Monetary Perspective On Underground Economic Activity In The United States

There are widespread reports of a growing underground, or unobserved, economy in the United States and in other countries. The unobserved economy seems to develop principally from efforts to evade taxes and government regulation. Although no single definition of such activity has been universally accepted, the term generally refers to activity – whether legal or illegal – generating income that either is underreported or not reported at all (see Chapter 1 in this volume). Some authors narrow the definition to cover income produced in legal activity that is not set down in the recorded national income statistics. Recent discussion of underground economic activity was stimulated by publication of two estimates, one by Gutmann (1977) and the other by Feige (1979), of the size of the underground economy in the United States; these estimates were derived from aggregate monetary statistics. In the ensuing years, numerous other estimates have been made of the underground economy in the United States and in other countries. The magnitude of some of these estimates has prompted congressional hearings and various government studies. In 1979, the Internal Revenue Service (IRS, 1979) estimated that, for 1976, individuals failed to report between $75 billion and$100 billion in income from legal sources and another $25 billion to$35 billion from three types of illegal activity – drugs, gambling, and prostitution. In a more recent study, the IRS estimated that unreported income from legal sources rose from $93.9 billion in 1973 to$249.7 billion in 1981 whereas unreported income from these same three illegal activities rose from $9.3 billion to$34 billion (IRS, 1983)

(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

Level Eulerian Posets

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even order. A condition for verifying shellability is introduced and is automated using the algebra of walks. Applying the Skolem--Mahler--Lech theorem, the ${\bf ab}$-series of a level poset is shown to be a rational generating function in the non-commutative variables ${\bf a}$ and ${\bf b}$. In the case the poset is also Eulerian, the analogous result holds for the ${\bf cd}$-series. Using coalgebraic techniques a method is developed to recognize the ${\bf cd}$-series matrix of a level Eulerian poset

Engineering of spin-lattice relaxation dynamics by digital growth of diluted magnetic semiconductor CdMnTe

The technological concept of "digital alloying" offered by molecular-beam epitaxy is demonstrated to be a very effective tool for tailoring static and dynamic magnetic properties of diluted magnetic semiconductors. Compared to common "disordered alloys" with the same Mn concentration, the spin-lattice relaxation dynamics of magnetic Mn ions has been accelerated by an order of magnitude in (Cd,Mn)Te digital alloys, without any noticeable change in the giant Zeeman spin splitting of excitonic states, i.e. without effect on the static magnetization. The strong sensitivity of the magnetization dynamics to clustering of the Mn ions opens a new degree of freedom for spin engineering.Comment: 9 pages, 3 figure