Woodin proved the theorem in perhaps 1986 or 1987, using stationary tower forcing and (through the work of Martin and the author) iteration trees. The proof we give here uses only iteration trees. Stationary tower forcing is replaced by “genericity iterations”, as it can be in certain related contexts as well. We believe that the unity of method in the resulting proof gives it some interest. Th...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

It is shown that for any sufficiently regular even Minkowski valuation Φ which homogeneous and intertwines rigid motions, convex body K in a smooth neighborhood of the unit ball, there exists sequence positive numbers (γm)m=1∞ such (γmΦmK)m=1∞ converges to ball with respect Hausdorff metric.

Using countable support iterations of S -proper posets, we show that the existence of a ∆3 definable wellorder of the reals is consistent with each of the following: d < c, b < a = s, b < g.

Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T . We prove that T is exact: ∩ k=1 σ(T (S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scal...

in this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. the error dynamics of each player depends on its neighbors’ information. detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. the introduced reinforcement learning-based algorithms learn online the approximate solution...