Non-recurrence sets for weakly mixing linear dynamical systems

We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space when endowed with a non-degenerate Gaussian measure. We generalize some recent results of Bergelson, del Junco, Lema\'nczyk and Rosenblatt, and show in particular that sets \{n_k\} such that n_{k+1}/{n_k} tends to infinity, or such that n_{k} divides n_{k+1} for each k, are non-recurrence sets for weakly mixing linear dynamical systems. We also give examples, for each r, of r-Bohr sets which are non-recurrence sets for some weakly mixing systems

The Inhomogeneous Hall's Ray

We show that the inhomogenous approximation spectrum, associated to an irrational number \alpha\ always has a Hall's Ray; that is, there is an \epsilon>0 such that [0,\epsilon) is a subset of the spectrum. In the case when \alpha\ has unbounded partial quotients we show that the spectrum is just a ray.Comment: Fixed typos in bibliograph

Microwave effects on some zeolite catalysed reactions

This research was prompted by the growing body of information accumulating in the literature which refers to the advantages of microwave irradiation as opposed to normal conventional heating. Many of the reports claim that activation by microwave radiation results in enhanced rates and changes in product selectivities. Of special interest were reports that microwave irradiation had beneficial effects on heterogeneous catalysed reactions. Microwave irradiation should be able to activate specifically the actual catalytic sites and hence could be used to affect reactions where the bulk of the catalyst, the reactants and products are transparent to microwaves. Investigation of this effect was conducted on zeolite catalysed reactions, namely the disproportionation of toluene and the alkylation of toluene with methanol.Most of the reports fail to address the problem of accurate temperature measurement within a microwave field. This is of paramount importance and this study describes the development and use of a gas thermometer to overcome this problem. This development has been used to measure the temperature of solvents under thermal and microwave conditions. Using this device it was discovered that polar solvents could attain temperatures in excess of 20°C above their normal boiling point and this phenomenon was investigated further to quantify the effect as a function of the microwave power, the volume of the solvent, the dielectric properties associated with the solvent and the surface of the container used.A comprehensive study of the effect of microwave radiation on disproportionation and alkylation of toluene has been made using hydrogen forms of mordenite and ZSM-5 catalysts. The aim of this reaction is to make paraxylene which is then used in the production of terephthalic (1,4-benzenedicarboxylic) acid. This reaction has been studied under both microwave and thermal conditions at various temperatures. Microwave radiation has shown to have no beneficial effect on the reaction selectivity for the disproportionation and alkylation of toluene. Experiments on disproportionation of toluene under high pressure thermal conditions have shown that partial regeneration of the catalyst can be performed by raising the partial pressure of hydrogen.The study describes in detail the comparison between microwave radiation and normal conventional heating, the influence of carbon laydown on the catalyst under conventional and microwave conditions, and the possibilities of catalyst regeneration. Carbon is deposited on the catalyst and observations have shown that it preferentially absorbs microwaves offering novel techniques for regeneration of the catalyst

Comparative in vitro evaluation of CAD/CAM vs conventional provisional crowns

Objective This study compared the marginal gap, internal fit, fracture strength, and mode of fracture of CAD/CAM provisional crowns with that of direct provisional crowns. Material and Methods An upper right first premolar phantom tooth was prepared for full ceramic crown following tooth preparation guidelines. The materials tested were: VITA CAD-Temp®, Polyetheretherketone “PEEK”, Telio CAD-Temp, and Protemp™4 (control group). The crowns were divided into four groups (n=10), Group1: VITA CAD-Temp®, Group 2: PEEK, Group 3: Telio CAD-Temp, and Group 4: Protemp™4. Each crown was investigated for marginal and internal fit, fracture strength, and mode of fracture. Statistical analysis was performed using GraphPad Prism software version 6.0. Results The average marginal gap was: VITA CAD-Temp® 60.61 (±9.99) µm, PEEK 46.75 (±8.26) µm, Telio CAD-Temp 56.10 (±5.65) µm, and Protemp™4 193.07(±35.96) µm (P0.05). Conclusions CAD/CAM fabricated provisional crowns demonstrated superior fit and better strength than direct provisional crowns

Determining the accuracy of terrestrial LiDAR on red pine

This paper reviews the capabilities of the FARO Terrestrial LiDAR technology to produce accurate forest measurements. The study was conducted on single Red Pine trees in Northern Ontario. Field measurements were compared to scanned terrestrial LiDAR data. Results found that the FARO was accurate in producing tree heights. When determining diameter at breast height (DBH) and volume, there is still research that needs to be done. There was error due to target placement which distorted diameter at breast height measurements. With the proper training, better results could be omitted using terrestrial LiDAR. Terrestrial LiDAR has the potential to replace traditional field methods and technology is advancing very quickly. This study is important in order to update current forest measurement methods and produce faster, more accurate results. It is hoped that this study will inform foresters and researchers about the potential uses for terrestrial LiDAR in the forest stand environment

Comparative in vitro evaluation of CAD/CAM vs conventional provisional crowns

bjective This study compared the marginal gap, internal fit, fracture strength, and mode of fracture of CAD/CAM provisional crowns with that of direct provisional crowns. Material and Methods An upper right first premolar phantom tooth was prepared for full ceramic crown following tooth preparation guidelines. The materials tested were: VITA CAD-Temp®, Polyetheretherketone “PEEK”, Telio CAD-Temp, and Protemp™4 (control group). The crowns were divided into four groups (n=10), Group1: VITA CAD-Temp®, Group 2: PEEK, Group 3: Telio CAD-Temp, and Group 4: Protemp™4. Each crown was investigated for marginal and internal fit, fracture strength, and mode of fracture. Statistical analysis was performed using GraphPad Prism software version 6.0. Results The average marginal gap was: VITA CAD-Temp® 60.61 (±9.99) µm, PEEK 46.75 (±8.26) µm, Telio CAD-Temp 56.10 (±5.65) µm, and Protemp™4 193.07(±35.96) µm (

Fracture resistance of zirconia-composite veneered crowns in comparison with zirconia-porcelain crowns.

The objectives were to evaluate the fracture resistance and stress concentration in zirconia/composite veneered crowns in comparison to zirconia/porcelain crowns using occlusal fracture resistance and by stress analysis using finite element analysis method. Zirconia substructures were divided into two groups based on the veneering material. A static load was applied occlusally using a ball indenter and the load to fracture was recorded in Newtons (N). The same crown design was used to create 3D crown models and evaluated using FEA. The zirconia/composite crowns subjected to static occlusal load showed comparable results to the zirconia/porcelain crowns. Zirconia/composite crowns showed higher stress on the zirconia substructure at 63.6 and 50.9 MPa on the zirconia substructure veneered with porcelain. In conclusion, zirconia/composite crowns withstood high occlusal loads similar to zirconia/porcelain crowns with no significant difference. However, the zirconia/composite crowns showed higher stress values than the zirconia/porcelain crowns at the zirconia substructure