Multiplication Operators on Weighted Banach Spaces of a Tree

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determine estimates on the operator norm, and show there are no isometries

Mueller v. Allen: A New Direction in the Public School-Private School Controversy

The relationship between religion and schooling, while contributing to our heritage, has created extensive controversy

Geology of the Outer Hebrides : North Harris, and Uig, Morsgail and Aline in Lewis

The area of the Outer Hebrides described in this paper includes North Harris and the Uig, Morsgail and Aline districts in Lewis. In addition, a narrow strip of country is included, north of Loch Erisort and extending eastwards from Balallan as far as the river Laxay on the estate of Soval.North Harris and its adjacent islands such as Scarp and Fladday on the west, and Soay in West Loch Tarbert on the south, forms part of Inverness - shire; Uig, Morsgail and Aline are included in Ross- shire.North Harris, joined to South Harris by the narrow isthmus at Tarbert, is bounded on the south by East and West Loch Tarbert, on the east by Loch Seaforb and on the west by the Atlantic Ocean. Its northern limit is formed partly by Loch Resort and partly by a land boundary much disputed in the past, passing from the head of Loch Resort between Stulaval and Rapaire to Mullach Ruisk and thence to the Amhuin a Mhuil near Aline Lodge on Loch Seaforth. Seaforth Island in Loch Seaforth lies partly in Inverness -shire and partly in Ross -shire.The extensive estate of Uig includes the western part of Lewis west of Little Loch Roag from Loch Resort in the south to the Gallan Head in the north.Morsgail lies between Little Loch Roag and Loch Langavat while Aline includes most of the ground the last-named loch and Loch Seaforth.The area is interesting because of the varied types of scenery which it presents. Thus, North Harris is almost entirely mountainous including six peaks over two thousand feet in height, by far the highest in the Long Island. The hills of the western part of North Harris are continued north into the Uig ! district forming there one of the main areas of high ground in Lewis. North of Harris and east of Uig the hills die away gradually into an undulating moorland with occasional ridges and low isolated hills. This, in turn, passes into the great moor of central Lewis most of which however, lies beyond the area dealt with in this paper.The coast-line is equally varied presenting steep cliffs overlooking dark and narrow sea lochs liké Loch Seaforth and Loch Resort; frowning cliffs front- -ing the open sea as at the Gallan Head, Aird More, Mangersta, or Northwest Scarp; or open stretches of sandy beach fringed with blown sand as at Husinish and Scarp in Harris or the beautiful bay of Uig in Lewis. The physical features, however, will be more fully des - cribed before dealing with the glaciation (p. 76).North Harris, Uig, and Tiorsgail are occupied mainly as deer forests but partly also for grazing. Aline and the moorland near Balallan are devoted to the grazing of sheep and cattle. Cultivated ground which forms a very small proportion of the whole is confined mainly to the open coasts or to the shores of the sea lochs. The population is sparse and confined., in every case to the coast. With the exception of 'few inhabitants at the head of Loch Resort and at Loch Tamanavay the central parts are quite uninhabited and the stranger may walk over the hills for weeks without . meeting a human being. The lack of accommodation and the general inaccessability of the region accounts amply for the lack of attention which has been devoted' in the past to its geology

Retention capacity of random surfaces

We introduce a "water retention" model for liquids captured on a random surface with open boundaries, and investigate it for both continuous and discrete surface heights 0, 1, ... n-1, on a square lattice with a square boundary. The model is found to have several intriguing features, including a non-monotonic dependence of the retention on the number of levels in the discrete case: for many n, the retention is counterintuitively greater than that of an n+1-level system. The behavior is explained using percolation theory, by mapping it to a 2-level system with variable probability. Results in 1-dimension are also found.Comment: 5 page

