This paper is a review of the authors’ results on the Dynamical Systems Method (DSM) for solving operator equation (*) F (u)= f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*) ...

Page 2 1. Overview Page 10 2. Background Page 12 3. The differential calculus, sensitivity to errors and uncertainty Page 20 4. The notion of ‘differentials’ and ratio of differentials Page 27 5. The notion of a function Page 34 6. The exponential function Page 39 7. The natural logarithm Page 41 8. The derivative of the natural logarithm Page 41 9. The derivatives of some simple functions Page...

We present experimental evidence that, in the hard turbulence regime of Rayleigh-Bénard convection, the temperature fluctuations are produced by buoyancy, despite the presence of a mean horizontal flow at the plates. In a convection cell of aspect ratio 1, we measure the temperature time derivative for Ra from 2310 to 1310, which is skewed toward the negative in the region outside the cold ther...

An error occurs on Page 071302–3. The independent variable associated with the derivative of Ø1and Ø2 in Eqs. (6) and (7) is not described correctly.The right expressions for are (6)−(U1+∂Ø1∂x)∂η∂x+∂Ø1∂z=∂η∂t=−(U2+∂Ø2∂x)∂η∂x+∂Ø2∂zon z=η (7)−(U1)∂η∂x+∂Ø1∂z=∂η∂t=−(U2)∂η∂x+∂Ø2∂z z=0

HS-1200, a synthetic chenodeoxycholic acid derivative, has cytotoxic activity in various human cancer cells. The present study was undertaken to examine whether HS-1200 sensitizes radiation-induced apoptosis in MCF-7 human breast carcinoma cells. Clonogenic assay elucidated that the combination treatment with HS-1200 and radiation induced more cytotoxic effects than the radiation treatment alon...

Three known triterpenoids, namely ursolic acid (1), and the 27-E- and 27-Z-p-coumaric esters of ursolic acid (compounds 2, 3), were isolated together with a new triterpene 2,3-seco-taraxer-14-en-2,3-lactone [pycanocarpine (4)] from an ethanolic extract of Pleiocarpa pycnantha leaves. The structure of 4 was unambiguously assigned using NMR, HREIMS and X-ray crystallography. The cytotoxic activit...

The formation of 7-hydroxymethotrexate and its diglutamate has been established in rat hepatic parenchymal cells in culture. The formation of 7-hydroxymethotrexate increases with the extracellular methotrexate concentration (1-50 microM) and with time over a 24-h period. The majority of the 7-hydroxy derivative is found in the medium after 6- and 24-h incubations at all concentrations examined....

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel...