( t ) + A x ( t ) = 0, x ( 0 ) = x 0, (1.2).

It is known that many physically significant problems can be modeled by initial value problems of the form x ′ ( t ) + x ( t ) − A x ( t ) = 0, x ( 0 ) = x 0, where A is a pseudo-contractive operator in the framework of Banach spaces.

For example, at certain moments, the system changes their state rapidly, which cannot be modeled by traditional initial value problems.

In addition, also the influence of an As reservoir for processes without pre-growth overheating is modeled by an initial As adatom density n As(0)=1 ML.

A strong motivation for studying impulsive fractional differential equations comes from the fact they can be used to model phenomena that cannot be modeled by traditional initial value problems, such as the dynamics of populations subject to abrupt changes (harvesting, diseases, etc).

Consider the numerical solution of the non-Fickian flow in porous media modeled by an initial boundary value problem of the following parabolic integro-differential equation: textstylebegin{cases}phi u_{t}- operatorname{div} (Anabla u+int_{0}^{t} B s)nabla u x,ds,ds )=f,&text{in }Omegatimes 0,T], u=0,& text{on }partialOmegatimes 0,T], u x,0)=u_{0}(x),&forall xinOmega.

There are several factors that affect the failure in STT-RAM memories: access transistor manufacturing errors such as those due to RDFs, channel length, and width modulations, geometric variations in MTJ such as area and thickness variation, and thermal fluctuations that are modeled by the initial magnetization angle variation[15].

It is well known (see [1]) that many physically significant problems can be modeled by the initial-value problems of the form.