On the completion of Latin rectangles to symmetric Latin squares

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

Amodal completion with background determines depth from monocular gap stereopsis

Grove, Gillam, and Ono [Grove, P. M., Gillam, B. J., & Ono, H. (2002). Content and context. of monocular regions determine perceived depth in random dot, unpaired background and phantom stereograms. Vision Research, 42, 1859-1870] reported that perceived depth in monocular gap stereograms [Gillam, B. J., Blackburn, S., & Nakayama, K. (1999). Stereopsis based on monocular gaps: Metrical encoding of depth and slant without matching contours. Vision Research, 39, 493-502] was attenuated when the color/texture in the monocular gap did not match the background. It appears that continuation of the gap with the background constitutes an important component of the stimulus conditions that allow a monocular gap in an otherwise binocular surface to be responded to as a depth step. In this report we tested this view using the conventional monocular gap stimulus of two identical grey rectangles separated by a gap in one eye but abutting to form a solid grey rectangle in the other. We compared depth seen at the gap for this stimulus with stimuli that were identical except for two additional small black squares placed at the ends of the gap. If the squares were placed stereoscopically behind the rectangle/gap configuration (appearing on the background) they interfered with the perceived depth at the gap. However when they were placed in front of the configuration this attenuation disappeared. The gap and the background were able under these conditions to complete amodally. (c) 2006 Elsevier Ltd. All rights reserved.

Preparation of high purity ZnO nanobelts by thermal evaporation of ZnS

High purity one-dimensional ZnO nanobelts were synthesized by thermally evaporating commercial ZnS powders in a hydrogen-oxygen mixture gas at 1050 degrees C. It was found that these ZnO nanobelts had a single crystal hexagonal wurtzite structure growing along the [0001] direction. They had a rectangle-shaped cross-section with typical widths of 20 to 100 nanometers and lengths of up to hundreds of micrometers with lattice constants of a = 0.325 nm and c = 0.520 nm. The self-catalytic hydrogen-oxygen assisted growth of ZnO nanobelt is discussed. The photoluminescence (PL) characterization of the ZnO nanobelts shows strong near-band UV emission (about 383 nm) and one broad peak at 501 nm, which indicates that the ZnO nanobelts have good potential application in optoelectronic devices.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

Expansion-based algorithms for finding single pair shortest path on surface

Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorithms must traverse the entire polyhedral surface. With the rapid advance in areas like Global Positioning System (CPS), Computer Aided Design (CAD) systems and laser range scanner, surface models axe becoming more and more complex. It is not uncommon that a surface model contains millions of polygons. The single pair shortest path problem is getting harder and harder to solve. Based on the observation that the single pair shortest path is in the locality, we propose in this paper efficient methods by excluding part of the surface model without considering them in the search process. Three novel expansion-based algorithms are proposed, namely, Naive algorithm, Rectangle-based Algorithm and Ellipse-based Algorithm. Each algorithm uses a two-step approach to find the shortest path. (1) compute an initial local path. (2) use the value of this initial path to select a search region, in which the global shortest path exists. The search process terminates once the global optimum criteria are satisfied. By reducing the searching region, the performance is improved dramatically in most cases.