A closer look at semistability for singular principal bundles

We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure of a rational principal bundle in the sense of Ramanathan. Moreover, we arrive at a much simpler semistability condition. In the case of a semisimple group, this is just the Gieseker-version of Ramanathan's semistability condition for the corresponding rational principal $G$-bundle.Comment: To appear in the International Mathematics Research Notices. V2: Minor correction

Global Boundedness for Decorated Sheaves

An important classification problem in Algebraic Geometry deals with pairs (\E,\phi), consisting of a torsion free sheaf \E and a non-trivial homomorphism \phi\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes \L on a polarized complex projective manifold (X,\O_X(1)), the input data $a$, $b$, $c$, \L as well as the Hilbert polynomial of \E being fixed. The solution to the classification problem consists of a family of moduli spaces ${\cal M}^\delta:={\cal M}^{\delta-\rm ss}_{a/b/c/L/P}$ for the $\delta$-semistable objects, where \delta\in\Q[x] can be any positive polynomial of degree at most $\dim X-1$. In this note we show that there are only finitely many distinct moduli spaces among the ${\cal M}^\delta$ and that they sit in a chain of "GIT-flips". This property has been known and proved by ad hoc arguments in several special cases. In our paper, we apply refined information on the instability flag to solve this problem. This strategy is inspired by the fundamental paper of Ramanan and Ramanathan on the instability flag.Comment: To appear in the International Mathematics Research Notices. V2: A few typos corrected (notably in the definition of semistability in the introduction); Expanded Introductio

Investigation of the enhanced spatial density of submicron lunar ejecta between L values 1.2 and 3.0 in the earth's magnetosphere: Theory

Initial results from the measurement conducted by the dust particle experiment on the lunar orbiting satellite Lunar Explorer 35 (LE 35) were reported with the data interpreted as indicating that the moon is a significant source of micrometeroids. Primary sporadic and stream meteoroids impacting the surface of the moon at hypervelocity was proposed as the source of micron and submicron particles that leave the lunar craters with velocities sufficient to escape the moon's gravitational sphere of influence. No enhanced flux of lunar ejecta with masses greater than a nanogram was detected by LE 35 or the Lunar Orbiters. Hypervelocity meteoroid simulation experiments concentrating on ejecta production combined with extensive analyses of the orbital dynamics of micron and submicron lunar ejecta in selenocentric, cislunar, and geocentric space have shown that a pulse of these lunar ejecta, with a time correlation relative to the position of the moon relative to the earth, intercepts the earth's magnetopause surface (EMPs). As shown, a strong reason exists for expecting a significant enhancement of submicron dust particles in the region of the magnetosphere between L values of 1.2 and 3.0. This is the basis for the proposal of a series of experiments to investigate the enhancement or even trapping of submicron lunar ejecta in this region. The subsequent interaction of this mass with the upper-lower atmosphere of the earth and possible geophysical effects can then be studied

Presence of atrial natriuretic factor prohormone in enterochromaffin cells of the human large intestine

Atrial natriuretic factor is a hormone intimately involved in water and salt homeostasis. The heart constitutes the major but not exclusive site of synthesis of this hormone. Among other functions, the gastrointestinal tract has endocrine functions, plays an important role in volume regulation of the body, and seems to be a target organ for atrial natriuretic factor. Therefore, the presence of atrial natriuretic factor was investigated in the human gut. Immunoreactive atrial natriuretic factor was found in intraoperatively obtained samples of normal human colon. Acidic extracts of human large intestine contained about 0.4 pmol/g wet wt of atrial natriuretic factor. Analysis of atrial natriuretic factor immunoreactivity by gel-filtration and reverse-phase high-performance liquid chromatography showed that about 65% of the immunoreactivity corresponded to the atrial natriuretic factor phohormone and about 35% corresponded to the C-terminal ANF99-126. Immunohistochemistry showed atrial natriuretic factor prohormone location in enterochromaffin cells of the colon mucosa. Altogether, these findings show the presence of atrial natriuretic factor prohormone in enterochromaffin cells of the human large intestine and may suggest this organ as a site of atrial natriuretic factor synthesis in humans

