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## Strict measure rigidity for unipotent subgroups of solvable groups

### Inventiones mathematicae (1990-12-01) 101: 449-482 , December 01, 1990

## Complex manifolds and unitary representations

### Several Complex Variables II Maryland 1970 (1971-01-01) 185: 242-287 , January 01, 1971

## Transformation Groups in Differential Geometry

### Transformation Groups in Differential Geometry (1995-01-01): 70 , January 01, 1995

## Econometric Models and Optimal Economic Policy

### Stochastic Optimization and Economic Models (1986-01-01) 2: 1-10 , January 01, 1986

Specifying optimal economic policy using an econometric model has passed through three phases in its evolution. The first phase started with a two-stage approach in Tinbergen’s tradition: first, one estimates an econometric model by the standard techniques of statistical estimation, then one uses optimal control theory in the estimated model to determine an optimal policy. This approach failed to recognize two types of interdependence. One is that the changes in policy or optimal control would induce changes in the structural response of the model. Thus the post-control model equations would differ from the pre-control ones, thus generating some inconsistency. The second is that future errors or uncertainty conditional on the adoption of a given set of policies would be very different from the past by the same reasoning. The second phase of econometric model building for specifying an optimal economic policy explicitly allows for the interdependence of the two conditional aspects: the problem of optimal estimation given the control or policy variables and the problem of optimal regulation or control, given the estimated model using all past information upto the current date.

## Markov-Chain Monte Carlo

### Large Sample Techniques for Statistics (2010-01-01) 0: 523-551 , January 01, 2010

There are various things named after Monte Carlo, almost all of which originated from the Monte Carlo Casino in Monaco. In the mid-1940s, mathematicians John von Neumann and Stanislaw Ulam were working on a secret (nuclear) project at the Los Alamos National Laboratory in New Mexico. The project involved such calculations as the amount of energy that a neutron is likely to give off following a collision with an atomic nucleus. It turned out that the calculations could not be carried out analytically, so the two scientists suggested to solve the problem by using a random number-generating computer. Due to the secrecy of their project, they code-named their method Monte Carlo, referring to the Monaco casino, where Ulam’s uncle would borrow money to gamble (Ulam was born in Europe).

## Notes, Remarks and References

### Linking Methods in Critical Point Theory (1999-01-01): 255-268 , January 01, 1999

Here we include some observations pertaining to various sections.

## Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix

### Numerische Mathematik (2012-11-01) 122: 527-555 , November 01, 2012

Several *relative* eigenvalue condition numbers that exploit tridiagonal form are derived. Some of them use triangular factorizations instead of the matrix entries and so they shed light on when eigenvalues are less sensitive to perturbations of factored forms than to perturbations of the matrix entries. A novel empirical condition number is used to show when perturbations are so large that the eigenvalue response is not linear. Some interesting examples are examined in detail.

## On some Hasse Principles over formally real fields

### Mathematische Zeitschrift (1973-12-01) 134: 291-301 , December 01, 1973

## On sheets of orbit covers for classical semisimple lie groups

### Science in China Series A: Mathematics (2002-02-01) 45: 155-164 , February 01, 2002

David Vogan gave programmatic conjectures about the Dixmier’s map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed^{[1]}. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan’s first conjecture for geometric orbit datum: the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan’s conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.