Nonperturbative results for the mass dependence of the QED fermion determinant

The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the determinant's nonperturbative part is fixed by the anomaly. It is also shown that for a large class of such fields there is at least one value of the fermion mass at which the determinant's nonperturbative part reduces to its noninteracting value.Comment: This is an extended version of the author's paper in Phys.Rev.D81(2010)10770

Navigating Troubled Waters: Dealing with Personal Values When Representing Others

Legal academics have long struggled to define the appropriate role a lawyer\u27s moral judgment ought to play in client representation. In its simplest terms, the question is: Must a lawyer be a hired gun, seeking all lawful objectives sought by a client, or may a lawyer act independently to avoid the harm a client\u27s actions will cause innocent parties? Following disclosure of lawyer involvement in the Savings and Loan, Enron and WorldCom failures, many in society joined those scholars calling for greater moral responsibility. In this article, I provide an analytical approach consistent with existing law and practice that seeks to find a place for an individual lawyer\u27s moral principles. Lawyers, particularly new lawyers, need to know just how much discretion they will have to follow their consciences. Understanding the limits on one\u27s moral discretion will affect the way a lawyer practices and should influence her choice of practice environment. Prior to accepting a position, a lawyer should know whether she will be comfortable with the prevailing standards of practice

Book Review

Review of: MARC A. RODWIN, MEDICINE, MONEY & MORALS: PHYSICIANS\u27 CONFLICTS OF INTEREST. (Oxford University Press 1993). [430 pp.] Acknowledgements, acronyms, appendices, foreword, index, notes. LC: 92-49488; ISBN: 0-19-508096-3. [Cloth $25.00. 200 Madison Avenue, New York NY 10016.

Decision feedback loop for tracking a polyphase modulated carrier

A multiple phase modulated carrier tracking loop for use in a frequency shift keying system is described in which carrier tracking efficiency is improved by making use of the decision signals made on the data phase transmitted in each T-second interval. The decision signal is used to produce a pair of decision-feedback quadrature signals for enhancing the loop's performance in developing a loop phase error signal

Subdegree growth rates of infinite primitive permutation groups

A transitive group $G$ of permutations of a set $\Omega$ is primitive if the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. If $\alpha \in \Omega$, then the orbits of the stabiliser $G_\alpha$ on $\Omega$ are called the $\alpha$-suborbits of $G$; when $G$ acts transitively the cardinalities of these $\alpha$-suborbits are the subdegrees of $G$. If $G$ acts primitively on an infinite set $\Omega$, and all the suborbits of $G$ are finite, Adeleke and Neumann asked if, after enumerating the subdegrees of $G$ as a non-decreasing sequence $1 = m_0 \leq m_1 \leq ...$, the subdegree growth rates of infinite primitive groups that act distance-transitively on locally finite distance-transitive graphs are extremal, and conjecture there might exist a number $c$ which perhaps depends upon $G$, perhaps only on $m$, such that $m_r \leq c(m-2)^{r-1}$. In this paper it is shown that such an enumeration is not desirable, as there exist infinite primitive permutation groups possessing no infinite subdegree, in which two distinct subdegrees are each equal to the cardinality of infinitely many suborbits. The examples used to show this provide several novel methods for constructing infinite primitive graphs. A revised enumeration method is then proposed, and it is shown that, under this, Adeleke and Neumann's question may be answered, at least for groups exhibiting suitable rates of growth.Comment: 41 page

Introduction to a Resources Special Issue on Criticality of the Rare Earth Elements: Current and Future Sources and Recycling

The rare earth elements (REE) are vital to modern technologies and society and are amongst the most important of the critical elements. This special issue of Resources examines a number of facets of these critical elements, current and future sources of the REE, the mineralogy of the REE, and the economics of the REE sector. These papers not only provide insights into a wide variety of aspects of the REE, but also highlight the number of different areas of research that need to be undertaken to ensure sustainable and secure supplies of these critical metals into the future