Simple quantum feedback of a solid-state qubit

We propose an experiment on quantum feedback control of a solid-state qubit, which is almost within the reach of the present-day technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent (Rabi) oscillations in a qubit for an arbitrary long time; however, this is done in a significantly simpler way, which requires much smaller bandwidth of the control circuitry. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of qubit oscillations. The price for simplicity is a less-than-ideal operation: the fidelity is limited by about 95%. The feedback loop operation can be experimentally verified by appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization.Comment: 5 page

Equivalence of the Ehrenfest Theorem and the Fluid-rotor Model for Mixed Quantum/Classical Theory of Collisional Energy Transfer

The theory of two seemingly different quantum/classical approaches to collisional energy transfer and ro-vibrational energy flow is reviewed: a heuristic fluid-rotor method, introduced earlier to treat recombination reactions[M. Ivanov and D. Babikov, J. Chem. Phys.134, 144107 (Year: 2011)10.1063/1.3576103], and a more rigorous method based on the Ehrenfest theorem. It is shown analytically that for the case of a diatomic molecule + quencher these two methods are entirely equivalent. Notably, they both make use of the average moment of inertia computed as inverse of average of inverse of the distributed moment of inertia. Despite this equivalence, each of the two formulations has its own advantages, and is interesting on its own. Numerical results presented here illustrate energy and momentum conservation in the mixed quantum/classical approach and open opportunities for computationally affordable treatment of collisional energy transfer

Indenture as a Self-Enforced Contract Device: An Experimental Test

We experimentally test the efficacy of indenture as a self-enforced contract device. In an indenture game, the principal signals the intention of payment-on-delivery, by tearing a banknote and giving the agent half of it as "prepayment"; the agent receives the completing half after delivering the service. By forward induction, cooperation is incentive-compatibly self-enforcing. The indenture performs very well, inducing a significantly higher level of cooperation than that in a three-stage centipede game, which we use to benchmark the natural rate of cooperation. The difference between cooperation rates in both games increases over time.Cooperation, experiment, contracts, indenture, reciprocity

Synchro-Betatron Stop-Bands due to a Single Crab Cavity

We analyze the stop-band due to crab cavities for horizontal tunes that are either close to integers or close to half integers. The latter case is relevant for today's electron/positron colliders. We compare this stop-band to that created by dispersion in an accelerating cavity and show that a single typical crab cavity creates larger stop-bands than a typical dispersion at an accelerating cavity. We furthermore analyze whether it is beneficial to place the crab cavity at a position where the dispersion and its slope vanish. We find that this choice is worth while if the horizontal tune is close to a half integer, but not if it is close to an integer. Furthermore we find that stop-bands can be avoided when the horizontal tune is located at a favorable side of the integer or the half integer. While we are here concerned with the installation of a single crab cavity in a storage ring, we show that the stop-bands can be weakened, although not eliminated, significantly when two crab cavities per ring are chosen suitably.Comment: 7 pages, 9 figure

The Economics of Solidarity: A Conceptual Framework

For many people "solidarity" has become a meaningless word used in slogans - too often used without leading to any economic consequences. We show in this paper conditions under which solidarity can be a powerful instrument. In a solidary action, an individual in a group contributes to a series of actions that aims for a reallocation of scarce resources. The willingness to contribute is mainly influenced by the efficiency of the objective of the solidary action, and is enhanced by feelings of mutual exchange (solidarity) within a group. --solidarity,altruism,dynamic,mutual

CARETS: A prototype regional environmental information system. Volume 7: Land use information and air quality planning

The author has identified the following significant results. The pilot air quality system provided data for updating information on the sources of point and area emissions of SO2 and particulate matter affecting the Norfolk-Portsmouth area of Virginia for 1971-72 winter and the annual 1972 period. During the 1971-72 winter, estimated SO2 amounts over an area with a SW-NE axis in the central section of Norfolk exceeded both primary and secondary levels