Impossible and ambiguous shading patterns

A smooth object depicted in a monochrome image will often exhibit brightness variation, or shading. A problem much studied in computer vision has been that of how object shape may be recovered from image shading. When the imaging conditions are such that an overhead point-source illuminates a smooth Lambertian surface, the problem may be formulated as that of finding a solution to an eikonal equation. This article will focus on the existence and uniqueness of such solutions, reporting recent results obtained. With regard to existence, shading patterns are exhibited for which there is no corresponding object shape. Specifically, a necessary and sufficient condition is presented for a circularly symmetric eikonal equation to admit exclusively unbounded solutions; additionally, a sufficient condition is given for an eikonal equation to have no solution whatsoever. In connection with uniqueness, we consider eikonal equations, defined over a disc, such that the Euclidean norm of the gradient of any solution is circularly symmetric, vanishes exactly at the disc center, and diverges to infinity as the circumference of the disc is approached. Contrary to earlier influential work, a class of such eikonal equations is shown to possess simultaneously circularly symmetric and noncircularly symmetric bounded smooth solutions.     

Molecular orientation and stress in biaxially deformed polymers. II. Steady potential flow

The development of biaxial segmental orientation and stress in a flexible-chain polymer fluid subjected to steady biaxial extensional flow is analyzed. Closed-formula model based on the Padè approximation of the inverse Langevin function in the non-Gaussian distribution of the chain end-to-end vectors is considered. The approach is free from the limitations related to finite chain extensibility and slow convergence of the series expansion formulations at higher chain deformations.Segmental orientation is characterized by the average orientation tensor, related axial orientation factors and global orientation anisotropy. Orientational behavior and corresponding stresses in the biaxial elongational potential flow are discussed in a wide range of elongation rates. Orientation characteristics calculated for the biaxial flow deformation are much higher than those predicted for the affine biaxial stretch deformation in polymer solids.     

Inhibition of nitrification in the packed bed reactors by selected organic compounds

The effect of methanol, acetone, formalin and glucose on the nitrification process in the packed bed reactors has been investigated. For the utilized compounds the inhibition constant K_i was determined according to Dixon's method. The determined values were as follows: methanol K_i = 116.0 mg l^?1; acetone K_i = 804.2 mg l^?1; formalin K_i = 61.5 mg l^?1. The value of K_i for glucose has not been determined because glucose in applied concentration up to 11,325 mg l^?1 had no effect on the nitrification course.     

AlxGa−xAs/GaAs heterostructure characterization by wet chemical etching

Selective wet chemical etching of the Al_xGa_1−xAs/GaAs system has been applied to heterostructure characterization. Samples of LPE grown AlGaAs/GaAs laser double-heterostructures and separate confinement heterostructures as well as antiresonant reflecting optical waveguides heterostructures were treated with “I2 solution” (I₂:KI:H₂O) and hydrochloric acid. These compounds selectively etch the ternary Al_xGa_1−xAs layers, but with different “threshold composition” x_th values (the x value is that above which the etching rate of a given compound increases sharply). Selectively etched samples have been examined by SEM. The experimental dependence of etching rate on the x value for I2 solution has been derived. From this dependence, the x composition of any ternary layer can be estimated simply. Observations were made of the “microscopic” properties of the heterostructure, such as the smoothness of the interfaces and the uniformity of layers. All imperfections resulting from the growth process, such as interface perturbations or compositional nonuniformity of layers, are clearly seen. An additional advantage of this etching technique is its simplicity. It allows quick examination of grown heterostructure for the selection of wafers for further processing.     

Technical risk involved in long-term operation of steam turbines

The scope of the paper is the assessment of the technical risk involved in long-term operation of power units. Detailed analyses have been conducted for steam turbine components. The sources and consequences of risk have been identified and the probability of turbine components failure calculated. The quantitative assessment of the risk has been made and possibilities of its reduction discussed.     

Influence of the amount of ferromagnetic addition on the rheological properties of spinning solutions,the structure,the strength,and thermal properties of polyacrylonitrile fibres

The rheological properties of spinning solutions of polyacrylonitrile in dimethyl formamide (DMF) containing various amounts of a ferromagnetic nanoaddition were investigated. The porous structure, the strength and thermal properties of fibers obtained from these solutions were assessed, as well as the uniformity of the nanoaddition distribution on the fiber surface was estimated. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Mode of deformation and the rate of energy storage during uniaxial tensile deformation of austenitic steel

The mechanism of slip and its consequence in the process of energy storage during uniaxial tension of austenitic steel was studied. The interpretation of the energy storage process in terms of the slip development and microscopic shear band formation is presented.     

Note on covering monotone orthogonal polygons with star-shaped polygons

In 1986, Keil provided an O(n²) time algorithm for the problem of covering monotone orthogonal polygons with the minimum number of r-star-shaped orthogonal polygons. This was later improved to O(n) time and space by Gewali et al. in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63]. In this paper we simplify the latter algorithm—we show that with a little modification, the first step Sweep1 of the discussed algorithm—which computes the top ceilings of horizontal grid segments—can be omitted.In addition, for the minimum orthogonal guard problem in the considered class of polygons, our approach provides a linear time algorithm which uses O(k) additional space, where k is the size of the optimal solution—the algorithm in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63] uses both O(n) time and O(n) additional space.