Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions

We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it has a noncommutative complex hessian that is positive semidefinite when evaluated on open sets of matrix tuples of sufficiently large size. In this paper, we show that if a noncommutative polynomial is noncommutative plurisubharmonic on a noncommutative open set, then the polynomial is actually noncommutative plurisubharmonic everywhere and has the form p = \sum f_j^T f_j + \sum k_j k_j^T + F + F^T where the sums are finite and f_j, k_j, F are all noncommutative analytic. In the paper by Greene, Helton, and Vinnikov, it is shown that if p is noncommutative plurisubharmonic everywhere, then p has the form above. In other words, the paper by Greene, Helton, and Vinnikov makes a global assumption while the current paper makes a local assumption, but both reach the same conclusion. This paper uses a Gram-like matrix representation of noncommutative polynomials. A careful analysis of this Gram matrix plus the main theorem in the paper by Greene, Helton, and Vinnikov ultimately force the form in the equation above.Comment: 26 page

Pinhole-coronograph tracking control

The pinhole occulter system, a space shuttle based experiment for the production of hard X-ray images taken primarily from the Sun is described. The system is a pinhole camera utilizing a deployable 50 m flexible boom for separating the pinhole from the recording devices located in the shuttle. The system is subjected to the disturbances of the shuttle. The worst of these are thruster firing for orbit correction, man motion, motion induced by other systems, and gravity gradient torques. The control system of the pointing mount senses both position and velocity of the mask tip and uses these to estimate accurately the flexible modes of the system

Socio-spatial analysis of four university campuses: the implications of spatial configuration on creation and transmission of knowledge

An exploratory study of space use, interaction and students? and academics? subjectiveperceptions of interaction and vitality in the four campus sites of the PontificiaUniversidad Católica de Chile (PUC), in Santiago de Chile is presented. The fourcampuses, which differ substantially in their architecture, size and the programmaticnature of the disciplines they house, were modelled as spatial configurations usingspace syntax methods. Observations of patterns of space use and movement werecarried out and a questionnaire survey of staff and students was used to elicit perceptualand reported communication network strengths for both academic staff andstudents. One might expect that, given the twin roles of a university institution in thegeneration of new knowledge and induction of alumni into a ?professional? socialsolidarity, the roles of global and local integration would tend to compete. Globalsegregation in combination with local integration can construct the conditions forstudents to appropriate the open space and generate a powerful local identity at thelevel of the academic unit. However, global integration appears to play an importantrole in making those local solidarities accessible to one another and therefore in thegeneration of new knowledge and solidarities. The data at hand, though exploratoryin nature, suggest that the dynamic is more complex: local identity of the disciplineappears to be a necessary component in the construction of interdisciplinary ?weak?networks at the scale of the institution as a whole

Information Storage in Black Holes

The information loss paradox for Schwarzschild black holes is examined, using the ADS/CFT correspondence extended to the $M_6 (4,2)$ bulk. It is found that the only option compatible with the preservation of the quantum unitarity is when a regular remnant region of the black hole survives to the black hole evaporation process, where information can be stored and eventually retrieved.Comment: 5 pages Latex file, no figures. A honourable mention in the 2005 GRF essay competitio

Offset Active Galactic Nuclei as Tracers of Galaxy Mergers and Supermassive Black Hole Growth

Offset active galactic nuclei (AGNs) are AGNs that are in ongoing galaxy mergers, which produce kinematic offsets in the AGNs relative to their host galaxies. Offset AGNs are also close relatives of dual AGNs. We conduct a systematic search for offset AGNs in the Sloan Digital Sky Survey, by selecting AGN emission lines that exhibit statistically significant line-of-sight velocity offsets relative to systemic. From a parent sample of 18314 Type 2 AGNs at z<0.21, we identify 351 offset AGN candidates with velocity offsets of 50 km/s < |v| < 410 km/s. When we account for projection effects in the observed velocities, we estimate that 4% - 8% of AGNs are offset AGNs. We designed our selection criteria to bypass velocity offsets produced by rotating gas disks, AGN outflows, and gravitational recoil of supermassive black holes, but follow-up observations are still required to confirm our candidates as offset AGNs. We find that the fraction of AGNs that are offset candidates increases with AGN bolometric luminosity, from 0.7% to 6% over the luminosity range 43 < log(L_bol) [erg/s] < 46. If these candidates are shown to be bona fide offset AGNs, then this would be direct observational evidence that galaxy mergers preferentially trigger high-luminosity AGNs. Finally, we find that the fraction of AGNs that are offset AGN candidates increases from 1.9% at z=0.1 to 32% at z=0.7, in step with the growth in the galaxy merger fraction over the same redshift range.Comment: 14 pages, 14 figures, accepted for publication in Ap

“Robbing Peter to Pay Paul”: Economic and Cultural Explanations for How Lower-Income Families Manage Debt

This article builds upon classic economic perspectives of financial behavior by applying the narrative identity perspective of cultural sociology to explain how lower-income families respond to indebtedness. Drawing on in-depth qualitative interviews with 194 lower-income household heads, we show that debt management strategies are influenced by a desire to promote a financially responsible, self-sufficient social identity. Families are reluctant to ask for assistance when faced with economic hardship because it undermines this identity. Because the need to pay on debts is less acute than the need to pay for regular monthly expenses like rent or groceries, debts receive a lower priority in the monthly budget and families typically juggle their debts in private rather than turning to social networks for assistance. In some cases, however, debts take on special meanings and are handled differently. Respondents prioritize debts when they perceive payment as affirming a self-sufficient or upwardly mobile identity, but they reject and ignore debts they view as unfair or unjust. Because the private coping strategies families employ trap them in costly cycles of indebtedness and hinder future mobility prospects, debt management strategies are consequential for long-term financial well-being

Tunneling into the normal state of Pr(2-x)CexCuO4

The temperature dependence of the tunneling conductance was measured for various doping levels of Pr(2-x)CexCuO4 using planar junctions. A normal state gap is seen at all doping levels studied, x=0.11 to x=0.19. We find it to vanish above a certain temperature T*. T* is greater than Tc for the underdoped region and it follows Tc on the overdoped side. This behavior suggests finite pairing amplitude above Tc on the underdoped side