A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m2n) operations, where m is the number of Chebyshev points needed to resolve the coefficients of the differential operator and n is the number of Chebyshev coefficients ...

In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of R with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a...

in this study, the densities, excess molar volumes and partial molar volumes of four binary systems containing n,n-dimethyl acetamide (dmac) with 1-alkanols (1-butanol up to 1-heptanol) are measured at 298.15 k. the results showed both constructive and expansive excess volumetric behavior for studying binary mixtures. deviation values of heavy alcohol have more positive and less negative excess...

High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases. We consider the problem of variable selection in high-dimensional linear models with longitudinal data. A new variable selection procedure is proposed using the smooth-threshold generaliz...

In this paper, we present an algorithm to decompose nonlinear differential polynomials in one variable and with rational functions as coefficients. Besides arithmetic operations, the algorithm needs decomposition of LODEs, decomposition of multi-variable polynomials, factorization of multi-variable polynomials and solution of linear equation systems.