Basic Relevant Theories for Combinators at Levels I and II

The system B+ is the minimal positive relevant logic. B+ is trivially extended to B+T on adding a greatest truth (Church constant) T. If we leave ∨ out of the formation apparatus, we get the fragment B∧T. It is known that the set of ALL B∧T theories provides a good model for the combinators CL at Level-I, which is the theory level. Restoring ∨ to get back B+T was not previously fruitful at Level-I, because the set of all B+T theories is NOT a model of CL. It was to be expected from semantic completeness arguments for relevant logics that basic combinator laws would hold when restricted to PRIME B+T theories. Overcoming some previous difficulties, we show that this is the case, at Level I. But this does not form a model for CL. This paper also looks for corresponding results at Level-II, where we deal with sets of theories that we call propositions. We adapt work by Ghilezan to note that at Level-II also there is a model of CL in B∧T propositions. However, the corresponding result for B+T propositions extends smoothly to Level-II only in part. Specifically, only some of the basic combinator laws are proved here. We accordingly leave some work for the reader.&nbsp

Influence of a humidor on the aerodynamics of baseballs

We investigate whether storing baseballs in a controlled humidity environment significantly affects their aerodynamic properties. To do this, we measure the change in diameter and mass of baseballs as a function of relative humidity (RH) in which the balls are stored. We then model trajectories for pitched and batted baseballs to assess the difference between those stored at 30% RH versus 50% RH. The results show that a drier baseball may be expected to curve slightly more than a humidified one for a given pitch velocity. We also find that the aerodynamics alone would add ~2 feet to the distance a moister ball is hit. However, this is compensated by a ~6 foot reduction in batted distance due to the well known change in coefficient of restitution of the ball. We discuss consequences of these results for baseball played at Coors Field in Denver, where baseballs have been stored in a humidor at 50% RH since 2002.Comment: 21 pages, 7 figures, modified and re-posted 2/2

Length of Need and Minimum System Length for F-Shape Portable Concrete Barrier

Portable concrete barrier (PCB) systems are often used to redirect errant vehicles through a combination of inertial resistance, lateral friction loads, and tensile loads developed from the mass and friction of the barrier segments. State departments of transportation (DOTs) and other end users may wish to utilize minimal length PCB installations to shield a hazard or work zone or limit the number of barriers required on the upstream and downstream ends to reduce overall system length. However, concerns with the performance of shorter PCB installations include increased lateral deflections and working widths and barrier pocketing. Additionally, no impact testing has been performed near the upstream or downstream ends of the free-standing PCB system to determine the limits of the length of need (LON) of the system. These impacts may increase the potential for gating through the system, pocketing, rapid deceleration, and/or vehicle instability. The objective of this research study was to investigate and evaluate the safety performance of a previously developed F-shape PCB system to determine minimum system length and the number of barriers required for the beginning and end of the LON. LS-DYNA simulation modeling was applied to determine potential beginning and end of LON points on reduced system lengths to select a configuration for full-scale testing and evaluation of a minimum length PCB system. A 100-ft long PCB installation was selected, and full-scale crash testing was conducted on the beginning and end of LON of the reduced length system. Test no. NELON-1 was conducted to MASH test designation 3-35 criteria on the beginning of LON of the 100-ft long PCB installation, and the vehicle was safely redirected. Test no. NELON-2 was conducted to modified MASH test designation no. 3-37 criteria on the end of LON of the 100-ft long PCB installation, but the test was deemed a failure as the vehicle demonstrated a roll angle in excess of 75 degrees. Review of the crash test results suggested that a nine barrier or 112.5-ft long PCB installation would perform acceptably

Basic Relevant Theories for Combinators at Levels I and II

The system B+ is the minimal positive relevant logic. B+ is trivially extended to B+T on adding a greatest truth (Church constant) T. If we leave ∨ out of the formation apparatus, we get the fragment B∧T. It is known that the set of ALL B∧T theories provides a good model for the combinators CL at Level-I, which is the theory level. Restoring ∨ to get back B+T was not previously fruitful at Level-I, because the set of all B+T theories is NOT a model of CL. It was to be expected from semantic completeness arguments for relevant logics that basic combinator laws would hold when restricted to PRIME B+T theories. Overcoming some previous difficulties, we show that this is the case, at Level I. But this does not form a model for CL. This paper also looks for corresponding results at Level-II, where we deal with sets of theories that we call propositions. We adapt work by Ghilezan to note that at Level-II also there is a model of CL in B∧T propositions. However, the corresponding result for B+T propositions extends smoothly to Level-II only in part. Specifically, only some of the basic combinator laws are proved here. We accordingly leave some work for the reader.&nbsp

