Sentence examples for bounded by the initial from inspiring English sources
Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time.
It was found for nonlinear Lagrangian mixing times that for this paradigm helical coherent structure, 22% of the trajectory pairs were bounded by the initial separation (non-mixing) and 78% mixed in various classifications of convective dispersal.
When (trightarrow0), the solution (46) of the Cauchy problem (5 - 6) is bounded by the initial data biglVert u x,t) bigrVert _{L^{p}(R)} leq biglVert u x,0) bigrVert _{L^{p}(R)}, quad xin R, pgeq1.
We show that the spacetime integral of an energy-type density is bounded by the initial conserved flux corresponding to the stationary Killing field T, and we derive boundedness of the non-degenerate energy flux corresponding to a globally timelike vector field N. Finally, we prove uniform pointwise boundedness and power-law decay for ψ up to and including the event horizon H+.
Thus, the optimum radius would be the summation of squared noise terms (left (sum _{i=1}^{N_{t}}vert v {vert ^{2}_{i}}right)) of the detection layers, which follows χ 2distribution with N t degree of freedom and upper bounded by the initial radius (p^{prime }_{text {SD}}).
The vertical position error was always found to be bounded by the protection level proven initial validity of the proposed integrity model.
It is bounded by the constants B, V, ε → and the initial status of Q → ( 0 ).
All search positions of each individual PU partition are created in a sub-sampled manner of the full search with iRaster equal to 3, and these points are only generated within their initial search regions bounded by the large squares, as depicted in Fig. 6.
Briefly, the interval bounded by the smallest (m) and the largest (M) initial rate estimates is divided up into k groups; the coordinates of the cutoff points are solely a function of m, M and k.
