On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

New York - New Jersey job expansion to moderate in 2001

New York City will set the pace for job growth in the New York-New Jersey region in 2001, with employment advancing 1.9 percent over the year. For the region as a whole, the rate of job growth will drop to 1.5 percent, from 2.2 percent in 2000.Employment - New York (State) ; Employment - New Jersey ; Federal Reserve District, 2nd

The New York - New Jersey job recovery

Modest employment is expected to continue through 1997, with the New York City metropolitan area creating the bulk of new jobs.Federal Reserve District, 2nd ; Employment (Economic theory)

New York - New Jersey job expansion to continue in 2000

Employment growth in the New York-New Jersey region in 2000 is expected to reach 1.8 percent, or 290,000 new jobs--continuing a seven-year expansion trend. However, some moderation in the growth in the national economy over the second half of 2000 may slow the region's job growth and prevent it from matching last year's rate.Employment - New York (State) ; Employment - New Jersey ; Federal Reserve District, 2nd

1997 job outlook: the New York-New Jersey region

Major industrial and government restructurings have dominated employment reports in the New York-New Jersey region, leading to widespread pessimism about the region's job prospects. Nevertheless, for the past several years, the two states have managed to achieve modest job gains. In 1997, employment growth in New York and New Jersey will accelerate slightly as the pace of restructurings slows.Employment (Economic theory) ; New York (State) ; New Jersey ; Federal Reserve District, 2nd

New York-New Jersey region's job growth to continue in 1999, but risks have risen

Employment growth in the New York-New Jersey region in 1998 is likely to match the previous year's pace of 1.7 percent, or 200,000 new jobs. Growth will continue in 1999, but it will slow modestly, to about 1.2 percent, or 145,000 new jobs.Federal Reserve District, 2nd ; Employment - New York (State) ; Employment - New Jersey ; Economic conditions - United States

Shuttle orbiter S-band quad antenna switching evaluation

Automatic switching of the shuttle orbiter S-band quad antennas by the orbiter on-board computers was evaluated. The development and use of an extensive computer program to determine antenna switch position states as a function of time for various orbital activities is described. The selection of the optimum quad antenna element at any given time is based on the look angle to the appropriate Tracking Data Relay Satellite (TDRS). It is shown that a 2.4 second period is required for updating the S-band quad antenna switch state based on a maximum roll rate of 2 deg per second. The possibility of a variable update period is suggested since the 2 deg per second attitude rate is seldom encountered and would, for example, dictate approximately 248,000 on-board computer calculations during Reference Mission 2. The average number of antenna switch state changes was found to be in the range of 1,300 for Reference Mission 2