Practical Quasi-Newton algorithms for singular nonlinear systems

Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this paper. Singular roots cause a number of problems in implementation of iterative methods and in general deteriorate the rate of convergence. We propose two modifications of QN methods based on Newton’s and Shamanski’s method for singular problems. The proposed algorithms belong to the class of two-step iterations. Influence of iterative rule for matrix updates and the choice of parameters that keep iterative sequence within convergence region are empirically analyzed and some conclusions are obtained.     

Palladium-catalyzed cross-couplings of allylic phosphates

A range of palladium-catalyzed cross-coupling reactions can be performed using allylic phosphates as electrophiles. Both conventional heating and microwave irradiation can be used.     

Comparison of Numerical Simulation Models for Open Loop Flight Simulations in the Human Centrifuge

To achieve predefined Gz load profile in high G training in human centrifuge, it is necessary to determine angular velocity and acceleration of a planetary axis (centrifuge arm). Initial value problem that can not be solved in closed form was obtained. Several discretization methods for calculating angular velocity of centrifuge arm driven by DC servo motor are presented. Simulations are performed for different positive and negative values of Gz onset. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Information,no-arbitrage and completeness for asset price models with a change point

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time τ$\tau$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations which naturally arise in this setting, establishing martingale representation results and characterizing the validity of the NA1 and NFLVR no-arbitrage conditions.     

A novel C,D-spirolactone analogue of paclitaxel: autophagy instead of apoptosis as a previously unknown mechanism of cytotoxic action for taxoids

The design, synthesis and biological evaluation of a novel C,D-spirolactone analogue of paclitaxel is described. This is the first paclitaxel analogue without an oxetane D-ring that shows a significant cytotoxic effect (activity one order of magnitude lower than paclitaxel). More importantly, its cytotoxicity is a result of a different mechanism of action, involving mTOR inhibition-dependent autophagy instead of G(2)/M cell cycle arrest-dependent apoptosis.