Analytic Continuation of Dirichlet Series with Almost Periodic Coefficients

We consider Dirichlet series ζ[subscript g,α](s)=∑[∞ over n=1]g(nα)e[superscript −λ[subscript n]s] for fixed irrational α and periodic functions g. We demonstrate that for Diophantine α and smooth g, the line Re(s) = 0 is a natural boundary in the Taylor series case λ[subscript n] = n, so that the unit circle is the maximal domain of holomorphy for the almost periodic Taylor series ∑[∞ over n=1]g(nα)z[superscript n] . We prove that a Dirichlet series ζ[subscript g,α](s)=∑[∞ over n=1](nα)/n[superscript s] has an abscissa of convergence σ[subscript 0] = 0 if g is odd and real analytic and α is Diophantine. We show that if g is odd and has bounded variation and α is of bounded Diophantine type r, the abscissa of convergence σ[subscript 0] satisfies σ[subscript 0] ≤ 1 − 1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and α is Diophantine, then the Dirichlet series ζ[subscript g,α](s) has an analytic continuation to the entire complex plane

Property Rights and the Nature of the Firm

This paper provides a framework for addressing the question of when transactions should be carried out within a firm and when through the market. Following Grossman and Hart, we identify a firm with the assets that its owners control. We argue that the crucial difference for party 1 between owning a firm (integration) and contracting for a service from another party 2 who owns this firm (nonintegration) is that, under integration, party 1 can selectively fire the workers of the firm (including party 2), whereas under nonintegration he can "fire" (i.e., stop dealing with) only the entire firm: the combination of party 2, the workers, and the firm's assets. We use this idea to study how changes in ownership affect the incentives of employees as well as those of owner-managers. Our frame- work is broad enough to encompass more general control structures than simple ownership: for example, partnerships and worker and consumer cooperatives all emerge as special cases.Economic

Resting state correlates of subdimensions of anxious affect

Resting state fMRI may help identify markers of risk for affective disorder. Given the comorbidity of anxiety and depressive disorders and the heterogeneity of these disorders as defined by DSM, an important challenge is to identify alterations in resting state brain connectivity uniquely associated with distinct profiles of negative affect. The current study aimed to address this by identifying differences in brain connectivity specifically linked to cognitive and physiological profiles of anxiety, controlling for depressed affect. We adopted a two-stage multivariate approach. Hierarchical clustering was used to independently identify dimensions of negative affective style and resting state brain networks. Combining the clustering results, we examined individual differences in resting state connectivity uniquely associated with subdimensions of anxious affect, controlling for depressed affect. Physiological and cognitive subdimensions of anxious affect were identified. Physiological anxiety was associated with widespread alterations in insula connectivity, including decreased connectivity between insula subregions and between the insula and other medial frontal and subcortical networks. This is consistent with the insula facilitating communication between medial frontal and subcortical regions to enable control of physiological affective states. Meanwhile, increased connectivity within a frontoparietal-posterior cingulate cortex-precunous network was specifically associated with cognitive anxiety, potentially reflecting increased spontaneous negative cognition (e.g., worry). These findings suggest that physiological and cognitive anxiety comprise subdimensions of anxiety-related affect and reveal associated alterations in brain connectivity

HST ultraviolet spectral energy distributions for three ultraluminous infrared galaxies

We present HST Faint Object Camera ultraviolet (230 nm and 140 nm) images of three ultraluminous infrared galaxies (ULIG: L_ir > 10^12 L_sun) selected from the IRAS Revised Bright Galaxy Sample. The purpose is to estimate spectral energy distributions (SEDs) to facilitate the identification of similar objects at high redshift in deep optical, infrared, and submm surveys. All three galaxies (VII Zw031 = IRAS F12112+0305, and IRAS F22491-1808) were well detected at 230 nm. Two of the three were marginally detected at 140 nm. The fluxes, together with ground-based optical and infrared photometry, are used to compute SEDs over a wide wavelength range. The measured SEDs drop from the optical to the ultraviolet, but the magnitude of the drop ranges from a factor of ~3 in IRAS F22491-1808 to a factor of ~100 in VIIZw031. This is most likely due to different internal extinctions. Such an interpretation is also suggested by extrapolating to ultraviolet wavelengths the optical internal extinction measured in VIIZw031. K-corrections are calculated to determine the colors of the sample galaxies as seen at high redshifts. Galaxies like VIIZw031 have very low observed rest-frame UV fluxes which means that such galaxies at high redshift will be extremely red or even missing in optical surveys. On the other hand, galaxies like IRAS F12112+0305 and IRAS F22491-1808, if seen at high redshift, would be sufficiently blue that they would not easily be distinguished from normal field galaxies, and therefore, identified as ULIGs. The implication is then that submillimeter surveys may be the only means of properly identifying the majority of ULIGs at high redshift.Comment: AJ in press, TeX, 23 pages, 7 tab, 17 figs available also (at higher resolution) from http://www.ast.cam.ac.uk~trentham/ufigs.htm

Three view electronically scanned interferometer for plasma electron density measurements on the H-1 heliac

We report the development of a three view electronically scanned millimeter-wave interferometer for plasma electron density profile measurement on the H-1 heliac. The system utilizes an electronically tunable backward-wave oscillator whose output is incident on a fixed blazed diffraction grating such that sweeping the source frequency effects a spatial scan of the plasma cross section. Two diagonal views essentially span most of the plasma cross section, while the horizontal arm views the lower half of the plasma. The diffracted beams traverse the plasma in <1ms with a spatial resolution ∼20mm. A study of the density projection dependence on magnetic configuration shows that the presence of low-order rational surfaces in the plasma gives rise to sharp density gradients in the vicinity of the surface