The results can then be transformed to derive a pseudo-three dimensional solution to the problem.
These curves were transformed to derived melting curves (-d(F2)/dT vs. T).
We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems.
In this paper, we propose a new semi-analytical approach based on Fourier transform inversion to derive a semi-analytical expression of error probability.
This study used first- and second-order statistics (GLC Mand RLM) and also the wavelet transform method to derive texture parameters that were then selected based on their discriminative value in differentiating cysts from haemangiomas and subsequently used in the computer-assisted classification algorithm.
As an application, we apply the Laplace transform method to derive explicit solutions to the homogeneous equations of the form _{a}^{C}nabla_{ q,h)}^{alpha} y(t)- lambda y(t)=0,qquad d_{k}=nabla ^{k}y(a), quad k=0, ldots, m-1, (42) where (tinwidetilde{mathbb{T}}^{sigma^{m} (a)}_{ q,h)}) ((minmathbb {N})), (m-1
In the beginning of the paper, we first apply the Laplace transform method to derive that the linear Cauchy problem left { textstylebegin{array}{l} ^{mathrm{c}}D_{t}^{beta}(^{mathrm{c}}D_{t}^{alpha}+mu x t)=g(t), quad tin I:=[0,1], muin Rsetminus{0}, x 0)=a, qquad x'(0)=b,qquad [^{mathrm{c}}D_{t}^{alpha}x t)]_{t=0}=c,qquad [^{mathrm{c}}D_{t}^{alpha}x t)]'_{t=0}=d, end{array}displaystyle right.
deriving the transform to an explicit algebraic algebraic eigenvalue problem for a symmetric, banded matrix with bandwidth, providing the required formulas, so that an implementation of the construction is easily "accessible" for the reader, proving that the construction is always successful under the conditions (4.4) and (4.7) (which is the contents of Theorem 6.1).
Moreover, how ideas derived from concepts transform to strategies for controlling the reaction pathways is also discussed.
The Laplace transform is employed to derive the governing equation of the problem.
