By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...

Early detection of cancer is crucial for successful treatments. In this paper, we propose a multiclass Logistic Partial Least Squares (LPLS) algorithm for classification of normal vs. cancer using Mass Spectrometry (MS). LPLS combines the multiclass logistic regression with Partial Least Squares (PLS) algorithm. Wavelet decomposition is also proposed for pre-processing of original data. Wavelet...

0. Systems theory I. Part 1: Convergence A. Two approaches to convergence B. A mathematical formulation of convergence C. Convergence is a Markov process D. Starting configuration doesn’t matter II. Part 2: Analysis A. Background and mathematical foundation 1. Stochastic matrices 2. The Eigenvalue problem 3. Spectral Decomposition 4. Spectral Decomposition of M B. The Algebraic View 1. Partitio...

We develop a quasi-two-level, coarse-mesh-free characteristic nonoverlapping domain decomposition method for unsteady-state convection-diffusion partial differential equations in multidimensional spaces. The development of the domain decomposition method is carried out by utilizing an additive Schwarz domain decomposition preconditioner, by using an Eulerian-Lagrangian method for convection-dif...

In this paper, the relations between the weighted partial orderings on the set of rectangular complex matrices are first studied. Then, using the matrix function defined by Yang and Li [H. Yang and H.Y. LI, Weighted UDV ∗-decomposition and weighted spectral decomposition for rectangular matrices and their applications, Appl. Math. Comput. 198 (2008), pp. 150–162], some weighted partial ordering...

in the present study, a comprehensive and systematic strategy was described to evaluate the performance of several three-way calibration methods on a bio-analytical problem. parallel factor analysis (parafac), alternating trilinear decomposition (atld), self-weighted alternating trilinear decomposition (swatld), alternating penalty trilinear decomposition (aptld) and unfolded partial least squa...

iut + Lu = F (u), (1) where u : IR × IR → I C and L is a linear (pseudo -) differential operator of order m with real valued symbol denoted by l(ξ), and F is a nonlinear, possibly nonlocal operator. We will only consider the case where the linear part of (1) is dispersive, i.e. l(ξ) 6= Cξ. Actually, we will address cases where the linear group e satisfies some “decay” properties, see Section 1....