On the Rates of Type Ia Supernovae in Dwarf and Giant Hosts with ROTSE-IIIb

We present a sample of 23 spectroscopically confirmed Type Ia supernovae that were discovered in the background of galaxy clusters targeted by ROTSE-IIIb and use up to 18 of these to determine the local (z = 0.05) volumetric rate. Since our survey is flux limited and thus biased against fainter objects, the pseudo-absolute magnitude distribution (pAMD) of SNeIa in a given volume is an important concern, especially the relative frequency of high to low-luminosity SNeIa. We find that the pAMD derived from the volume limited Lick Observatory Supernova Search (LOSS) sample is incompatible with the distribution of SNeIa in a volume limited (z<0.12) sub sample of the SDSS-II. The LOSS sample requires far more low-luminosity SNeIa than the SDSS-II can accommodate. Even though LOSS and SDSS-II have sampled different SNeIa populations, their volumetric rates are surprisingly similar. Using the same model pAMD adopted in the SDSS-II SNeIa rate calculation and excluding two high-luminosity SNeIa from our sample, we derive a rate that is marginally higher than previous low-redshift determinations. With our full sample and the LOSS pAMD our rate is more than double the canonical value. We also find that 5 of our 18 SNeIa are hosted by very low-luminosity (M_B > -16) galaxies, whereas only 1 out 79 nearby SDSS-II SNeIa have such faint hosts. It is possible that previous works have under-counted either low luminosity SNeIa, SNeIa in low luminosity hosts, or peculiar SNeIa (sometimes explicitly), and the total SNeIa rate may be higher than the canonical value.Comment: 18 pages; accepted for publication in The Astronomical Journa

Vapor Phase Adsorption of Water on Hydroxyapatite

Water vapor adsorption isotherms were determined gravimetrically on three hydroxyapatite samples differing in preparation and with surface areas of 70.4, 22.5, and 3.0 M 2/gm, respectively. Heats of adsorption for the first layer of water were found to be 13.3, 13.2, and 13.9 kcallmole on these hydroxyapatites. From repeated thermal desorption and adsorption cycles of water, stepwise adsorption was observed which diminished with each outgassing cycle until it disappeared after the fourth cycle. Cross-sectional area of adsorbed water molecule on hydroxyapatite surface was estimated at 11.5 Å2. Standard free energies, isosteric heats, changes in enthalpy, and entropy of adsorption of water on HAP samples outgassed at 300 C were determined.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67213/2/10.1177_00220345770560120101.pd

Wear of Fluorapatite Single Crystals: I. A Method for Quantitative Evaluation of Wear

A quantitative method for characterizing the surface failure of nonmetallic single crystals under sliding was evaluated. It was found that strain rate, load, and slider design influenced the wear of natural fluorapatite single crystals. High loads and slider designs with small radiuses and sharp angles resulted in the deepest penetration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67060/2/10.1177_00220345720510011201.pd

Synthesis and exploration of electronically modified (R)-5,5-dimethyl-(p-CF_3)_3-i-PrPHOX in palladium-catalyzed enantio- and diastereoselective allylic alkylation: a practical alternative to (R)-(p-CF_3)_3-t-BuPHOX

The synthesis of the novel electronically modified phosphinooxazoline (PHOX) ligand, (R)-5,5-dimethyl-(p-CF_3)_3-i-PrPHOX, is described. The utility of this PHOX ligand is explored in both enantio- and diastereoselective palladium-catalyzed allylic alkylations. These investigations prove (R)-5,5-dimethyl-(p-CF_3)_3-i-PrPHOX to be an effective and cost-efficient alternative to electronically modified PHOX ligands derived from the prohibitively expensive (R)-t-leucine

Color Stability of a Pigmented Elastomer for Maxillofacial Appliances

The color stability of a series of eleven maxillofacial pigments was determined after accelerated aging using reflection spectrophotometry. The results indicate that seven of the pigments demonstrated good to excellent color stability, while four of the pigments were less promising for clinical use.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67027/2/10.1177_00220345790580050301.pd