Not All Saturated 3-Forests Are Tight

A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz

The Resumption of Protestantism Under Queen Elizabeth

The subject which we are about to discuss is of vital interest to the student of English Church History. If it is important for him to know the early phases and developments of that history reaching down into the Roman period of English History; if it is necessary for him to observe the tendencies, persuasions, and movements during the subsequent centuries; then it is truly essential for him to be acquainted with the lace-work of causes, events, and personalities out of which grew the pattern known to us as the Anglican Church

Total Synthesis of the Biphenyl Alkaloid (−)-Lythranidine

A sequence comprising a ring-closing alkyne metathesis of a propargyl alcohol derivative, followed by a ruthenium-catalyzed redox isomerization of the derived cycloalkyne and a transannular aza-Michael addition allowed the formation of the distinguishing piperidine-metacyclophane framework of the Lythraceum alkaloid lythanidine in a few high-yielding steps. This application attests to the excellent functional-group tolerance of a molybdenum alkylidyne complex endowed with triphenylsilanolate ligands, which enabled the macrocyclization even in the presence of protic functionalities, and thus illustrates the power of contemporary catalytic acetylene chemistry for target-oriented synthesis

A Quantum Lovasz Local Lemma

The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then apply our results to the recently studied model of random k-QSAT. Recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit, where the density is the ratio of projectors to qubits. Using a hybrid approach building on work by Laumann et al. we greatly extend the known satisfiable region for random k-QSAT to a density of $\Omega(2^k/k^2)$. Since our tool allows us to show the existence of joint satisfying states without the need to construct them, we are able to penetrate into regions where the satisfying states are conjectured to be entangled, avoiding the need to construct them, which has limited previous approaches to product states.Comment: 19 page

The use of plasma ashers and Monte Carlo modeling for the projection of atomic oxygen durability of protected polymers in low Earth orbit

The results of ground laboratory and in-space exposure of polymeric materials to atomic oxygen has enabled the development of a Monte Carlo computational model which simulates the oxidation processes of both environments. The cost effective projection of long-term low-Earth-orbital durability of protected polymeric materials such as SiO(x)-coated polyimide Kapton photovoltaic array blankets will require ground-based testing to assure power system reliability. Although silicon dioxide thin film protective coatings can greatly extend the useful life of polymeric materials in ground-based testing, the projection of in-space durability based on these results can be made more reliable through the use of modeling which simulates the mechanistic properties of atomic oxygen interaction, and replicates test results in both environments. Techniques to project long-term performance of protected materials, such as the Space Station Freedom solar array blankets, are developed based on ground laboratory experiments, in-space experiments, and computational modeling

Monte Carlo modeling of atomic oxygen attack of polymers with protective coatings on LDEF

Characterization of the behavior of atomic oxygen interaction with materials on the Long Duration Exposure Facility (LDEF) assists in understanding of the mechanisms involved. Thus the reliability of predicting in-space durability of materials based on ground laboratory testing should be improved. A computational model which simulates atomic oxygen interaction with protected polymers was developed using Monte Carlo techniques. Through the use of an assumed mechanistic behavior of atomic oxygen interaction based on in-space atomic oxygen erosion of unprotected polymers and ground laboratory atomic oxygen interaction with protected polymers, prediction of atomic oxygen interaction with protected polymers on LDEF was accomplished. However, the results of these predictions are not consistent with the observed LDEF results at defect sites in protected polymers. Improved agreement between observed LDEF results and predicted Monte Carlo modeling can be achieved by modifying of the atomic oxygen interactive assumptions used in the model. LDEF atomic oxygen undercutting results, modeling assumptions, and implications are presented

LDEF yaw and pitch angle estimates

Quantification of the LDEF yaw and pitch misorientations is crucial to the knowledge of atomic oxygen exposure of samples placed on LDEF. Video camera documentation of the LDEF spacecraft prior to grapple attachment, atomic oxygen shadows on experiment trays and longerons, and a pinhole atomic oxygen camera placed on LDEF provided sources of documentation of the yaw and pitch misorientation. Based on uncertainty-weighted averaging of data, the LDEF yaw offset was found to be 8.1 plus or minus 0.6 degrees, allowing higher atomic oxygen exposure of row 12 than initially anticipated. The LDEF pitch angle offset was found to be 0.8 plus or minus 0.4 degrees, such that the space end was tipped forward toward the direction of travel. The resulting consequences of the yaw and pitch misorientation of LDEF on the atomic oxygen fluence is a factor of 2.16 increase for samples located on row 12, and a factor of 1.18 increase for samples located on the space end compared to that which would be expected for perfect orientation

The population of deformed bands in 48^{48}Cr by emission of 8^{8}Be from the 32^{32}S + 24^{24}Mg reaction

Using particle-$\gamma$ coincidences we have studied the population of final states after the emission of 2 $\alpha$-particles and of $^{8}$Be in nuclei formed in $^{32}$S+$^{24}$Mg reactions at an energy of $\textrm{E}_{\rm L}(^{32}\textrm{S}) = 130 {\rm MeV}$. The data were obtained in a setup consisting of the GASP $\gamma$-ray detection array and the multidetector array ISIS. Particle identification is obtained from the $\Delta$E and E signals of the ISIS silicon detector telescopes, the $^{8}$Be being identified by the instantaneous pile up of the $\Delta$E and E pulses. $\gamma$-ray decays of the $^{48}$Cr nucleus are identified with coincidences set on 2 $\alpha$-particles and on $^{8}$Be. Some transitions of the side-band with $K^\pi=4^{-}$ show stronger population for $^{8}$Be emission relative to that of 2 $\alpha$-particles (by a factor $1.5-1.8$). This observation is interpreted as due to an enhanced emission of $^{8}$Be into a more deformed nucleus. Calculations based on the extended Hauser-Feshbach compound decay formalism confirm this observation quantitatively.Comment: 17 pages, 9 figures accepted for publication in J. Phys.