Jeffreys's law for general games of prediction: in search of a theory

We are interested in the following version of Jeffreys's law: if two predictors are predicting the same sequence of events and either is doing a satisfactory job, they will make similar predictions in the long run. We give a classification of instances of Jeffreys's law, illustrated with examples.Comment: 12 page

Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte

Methods of Increase of Ductility in Explosion Shaping of High-Strength Sheet Material

The outcomes of research on the increase of ductility of low-ductile materials are indicated in this work. Dynamic effects of increase of materials ductility and special technological methods are used to obtain by a method of explosive forming high-strength details. On the one hand, these methods are based on the increase of stability of the shaping process. On the other hand, they are based on the use of mass forces for additional submission of a material from a flange. The features of explosive forming also allow for an effective application of a universal equipment with special inserts from plastic mixture

Competing with stationary prediction strategies

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to consider only stationary strategies even for highly non-stationary environments.Comment: 20 page

Mathematical Modeling of Impulsive Forming Processes Using Various Energy Sources and Transmitting Medium

High-speed forming uses high explosives, gun powder, combustible gas mixes and compressed gases as sources of energy. Special mathematical models are used to take into account specific dynamic properties. Different technological processes of forming have been modeled in the work. They use liquid (water), elastic (polyurethane), and gaseous transmitting medium. The difference between impulse energy transference, load distribution on a blank and tool surface, and also wave propagation is shown for used transmitting medium. The developed procedures allow taking account significant thermal effects at adiabatic compression of the material and heat transference directly from products of explosion. Specially developed modules and mathematical models have allowed the application of standard software products for modeling high-speed forming and sheet metal punching processes