Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

CLOSED SPACES IN COSMOLOGY

This paper deals with two aspects of relativistic cosmologies with closed spatial sections. These spacetimes are based on the theory of general relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a three-dimensional closed Riemannian manifold. The topics discussed are: (i) a comparison, previously obtained, between Thurston geometries and Bianchi-Kantowski-Sachs metrics for such three-manifolds is here clarified and developed; and (ii) the implications of global inhomogeneity for locally homogeneous three-spaces of constant curvature are analyzed from an observational viewpoint.

Deproteinized bovine bone mineral in marginal defects at implants installed immediately into extraction sockets: an experimental study in dogs

Aim: To evaluate the influence of deproteinized bovine bone mineral (DBBM) particles concomitant with the placement of a collagen membrane on alveolar ridge preservation and on osseointegration of implants placed into alveolar sockets immediately after tooth extraction. Material and methods: The pulp tissue of the mesial roots of 3P3 was removed in six Labrador dogs and the root canals were filled. Flaps were elevated in the right side of the mandible, and the buccal and lingual alveolar bony plates were exposed. The third premolar was hemi-sectioned and the distal root was removed. A recipient site was prepared and an implant was placed lingually. After implant installation, defects of about 0.6mm wide and 3.1mm depth resulted at the buccal aspects of the implant, both at the test and at the control sites. The same surgical procedures and measurements were performed on the left side of the mandible. However, DBBM particles with a size of 0.25-1mm were placed into the remaining defect concomitant with the placement of a collagen membrane. Results: All implants were integrated into mature bone. No residual DBBM particles were detected at the test sites after 4 months of healing. Both the test and the control sites showed buccal alveolar bone resorption, 1.8 +/- 1.1 and 2.1 +/- 1mm, respectively. The most coronal bone-to-implant contact at the buccal aspect was 2 +/- 1.1 an 2.8 +/- 1.3mm, at the test and the control sites, respectively. This difference in the distance was statistically significant. Conclusion: The application of DBBM concomitant with a collagen membrane to fill the marginal defects around implants placed into the alveolus immediately after tooth extraction contributed to improved bone regeneration in the defects. However, with regard to buccal bony crest preservation, a limited contribution of DBBM particles was achieved.

Evaluation of Different Methods of Optical Impression Making on the Marginal Gap of Onlays Created with CEREC 3D

Objectives: This study evaluated the marginal gaps on several surfaces of onlays created with the Cerec 3D system using one intraoral and two extraoral optical impression methods. Methods: A human molar (#19) was mounted with its adjacent teeth on a typodont (Frasaco) and prepared for a MODL onlay. The typodont was assembled in the mannequin head in order to simulate clinical conditions. The same operator took 36 individual optical impressions using a CEREC 3D camera. For group 1 (IP), a thin layer of titanium dioxide powder (CEREC powder-VITA) was applied directly onto the surface of the preparation for imaging (n=12). For group 2 (EP), a sectional impression was taken with hydrocolloid Identic Syringable (Dux Dental), a die made with polyvinylsiloxane KwikkModel Scan (R-dental Dentalerzeugnisse GmbH) and powdered with titanium dioxide for imaging (n=12). For group 3 (ES), a sectional impression was taken with PVS and a sectional stock tray, a die fabricated in stone (Diamond die- HI-TEC Dental Products) and the die being imaged without powdering (n=12). One operator designed and machined the onlays in Vita Blocks Mark II for Cerec (VITA) using a CEREC 3D. The marginal gaps (pm) were measured with an optical microscope (50x) at 12 points, three on each surface of the MODL. The results were analyzed by two-way ANOVA/Tukey's (p=0.05). Results: The overall mean marginal gaps (mu m) for the three methods were: IP=111.6 (+/- 34.0); EP=161.4 (+/- 37.6) and ES=116.8 (+/- 42.3). IP and ES were equal, but both were significantly less than EP. The pooled mean marginal gaps (mu m) for the occlusal = 110.5 (+/- 39) and lingual = 111.5 (+/- 30.5) surfaces were equivalent and significantly less than the distal = 136.5 (+/- 42.5) and mesial = 161.1 (+/- 43.3). Conclusion: The marginal gap of CEREC 3D onlay restorations was not different when the optical impression was taken intraorally vs extraorally using a stone cast that does not require powdering. The lingual and occlusal surfaces showed the lowest gaps.