Small Business: Big Challenge

In recent years, the contributions of small business to the American economy have become increasingly apparent. Small firms are a significant source of new jobs, and play crucial roles in the development of new technologies and provision of economic opportunities. Small businesses may be especially critical to the regional economies of upstate New York, where a number of large employers have either moved their operations or scaled back their workforces. As a result, it is important to understand the factors that affect small business growth in the region. Recognizing the growing importance of small firms to the upstate New York economy, the Buffalo Branch of the Federal Reserve Bank of New York in partnership with the Center for Governmental Research (CGR) surveyed small businesses in western and central New York State. Small business owners know firsthand the challenges of operating a business in the region, and their insight is vital to comprehending what is necessary for future job growth

The demand for local services and infrastructure created by an aging population

Upstate New York, with a growing senior population, is seeing an increase in the number of frail and disabled elderly who rely on local services and infrastructure and are concentrated in the inner cities and older suburbs. While local governments and institutions will face greater pressure to provide services and infrastructure to this expanding segment, the challenge may prove especially difficult for many upstate communities, given their environment of slow economic growth and fiscal stress.

Recent progress on truncated Toeplitz operators

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.Comment: 46 page

Complex symmetric partial isometries

An operator T \in B(\h) is complex symmetric if there exists a conjugate-linear, isometric involution C:\h\to\h so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.Comment: 9 page