The phrase "a continuous boundary of" is correct and usable in written English.
It can be used when describing an unbroken or uninterrupted limit or edge of a particular area or object.
Example: "The park is surrounded by a continuous boundary of trees that provides a natural barrier from the outside world."
Alternatives: "an unbroken edge of" or "a seamless border of".
Consider the fourth order problem with homogeneous boundary conditions called the biharmonic homogeneous problem textstylebegin{cases} Delta^{2} varphi=f &text{in } Omega, varphi=0 & text{on } partialOmega, frac{partialvarphi}{partial n}=0 & text{on } partialOmega, end{cases} (1) where Ω is a polygonal domain of (mathbb {R}^{d}, d=2,3) and ∂Ω is a Lipschitz-continuous boundary of Ω [1].
We suppose that ω has a Lipschitz continuous boundary and is the bottom of the fluid.
The following Plemelj-Sokhotski formula, proven in [4], then asserts the existence of the continuous boundary limits of the Q-Hermitian Cauchy transform.
Let, then the continuous boundary values of its Hermitean Cauchy integral exist and are given by.
The present decomposition problem is discussed using the matrix Cauchy integral of (see also [16]) and its singular version, called the Hilbert transform; they are shown to be related to each other by Plemelj-Sokhotzki type formulae for the continuous boundary values of.
Some of the recent progress in the continuous fractional calculus has included a paper in which the authors explored a continuous fractional boundary value problem of conjugate type, using cone theory, they then deduced the existence of one or more positive solutions[2].
Some of the recent progress in the continuous fractional calculus includes the paper [2], in which the authors explored a continuous fractional boundary value problem of conjugate type using cone theory, they then deduced the existence of one or more positive solutions.
Free sliding of the grain boundaries, a continuous nucleation of the grain boundary cavities, their diffusional growth and coalescence to form grain boundary facet cracks are fully accounted for in the analyses.
The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of "nonreflecting kernels" nor discretization of the continuous boundary conditions is required.
As a consequence, object clusters can build continuous boundaries for objects of coarser granularity levels, thereby marking the border of these higher level objects.
