Sentence examples for fixed expansion from inspiring English sources
In summary, we iteratively determine the expansion coefficients of the state function X (t ) for fixed parameters in the ODE by (10 ) and estimate the coefficient functions in the ODE for fixed expansion coefficients by (16 ).
However, there is a maximal possible velocity of a curved stationary two-dimensional flame of a fixed expansion coefficient, which cannot be exceeded with the increase of the tube width.
For any fixed expansion order p, the relation between time and error can be approximated by a constant plus a power law that becomes flatter for larger p. At any given error, there is an optimal expansion order p in the sense of providing the fastest approximation.
Thus, for each fixed expansions.
The results show significant vulnerabilities in the reinforced concrete columns and in the steel fixed and expansion bearings.
end{aligned} Then, by using cone expansion fixed point theorem they obtain the existence of positive solutions.
In order to obtain the existence of the positive solutions of system (1), we will use the following cone compression and expansion fixed point theorem.
In order to obtain the main results in this paper, we will use the following cone compression and expansion fixed point theorem.
By means of the properties of the Green function and the compression and expansion fixed point theorem (Kwong in Fixed Point Theory Appl. 2008:164537, 2008), sufficient conditions are obtained to guarantee the existence of a solution to the posed problem.
Recently, by cone expansion fixed point theorem, Li et al. [10], obtained the positive solutions of the following class of singular fractional differential equations: left { textstylebegin{array}l} D_{0^^{alpha}x t)+p(t)f t,x t))+q(t g t,x t))=0,quad 0< t< 1, x 0)=x'(0)=cdots=x^{ n-2)}(0)=x^{ n-2=int_{0}^{1}k(s)x(s),dA(s), end{array}displaystyle right.
In [30], the authors consider a new conformable fractional derivative and apply a functional compression-expansion fixed point theorem to prove the existence of a positive solution for fractional boundary value problem with S-L boundary conditions.
