On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation

We consider an initial boundary‐value problem for the generalized Benjamin–Bona–Mahony equation. A three‐level conservative difference schemes are studied. The obtained algebraic equations are linear with respect to the values of unknown function for each new level. It is proved that the scheme is convergent with the convergence rate of order k – 1, when the exact solution belongs to the Sobolev space of order . © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 301–320, 2014     

Thermostability of rat sarcoma M1 procollagen solutions,procollagen fibers and whole tissues

In close to equilibrium conditions (1° per 400 min), the DSC measurements demonstrated that the melting parameters of white rat sarcoma M1 procollagen equaled to T_m?=?34.4 °C and ΔT_m?=?2.7°, and the same parameters of fibers reconstructed from those solutions of procollagen were T_m?=?38.5 °C and ΔT?=?3.1°. These values were by 1.0° lower and 0.8° wider, and by 1.7° lower and 0.7° wider in comparison with the parameters of procollagen and fibers of healthy rat tissue, accordingly. The simultaneous increase in melting temperature and melting width, and a weak decrease in melting enthalpy demonstrated that sarcoma M1 procollagen had some defects. The considerable decrease by 7° in melting temperature and decrease in thermostability of procollagen fibrils in case of sarcoma M1 in comparison to the healthy norm gives a good prospective potential of using this approach as a quick DSC test to detect various sarcomas, including human sarcomas, by comparing the biopsy material or postsurgical tissues with the normal samples.