in a closed die forging process, it is impossible to form complex shapes in one stage, and thus it becomes necessary to use preform dies. in the present study, backward deformation method and fe simulation via abaqus software has been used in order to design preform die of the h-shaped parts. in the backward deformation method, the final shape of the part is considered as a starting point and u...

in this paper, we consider an implicit block backwarddifferentiation formula (bbdf) for solving volterraintegro-differential equations (vides). the approach given in thispaper leads to numerical methods for solving vides which avoid theneed for special starting procedures. convergence order and linearstability properties of the methods are analyzed. also, methods withextensive stability region ...

Given an approximate solution to a data least squares (DLS) problem, we would like to know its minimal backward error. Here we derive formulas for what we call an “extended” minimal backward error, which is at worst a lower bound on the minimal backward error. When the given approximate solution is a good enough approximation to the exact solution of the DLS problem (which is the aim in practic...

This paper introduces backward conditioning. Like forward conditioning (used in conditioned slicing), backward conditioning consists of specialising a program with respect to a condition inserted into the program. However, whereas forward conditioning deletes statements which are not executed when the initial state satisfies the condition, backward conditioning deletes statements which cannot c...

A solution concept that satisfies the axioms of invariance and strong backward induction selects a stable set of a game’s equilibria.

Standard structures of information, in particular partition structures, are inadequate for the modeling of strategic thinking. They fail to capture the inner structure of hypotheses players make about situations they know will not occur. An extension of the partition structure is proposed in which such hypotheses can be modeled in detail. Hypothetical knowledge operators are defined for extende...

OBJECTIVE To use forward dynamic simulations of forward and backward pedaling in order to determine whether backward pedaling offers theoretical advantages over forward pedaling to rehabilitate common knee disorders.DESIGN. A comparison of knee joint loads was performed during forward and backward pedaling.BACKGROUND. Pedaling has been shown to be an effective rehabilitation exercise for a vari...

We apply backward induction to derive optimal price functions. In the second period, given first period price p 1 , the firm selects second period price p 2 (p 2 < Max{q, R}) to maximize its second period profit: The profit function can be reduced to four possibilities based on the value of p 1 : By maximizing profit in each of the four cases, we can derive the optimal second period price p 2 a...

Finite perfect information extensive (FPIE) games are quite well-understood: backward induction yields all of the pure strategy subgame perfect equilibria of such games. Iterative elimination of weakly dominated strategies (IEWDS), which can be hazardous in general games due to orderdependence of outcomes, can be much better behaved. In fact, for a large class of FPIE games, the outcomes of IEW...