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Hu and Wang presented in [16] a method of degree reduction without any boundary conditions based on quadratic programming.

That is, using the same method of degree reduction without boundary conditions gives less error than with boundary conditions.

Geometric conditions are considered with the method of degree reduction for the first time, which makes the methods novel and new.

In order to make this paper self-contained, Appendix A summarizes the general concept of the Gordon Coons method of degree n in detail and present explicit formulas for n = 0 and n = 1.

A general construction scheme of the Gordon Coons method of degree n for generating a C n -function h : T → R is as follows: (i) Let h i, j (u, v ) = ∂ i + j ∂ r i ∂ s j h (r, s ) | (r, s ) = (u, v ) for i, j ∈ { 0, …, n }.

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Although it is not fair to compare the numerical results of a method with boundary conditions to a method without boundary conditions, our proposed methods of degree reduction give errors that are smaller than existing methods.

A reduction and recovering methods of degree-of-freedom in structural dynamic analysis is proposed.

In Section 3, by using the method of coincidence degree theory, we obtain the existence of the anti-periodic solutions of system (1.1).

Lazer and Solimini in a pioneering paper [6] first used the method of topological degree to study equation (1.1) for the case of (c=0) and (lambdage1).

Ultrasound has the potential to be a cost-effective, non-invasive method of determining degree and location of Achilles tendon disease.

Sir Bob has thought long and hard about the archaic British method of classifying degrees into First, 2.1, 2.2, and so on.

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