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The solution and analysis of Kuramoto-Sivashinsky equation by cubic Hermite collocation method is performed and a bound for maximum norm of the semi-discrete solution is derived by using Lyapunov functional. Error estimates are also obtained for semi-discrete solutions and verified by numerical experiments.

Breast cancer is a major global health concern, appealing for precise prognostic approaches. Thus, the need is to have studies focusing on the identification and recognition of preliminary events leading to the disease. The present study reports the tracing of precancerous progression and serum proteomic analysis in a breast cancer model developed as a result of 7,12-dimethylbenz[a]anthracene (DMBA) administration. Mammary gland histological changes of prime importance were examined by histopathology, and immunohistochemical analysis with Ki-67 was performed to monitor enhanced cell proliferation, right from the onset of hyperplasia till neoplasia. Serum proteomics (one-dimensional (1D) and two-dimensional (2D) electrophoresis, followed by MALDI-TOF MS characterization) was performed to decipher the differentially expressed serum proteins in animals undergoing tumorigenesis vis-à-vis controls. The significance of our study lies in reporting the significantly reduced expression of two proteins: histone-lysine N-methyltransferase (SETD2) and sorting nexin-9 (SNX9) at very early stage (13 weeks) of tumorigenesis, while the full-fledged tumors developed after 6 months. The reduced expression of SETD2 and SNX9 was validated by western blotting and relative expression analysis using quantitative real-time PCR. These proteins may hence prove as potentially useful tools in search for prognostic markers for the early detection of mammary cancer.

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A convenient computational approach for solving mathematical model related to diffusion dispersion during flow through packed bed is presented. The algorithm is based on the mixed collocation method. The method is particularly useful for solving stiff system arising in chemical and process engineering. The convergence of the method is found to be of order 2 using the roots of shifted Chebyshev polynomial. Model is verified using the literature data. This method has provided a convenient check on the accuracy of the results for wide range of parameters, namely, Peclet numbers. Breakthrough curves are plotted to check the effect of Peclet number on average and exit solute concentrations.

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