A Boolean algebra and a Banach space obtained by push-out iteration

Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(omega)/fin has under CH and in the N(2)-Cohen model. We prove a similar result in the category of Banach spaces. (C) 2011 Elsevier B.V. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

The effects of repetitive loading on bone mass and geometry in young male tennis players : a quantative study using magnetic resonance imaging

Pre- and early puberty seem to be the most opportune times for exercise to  improve bone strength in girls, but few studies have addressed this issue in boys. This study investigated the site-, surface-, and maturity-specific exercise-induced changes in bone mass and geometry in young boys. The osteogenic effects of loading were analyzed by comparing the playing and nonplaying humeri of 43 male pre-, peri-, and postpubertal competitive tennis players 10-19 yr of age. Total bone area, medullary area, and cortical area were determined at the mid (40-50%) and distal humerus (60-70%) of both arms using MRI. Humeral bone mass (BMC) was derived from a whole body DXA scan. In prepubertal boys, BMC was 17% greater in the playing compared with nonplaying arm (p < 0.001), which was accompanied by a 12-21% greater cortical area, because of greater periosteal expansion than medullary expansion at the midhumerus and periosteal expansion associated with medullary contraction at the distal humerus. Compared with prepuberty, the side-to-side differences in BMC (27%) and cortical area (20-33%) were greater in peripuberty (p < 0.01). No differences were found between peri- and postpuberty despite longer playing history in the postpubertal players.The osteogenic response to loading was greater in peri- compared with prepubertal boys, which is in contrast with our previous findings in girls and may be caused by differences in training history. This suggests that the window of opportunity to improve bone mass and size through exercise may be longer in boys than in girls.

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

So(2,1) Lie algebra and the Green's functions for the conditionally exactly solvable potentials

The Green's functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials. © 1994 The American Physical Society.

Further investigation of the initial fission-track length and geometry factor in apatite fission-track thermochronology

The external detector method (EDM) is a widely used technique in fission track thermochronology (FTT) in which two different minerals are concomitantly employed: spontaneous tracks are observed in apatite and induced ones in the muscovite external detector. They show intrinsic differences in detection and etching properties that should be taken into account. In this work, new geometry factor values, g, in apatite, were obtained by directly measuring the ρed/ρis ratios and independently determined [GQR]ed/is values through the measurement of projected lengths. Five mounts, two of which were large area prismatic sections and three samples composed of random-orientation pieces have been used to determine the g-values. A side effect of applying EDM is that the value of the initial confined induced fission track, L0, is not measured in routine analyses. The L 0-value is an important parameter to quantify with good confidence the degree of annealing of the spontaneous fission tracks in unknown-age samples, and is essential for accurate thermal history modeling. The impact of using arbitrary L0-values on the inference of sample thermal history is investigated and discussed. The measurement of the L0-value for each sample to be dated using an extra irradiated apatite mount is proposed. This extra mount can be also used for determining the g value as an extension of the ρed/ρis ratio method. Eight apatite samples from crystalline basement, with grains at random orientation, were used to determine the g-values. The results found are statistically in agreement with the values found for apatite samples (from Durango, Mexico) measured in prismatic section and also measured at random orientation. There was no observable variation in efficiency regarding crystal orientation, showing that it is relatively safe using non-prismatic grains, especially in samples with paucity of grains, as it is the case of most basin samples. Implications for the ζ-calibration and for the calibration of the direct (spectrometer-based) fission-track dating are also discussed.

Impact of Quantity of Resin, C-factor, and Geometry on Resin Composite Polymerization Shrinkage Stress in Class V Restorations

Objective: This study evaluated the effect of quantity of resin composite, C-factor, and geometry in Class V restorations on shrinkage stress after bulk fill insertion of resin using two-dimensional finite element analysis.Methods: An image of a buccolingual longitudinal plane in the middle of an upper first premolar and supporting tissues was used for modeling 10 groups: cylindrical cavity, erosion, and abfraction lesions with the same C-factor (1.57), a second cylindrical cavity and abfraction lesion with the same quantity of resin (QR) as the erosion lesion, and then all repeated with a bevel on the occlusal cavosurface angle. The 10 groups were imported into Ansys 13.0 for two-dimensional finite element analysis. The mesh was built with 30,000 triangle and square elements of 0.1 mm in length for all the models. All materials were considered isotropic, homogeneous, elastic, and linear, and the resin composite shrinkage was simulated by thermal analogy. The maximum principal (MPS) and von Mises stresses (VMS) were analyzed for comparing the behavior of the groups.Results: Different values of angles for the cavosurface margin in enamel and dentin were obtained for all groups and the higher the angle, the lower the stress concentration. When the groups with the same C-factor and QR were compared, the erosion shape cavity showed the highest MPS and VMS values, and abfraction shape, the lowest. A cavosurface bevel decreased the stress values on the occlusal margin. The geometry factor overcame the effects of C-factor and QR in some situations.Conclusion: Within the limitations of the current methodology, it is possible to conclude that the combination of all variables studied influences the stress, but the geometry is the most important factor to be considered by the operator.

Patients with diffuse idiopathic skeletal hyperostosis do not have increased peripheral bone mineral density and geometry

Recent studies have suggested that areal BMD (aBMD) measured by DXA is elevated in patients with DISH. We used peripheral QCT (pQCT) to assess volumetric BMD (vBMD) and bone geometry of the radius, tibia and the third metacarpal bone.

Un receuil: containing painting, penmanship, algebra and pieces selected from various authors in prose and verse, with a few pieces in French with their translation / by Phebe Folger of Nantucket : manuscript, 1797-1806

Written mostly in a copperplate hand in black ink, and illustrated with watercolor drawings.

The root extractor, exhibiting new rules and processes, for the formation and the resolution of equations of all orders in algebra; and for the evolution of the roots of any power in numbers: serving likewise as a key to all the examples of the cubic and higher equations in Bonnycastle's introduction to algebra.

Mode of access: Internet.

An easy algebra for beginners; being a simple, plain presentation of the essentials of elementary algebra, and also adapted to the use of those who can take only a brief course in this study.

"Answers": p. 143-157.