A disrupted circumstellar torus inside eta Carinae's Homunculus Nebula

We present thermal infrared images of the bipolar nebula surrounding eta Carinae at six wavelengths from 4.8 to 24.5 microns. These were obtained with the MIRAC3 camera system at the Magellan Observatory. Our images reveal new intricate structure in the bright core of the nebula, allowing us to re-evaluate interpretations of morphology seen in images with lower resolution. Complex structures in the core might not arise from a pair of overlapping rings or a cool (110 K) and very massive dust torus, as has been suggested recently. Instead, it seems more likely that the arcs and compact knots comprise a warm (350 K) disrupted torus at the intersection of the larger polar lobes. Some of the arcs appear to break out of the inner core region, and may be associated with equatorial features seen in optical images. The torus could have been disrupted by a post-eruption stellar wind, or by ejecta from the Great Eruption itself if the torus existed before that event. Kinematic data are required to rule out either possibility.Comment: 8 pages, 3 figures (Fig. 1 in color); to appear in ApJ Letter

QCD and the Chiral Critical Point

As an extension of $QCD$, consider a theory with ``$2+1$'' flavors, where the current quark masses are held in a fixed ratio as the overall scale of the quark masses is varied. At nonzero temperature and baryon density it is expected that in the chiral limit the chiral phase transition is of first order. Increasing the quark mass from zero, the chiral transition becomes more weakly first order, and can end in a chiral critical point. We show that the only massless field at the chiral critical point is a sigma meson, with the universality class that of the Ising model. Present day lattice simulations indicate that $QCD$ is (relatively) near to the chiral critical point.Comment: 7 pages + 2 figures, BNL-GGP-

Classical BI: Its Semantics and Proof Theory

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O'Hearn and Pym's logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave classically rather than intuitionistically (including in particular a multiplicative version of classical negation). At the semantic level, CBI-formulas have the normal bunched logic reading as declarative statements about resources, but its resource models necessarily feature more structure than those for other bunched logics; principally, they satisfy the requirement that every resource has a unique dual. At the proof-theoretic level, a very natural formalism for CBI is provided by a display calculus \`a la Belnap, which can be seen as a generalisation of the bunched sequent calculus for BI. In this paper we formulate the aforementioned model theory and proof theory for CBI, and prove some fundamental results about the logic, most notably completeness of the proof theory with respect to the semantics.Comment: 42 pages, 8 figure

Mash Test No. 3-10 of a Non-Proprietary, High-Tension Cable Median Barrier for Use in 6H:1V V-Ditch (Test No. MWP-8)

The Midwest States Pooled Fund Program has been developing a prototype design for a non-proprietary, high-tension cable median barrier for use in a 6H:1V V-ditch. This system incorporates four evenly spaced cables, Midwest Weak Posts (MWP) spaced at 8 to 16 ft (2.4-4.9 m) intervals, and a bolted, tabbed bracket to attach three or four cables to the sides of each post. According to the Manual for Assessing Safety Hardware (MASH) testing matrix for cable barriers installed within a 6H:1V median V-ditch, a series of eight full-scale tests are required to evaluate the safety performance of a system. A ninth test is required to establish the working width for the systems with variable post spacing. Several previous tests have failed due to posts penetrating the occupant compartment. In order to mitigate this behavior, a modified MWP was designed. Test no. MWP-8 was conducted on the modified barrier system, consisting of MWPs with rounded top edges and a ¾-in. (19-mm) diameter weakening hole at the groundline. This test was conducted according to MASH test designation no. 3-10 and utilized an 1100C passenger car impacting the barrier on a level terrain. The vehicle was contained by the system. Through the initial two vehicle crossover events across the barrier and posts, no floorpan tearing was observed. During the third impact series with the posts, post penetration into the occupant compartment and floorpan tearing was observed. Therefore, test no. MWP-8 was deemed unacceptable

Systematic Evaluation of Pancreas Allograft Quality, Outcomes and Geographic Variation in Utilization

Pancreas allograft acceptance is markedly more selective than other solid organs. The number of pancreata recovered is insufficient to meet the demand for pancreas transplants (PTx), particularly for patients awaiting simultaneous kidney-pancreas (SPK) transplant. Development of a pancreas donor risk index (PDRI) to identify factors associated with an increased risk of allograft failure in the context of SPK, pancreas after kidney (PAK) or pancreas transplant alone (PTA), and to assess variation in allograft utilization by geography and center volume was undertaken. Retrospective analysis of all PTx performed from 2000 to 2006 (n = 9401) was performed using Cox regression controlling for donor and recipient characteristics. Ten donor variables and one transplant factor (ischemia time) were subsequently combined into the PDRI. Increased PDRI was associated with a significant, graded reduction in 1-year pancreas graft survival. Recipients of PTAs or PAKs whose organs came from donors with an elevated PDRI (1.57–2.11) experienced a lower rate of 1-year graft survival (77%) compared with SPK transplant recipients (88%). Pancreas allograft acceptance varied significantly by region particularly for PAK/PTA transplants (p < 0.0001). This analysis demonstrates the potential value of the PDRI to inform organ acceptance and potentially improve the utilization of higher risk organs in appropriate clinical settings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78607/1/j.1600-6143.2009.02996.x.pd