Locally Finite Families, Completely Separated Sets and Remote Points

It is shown that if X is a nonpseudocompact space with a σ-locally finite π-base, then X has remote points. Within the class of spaces possessing a σ-locally finite π-base, this result extends the work of Chae and Smith, because their work utilized normality to achieve complete separation. It provides spaces which have remote points, where the spaces do not satisfy the conditions required in the previous works by Dow, by van Douwen, by van Mill, or by Peters. The lemma: Let X be a space and let {Cε: € \u3c α} be a locally finite family of cozero sets of X. Let {Zε: € \u3c α } be a family of zero sets of X such that for each € \u3c α, Zε с Cε. Then ∪ε\u3cα Zε is completely separated from X/∪εCε , is a fundamental tool in this work. An example is given which demonstrates the value of this tool. The example also refutes an appealing conjecture -- a conjecture for which the authors found that there existed significant confusion within the topological community as to its truth or falsity

Constraints on the Formation and Evolution of Circumstellar Disks in Rotating Magnetized Cloud Cores

We use magnetic collapse models to place some constraints on the formation and angular momentum evolution of circumstellar disks which are embedded in magnetized cloud cores. Previous models have shown that the early evolution of a magnetized cloud core is governed by ambipolar diffusion and magnetic braking, and that the core takes the form of a nonequilibrium flattened envelope which ultimately collapses dynamically to form a protostar. In this paper, we focus on the inner centrifugally-supported disk, which is formed only after a central protostar exists, and grows by dynamical accretion from the flattened envelope. We estimate a centrifugal radius for the collapse of mass shells within a rotating, magnetized cloud core. The centrifugal radius of the inner disk is related to its mass through the two important parameters characterizing the background medium: the background rotation rate \Omb and the background magnetic field strength \Bref. We also revisit the issue of how rapidly mass is deposited onto the disk (the mass accretion rate) and use several recent models to comment upon the likely outcome in magnetized cores. Our model predicts that a significant centrifugal disk (much larger than a stellar radius) will be present in the very early (Class 0) stage of protostellar evolution. Additionally, we derive an upper limit for the disk radius as it evolves due to internal torques, under the assumption that the star-disk system conserves its mass and angular momentum even while most of the mass is transferred to a central star.Comment: 23 pages, 1 figure, aastex, to appear in the Astrophysical Journal (10 Dec 1998

A Spherical Model for "Starless" Cores of Magnetic Molecular Clouds and Dynamical Effects of Dust Grains

In the standard picture of isolated star formation, dense ``starless'' cores are formed out of magnetic molecular clouds due to ambipolar diffusion. Under the simplest spherical geometry, I demonstrate that ``starless'' cores formed this way naturally exhibit a large scale inward motion, whose size and speed are comparable to those detected recently by Taffala et al. and Williams et al. in ``starless'' core L1544. My model clouds have a relatively low mass (of order 10 $M_\odot$) and low field strength (of order 10 $\mu$G) to begin with. They evolve into a density profile with a central plateau surrounded by a power-law envelope, as found previously. The density in the envelope decreases with radius more steeply than those found by Mouschovias and collaborators for the more strongly magnetized, disk-like clouds. At high enough densities, dust grains become dynamically important by greatly enhancing the coupling between magnetic field and the neutral cloud matter. The trapping of magnetic flux associated with the enhanced coupling leads, in the spherical geometry, to a rapid assemblage of mass by the central protostar, which exacerbates the so-called ``luminosity problem'' in star formation.Comment: 27 pages, 4 figures, accepted by Ap

Rotation and X-ray emission from protostars

The ASCA satellite has recently detected variable hard X-ray emission from two Class I protostars in the rho Oph cloud, YLW15 (IRS43) and WL6, with a characteristic time scale ~20h. In YLW15, the X-ray emission is in the form of quasi-periodic energetic flares, which we explain in terms of strong magnetic shearing and reconnection between the central star and the accretion disk. In WL6, X-ray flaring is rotationally modulated, and appears to be more like the solar-type magnetic activity ubiquitous on T Tauri stars. We find that YLW15 is a fast rotator (near break-up), while WL6 rotates with a significantly longer period. We derive a mass M_\star ~ 2 M_\odot and \simlt 0.4 M_\odot for the central stars of YLW15 and WL6 respectively. On the long term, the interactions between the star and the disk results in magnetic braking and angular momentum loss of the star. On time scales t_{br} ~ a few 10^5 yrs, i.e., of the same order as the estimated duration of the Class~I protostar stage. Close to the birthline there must be a mass-rotation relation, t_{br} \simpropto M_\star, such that stars with M_\star \simgt 1-2 M_\odot are fast rotators, while their lower-mass counterparts have had the time to spin down. The rapid rotation and strong star-disk magnetic interactions of YLW15 also naturally explain the observation of X-ray ``superflares''. In the case of YLW15, and perhaps also of other protostars, a hot coronal wind (T~10^6 K) may be responsible for the VLA thermal radio emission. This paper thus proposes the first clues to the rotation status and evolution of protostars.Comment: 13 pages with 6 figures. To be published in ApJ (April 10, 2000 Part 1 issue

