Rapid heuristic projection on simplicial cones

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution

Indentation of ceramic materials with smooth indenters such as parabolae of revolution and spheres can be conducted in the elastic regime to relatively high loads. Ceramic single crystals thus provide excellent calibration media for load-and depth-sensing indentation testing; however, they are generally anisotropic and a complete elastic analysis is cumbersome. This study presents a simplified procedure for the determination of the stiffness of contact for the indentation of an anisotropic half-space by a rigid frictionless parabola of revolution which, to first order, approximates spherical indentation. Using a similar approach, a new procedure is developed for analysing conical indentation of anisotropic elastic media. For both indenter shapes, the contact is found to be elliptical, and equations are determined for the size, shape and orientation of the ellipse and the indentation modulus.

The Kinematics of interference mechanisms in certain machining operations

The mechanism of "Helical Interference" in milled slots is examined and a coherent theory for the geometry of such surfaces is presented. An examination of the relevant literature shows a fragmented approach to the problem owing to its normally destructive nature, so a complete analysis is developed for slots of constant lead, thus giving a united and exact theory for many different setting parameters and a range of cutter shapes. For the first time, a theory is developed to explain the "Interference Surface" generated in variable lead slots for cylindrical work and attention is drawn to other practical surfaces, such as cones, where variable leads are encountered. Although generally outside the scope of this work, an introductory analysis of these cases is considered in order to develop the cylindrical theory. Special emphasis is laid upon practical areas where the interference mechanism can be used constructively and its application as the rake face of a cutting tool is discussed. A theory of rake angle for such cutting tools is given for commonly used planes, and relative variations in calculated rake angle between planes is examined. Practical tests are conducted to validate both constant lead and variable lead theories and some design improvements to the conventional dividing head are suggested in order to manufacture variable lead workpieces, by use of a "superposed" rotation. A prototype machine is manufactured and its kinematic principle given for both linear and non-linearly varying superposed rotations. Practical workpieces of the former type are manufactured and compared with analytical predictions,while theoretical curves are generated for non-linear workpieces and then compared with those of linear geometry. Finally suggestions are made for the application of these principles to the manufacture of spiral bevel gears, using the "Interference Surface" along a cone as the tooth form.

Pupil responses associated with coloured afterimages are mediated by the magno-cellular pathway

Sustained fixation of a bright coloured stimulus will, on extinction of the stimulus and continued steady fixation, induce an afterimage whose colour is complementary to that of the initial stimulus; an effect thought to be caused by fatigue of cones and/or of cone-opponent processes to different colours. However, to date, very little is known about the specific pathway that causes the coloured afterimage. Using isoluminant coloured stimuli recent studies have shown that pupil constriction is induced by onset and offset of the stimulus, the latter being attributed specifically to the subsequent emergence of the coloured afterimage. The aim of the study was to investigate how the offset pupillary constriction is generated in terms of input signals from discrete functional elements of the magno- and/or parvo-cellular pathways, which are known principally to convey, respectively, luminance and colour signals. Changes in pupil size were monitored continuously by digital analysis of an infra-red image of the pupil while observers viewed isoluminant green pulsed, ramped or luminance masked stimuli presented on a computer monitor. It was found that the amplitude of the offset pupillary constriction decreases when a pulsed stimulus is replaced by a temporally ramped stimulus and is eliminated by a luminance mask. These findings indicate for the first time that pupillary constriction associated with a coloured afterimage is mediated by the magno-cellular pathway. © 2003 Elsevier Science Ltd. All rights reserved.

Extracellular Nm23H1 stimulates neurite outgrowth from dorsal root ganglia neurons in vitro independently of nerve growth factor supplementation or its nucleoside diphosphate kinase activity

The nucleoside diphosphate (NDP) kinase, Nm23H1, is a highly expressed during neuronal development, whilst induced over-expression in neuronal cells results in increased neurite outgrowth. Extracellular Nm23H1 affects the survival, proliferation and differentiation of non-neuronal cells. Therefore, this study has examined whether extracellular Nm23H1 regulates nerve growth. We have immobilised recombinant Nm23H1 proteins to defined locations of culture plates, which were then seeded with explants of embryonic chick dorsal root ganglia (DRG) or dissociated adult rat DRG neurons. The substratum-bound extracellular Nm23H1 was stimulatory for neurite outgrowth from chick DRG explants in a concentration-dependent manner. On high concentrations of Nm23H1, chick DRG neurite outgrowth was extensive and effectively limited to the location of the Nm23H1, i.e. neuronal growth cones turned away from adjacent collagen-coated substrata. Nm23H1-coated substrata also significantly enhanced rat DRG neuronal cell adhesion and neurite outgrowth in comparison to collagen-coated substrata. These effects were independent of NGF supplementation. Recombinant Nm23H1 (H118F), which does not possess NDP kinase activity, exhibited the same activity as the wild-type protein. Hence, a novel neuro-stimulatory activity for extracellular Nm23H1 has been identified in vitro, which may function in developing neuronal systems. © 2010 Elsevier Inc.

On the dual-cone nature of the conical refraction phenomenon

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones. (C) 2015 Optical Society of America