Sum of Two Squares - Pair Correlation and Distribution in Short Intervals

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poissonian distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above stated result, may by generalized to other binary quadratic forms. While producing these pair correlation conjectures we arrive at a surprising result regarding Mertens' formula for primes in arithmetic progressions, and in order to test the validity of the conjectures, we present numericalz computations which support our approach.Comment: 3 figure

Revealing local failed supernovae with neutrino telescopes

We study the detectability of neutrino bursts from nearby direct black hole-forming collapses (failed supernovae) at Megaton detectors. Due to their high energetics, these bursts could be identified - by the time coincidence of N >= 2 or N >= 3 events within a ~ 1 s time window - from as far as ~ 4-5 Mpc away. This distance encloses several supernova-rich galaxies, so that failed supernova bursts could be detected at a rate of up to one per decade, comparable to the expected rate of the more common, but less energetic, neutron star-forming collapses. Thus, the detection of a failed supernova within the lifetime of a Mt detector is realistic. It might give the first evidence of direct black hole formation, with important implications on the physics of this phenomenon.Comment: LaTeX, 4 pages, 4 figures; minor changes to the text, results unchange

On the He(plus) triplet line intensities

The theoretical calculations of helium triplet line strengths, including collisional enhancement, are compared to astronomical observations. Both are plotted on an I(10830)/I(5876) vs I(5876)/I(4471) plane. It appears that the theory of helium triplet line strengths agrees with present observations, and that the question of an additional depopulation mechanism for the 2 3S population is probably predicted correctly within 30%

A plausible energy source and structure for quasi-stellar objects

If a collision of two large, massive, fast gas clouds occurs, their kinetic energy is converted to radiation in a pair of shock fronts at their interface. The resulting structure is described, and the relevance of this as a radiation source for quasi-stellar objects is considered

Benchmarking the performance of Density Functional Theory and Point Charge Force Fields in their Description of sI Methane Hydrate against Diffusion Monte Carlo

High quality reference data from diffusion Monte Carlo calculations are presented for bulk sI methane hydrate, a complex crystal exhibiting both hydrogen-bond and dispersion dominated interactions. The performance of some commonly used exchange-correlation functionals and all-atom point charge force fields is evaluated. Our results show that none of the exchange-correlation functionals tested are sufficient to describe both the energetics and the structure of methane hydrate accurately, whilst the point charge force fields perform badly in their description of the cohesive energy but fair well for the dissociation energetics. By comparing to ice Ih, we show that a good prediction of the volume and cohesive energies for the hydrate relies primarily on an accurate description of the hydrogen bonded water framework, but that to correctly predict stability of the hydrate with respect to dissociation to ice Ih and methane gas, accuracy in the water-methane interaction is also required. Our results highlight the difficulty that density functional theory faces in describing both the hydrogen bonded water framework and the dispersion bound methane.Comment: 8 pages, 4 figures, 1 table. Minor typos corrected and clarification added in Method

A conceptual design study for the secondary mirror drive of the shuttle infrared telescope facility (SIRTF)

Various conceptual designs for the secondary mirror actuator system to be used in the Shuttle Infrared Telescope Facility (SIRTF) were evaluated. In addition, a set of design concepts was developed to assist in the solution of problems crucial for optimum performance of the secondary mirror actuator system. A specific conceptual approach was presented along with a plan for developing that approach and identifying issues of critical importance in the developmental effort

Hyperopic Cops and Robbers

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in $[0,1/2].

Cell surface localization of tissue transglutaminase is dependent on a fibronectin-binding site in its N-terminal beta-sandwich domain

Increasing evidence indicates that tissue transglutaminase (tTG) plays a role in the assembly and remodeling of extracellular matrices and promotes cell adhesion. Using an inducible system we have previously shown that tTG associates with the extracellular matrix deposited by stably transfected 3T3 fibroblasts overexpressing the enzyme. We now show by confocal microscopy that tTG colocalizes with pericellular fibronectin in these cells, and by immunogold electron microscopy that the two proteins are found in clusters at the cell surface. Expression vectors encoding the full-length tTG or a N-terminal truncated tTG lacking the proposed fibronectin-binding site (fused to the bacterial reporter enzyme β-galactosidase) were generated to characterize the role of fibronectin in sequestration of tTG in the pericellular matrix. Enzyme-linked immunosorbent assay style procedures using extracts of transiently transfected COS-7 cells and immobilized fibronectin showed that the truncation abolished fibronectin binding. Similarly, the association of tTG with the pericellular matrix of cells in suspension or with the extracellular matrix deposited by cell monolayers was prevented by the truncation. These results demonstrate that tTG binds to the pericellular fibronectin coat of cells via its N-terminal β-sandwich domain and that this interaction is crucial for cell surface association of tTG