Cyclotron motion in graphene

We investigate cyclotron motion in graphene monolayers considering both the full quantum dynamics and its semiclassical limit reached at high carrier energies. Effects of zitterbewegung due to the two dispersion branches of the spectrum dominate the irregular quantum motion at low energies and are obtained as a systematic correction to the semiclassical case. Recent experiments are shown to operate in the semiclassical regime.Comment: 6 pages, 1 figure include

Association Between Urinary Markers of Nucleic Acid Oxidation and Mortality in Type 2 Diabetes:A population-based cohort study

OBJECTIVE: We recently showed that RNA oxidation, estimated by urinary excretion of 8-oxo-7,8-dihydroguanosine (8-oxoGuo), independently predicted mortality in a cohort of 1,381 treatment-naive patients with newly diagnosed type 2 diabetes. In the present investigation, we analyzed urine collected 6 years after the diagnosis to assess the association between urinary markers of nucleic acid oxidation and mortality in patients with established and treated diabetes. RESEARCH DESIGN AND METHODS: We used data from the 970 patients who attended the screening for diabetes complications 6 years after the diagnosis. Cox proportional hazards regression was used to examine the relationship between urinary markers of DNA oxidation (8-oxo-7,8-dihydro-2′-deoxyguanosine [8-oxodG] [n = 938]) and RNA oxidation (8-oxoGuo [n = 936]) and mortality. RESULTS: During a median of 9.8 years of follow-up, 654 patients died. Urinary 8-oxoGuo assessed 6 years after the diagnosis was significantly associated with mortality. The multivariate-adjusted hazard ratios for all-cause and diabetes-related mortality of patients with 8-oxoGuo levels in the highest quartile compared with those in the lowest quartile were 1.86 (95% CI 1.34–2.58) and 1.72 (1.11–2.66), respectively. Conversely, 8-oxodG was not associated with mortality. In addition, we found an association between changes in 8-oxoGuo from diagnosis to 6-year follow-up and mortality, with increased risk in patients with an increase and decreased risk in patients with a decrease in 8-oxoGuo. CONCLUSIONS: The RNA oxidation marker 8-oxoGuo is an independent predictor of mortality in patients with established and treated type 2 diabetes, and changes in 8-oxoGuo during the first 6 years after diagnosis are associated with mortality

Interestingness of traces in declarative process mining: The janus LTLPf Approach

Declarative process mining is the set of techniques aimed at extracting behavioural constraints from event logs. These constraints are inherently of a reactive nature, in that their activation restricts the occurrence of other activities. In this way, they are prone to the principle of ex falso quod libet: they can be satisfied even when not activated. As a consequence, constraints can be mined that are hardly interesting to users or even potentially misleading. In this paper, we build on the observation that users typically read and write temporal constraints as if-statements with an explicit indication of the activation condition. Our approach is called Janus, because it permits the specification and verification of reactive constraints that, upon activation, look forward into the future and backwards into the past of a trace. Reactive constraints are expressed using Linear-time Temporal Logic with Past on Finite Traces (LTLp f). To mine them out of event logs, we devise a time bi-directional valuation technique based on triplets of automata operating in an on-line fashion. Our solution proves efficient, being at most quadratic w.r.t. trace length, and effective in recognising interestingness of discovered constraints

Relaxation of a Collisionless System and the Transition to a New Equilibrium Velocity Distribution

In this paper, we present our conclusions from the numerical study of the collapse of a destabilized collisionless stellar system. We use both direct integration of the Vlasov-Poisson equations and an N-body tree code to obtain our results, which are mutually confirmed. We find that spherical and moderately nonspherical collapse configurations evolve to new equilibrium configurations in which the velocity distribution approaches a Gaussian form, at least in the central regions. The evolution to this state has long been an open question, and in this work we are able to clarify the process responsible and to support predictions made from statistical considerations (Lynden-Bell 1967; Nakamura 2000). The simulations of merging N-body systems show a transition to a Gaussian velocity distribution that is increasingly suppressed as the initial separation of centres is increased. Possible reasons for this are discussed.Comment: 25 pages, LaTeX. Accepted for publication in Ap