Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Ana

Wavelets for iterated function systems

We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions generalising in this way some previous work of Jorgensen and Dutkay to the non-linear setting.Comment: 17 pages, 3 figure

Macroeconomic Policy Advice and the Article IV Consultations: A European Union Case Study

The IMF makes policy recommendations to European countries through its Article IV consultations and resulting papers. This paper examines IMF policy recommendations to see whether they have contributed to the ongoing crisis in Europe, and also how they might affect other European Union goals such as those of Europe 2020, which seeks to reduce social exclusion, promote public investment in research and development, and promote employment and education.The paper examines the policy advice given by the IMF to European Union countries in 67 Article IV agreements for the four years 2008-2011 (IMF 2012c).Content analysis finds a consistent pattern of policy recommendations, which indicates (1) a macroeconomic policy that focuses on reducing spending and shrinking the size of government, in many cases regardless of whether this is appropriate or necessary, or may even exacerbate an economic downturn; and (2) a focus on other policy issues that would tend to reduce social protections for broad sectors of the population (including public pensions, health care, and employment protections), reduce labor's share of national income, and possibly increase poverty, social exclusion, and economic and social inequality as a result.Europe remains mired in its second recession in three years, and the International Monetary Fund's (IMF's) most recent (October 2012) World Economic Outlook (WEO) sees its problems as perhaps the most important drag on world economic growth. The IMF is also part of the so-called "troika" -- with the European Commission (EC) and European Central Bank (ECB) that has been deciding or strongly influencing economic policy in the eurozone, as well as affecting policy in the rest of the European Union, especially since the world economic crisis and recession of 2008-2009. This paper raises questions as to whether the IMF's policy advice has contributed to the ongoing economic problems in Europe

In-Class Hard-Copy Worksheets

This teaching practice is the use of hard-copy in-class worksheets for guided note taking and simple practice exercises primarily targeted for lower division classes. The worksheets are done in hard-copy requiring the student to actually write an answer which helps reinforce the topic or concept. All answers are provided to the students (either as part of the lecture or after a brief discussion). As such, the worksheets help highlight key topics and familiarize the students with how questions on the topic are asked and how they should be answered. Depending on the topic, most worksheets include simple exercises which are completed in class. Such exercises are typically worked at the end of class and students are allowed and encouraged to work together and help each other as needed to ensure they understand the problem and the approach used to obtain the solution. This encourages peer-to-peer interaction especially when a student is unclear regarding how to approach the problem. Based on availability, the Teaching Assistant (TA) is often in class to help students which provides an introduction to the class TA which facilitates follow on questions regarding the more complex assignments. This addresses a common issue in technical classes where a student feels they understand the material yet lack the experience in applying such knowledge to practical problems. In all cases the final correct answer is provided. The worksheets provide key additional study material for tests. As the semester progresses, students are able to gain experience and build confidence applying skills to practical problems prior to test situations. Additionally, the worksheets provide an informal attendance mechanism allowing attendance to be tracked and encouraged in a more meaningful manner.https://digitalscholarship.unlv.edu/btp_expo/1102/thumbnail.jp

Recognizing dualizing complexes

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A \ltimes M is a Gorenstein Differential Graded Algebra. As a corollary follows that A has a dualizing complex if and only if it is a quotient of a Gorenstein local Differential Graded Algebra.Comment: 9 pages. To appear in Fundamenta Mathematica