An algorithm for constructing Hjelmslev planes

Projective Hjelmslev planes and affine Hjelmslev planes are generalisations of projective planes and affine planes. We present an algorithm for constructing projective Hjelmslev planes and affine Hjelmslev planes that uses projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelmslev planes can be constructed in this way. As a corollary it is shown that all $2$-uniform affine Hjelmslev planes are sub-geometries of $2$-uniform projective Hjelmslev planes.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.

Computed tomography analysis of sagittal plane parameters in adolescent idiopathic scoliosis treated by video assisted thoracoscopic spinal fusion and instrumentation

One of the primary treatment goals of adolescent idiopathic scoliosis (AIS) surgery is to achieve maximum coronal plane correction while maintaining coronal balance. However maintaining or restoring sagittal plane spinal curvature has become increasingly important in maintaining the long-term health of the spine. Patients with AIS are characterised by pre-operative thoracic hypokyphosis, and it is generally agreed that operative treatment of thoracic idiopathic scoliosis should aim to restore thoracic kyphosis to normal values while maintaining lumbar lordosis and good overall sagittal balance. The aim of this study was to evaluate CT sagittal plane parameters, with particular emphasis on thoracolumbar junctional alignment, in patients with AIS who underwent Video Assisted Thoracoscopic Spinal Fusion and Instrumentation (VATS). This study concluded that video-assisted thoracoscopic spinal fusion and instrumentation reliably increases thoracic kyphosis while preserving junctional alignment and lumbar lordosis in thoracic AIS.

Tracking road edges in the panospheric image plane

This paper presents a technique for tracking road edges in a panoramic image sequence. The major contribution is that instead of unwarping the image to find parallel lines representing the road edges, we choose to warp the parallel groundplane lines into the image plane of the equiangular panospheric camera. Updating the parameters of the line thus involves searching a very small number of pixels in the panoramic image, requiring considerably less computation than unwarping. Results using real-world images, including shadows, intersections and curves, are presented.

Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Quantifying in-plane deformation of plate elements using vibration characteristics

Plate elements are used in many engineering applications. In-plane loads and deformations have significant influence on the vibration characteristics of plate elements. Numerous methods have been developed to quantify the effects of in-plane loads and deformations of individual plate elements with different boundary conditions based on their natural frequencies. However, these developments cannot be applied to the plate elements in a structural system as the natural frequency is a global parameter for the entire structure. This highlights the need for a method to quantify in-plane deformations of plate elements in structural framing systems. Motivated by this gap in knowledge, this research has developed a comprehensive vibration based procedure to quantify in-plane deformation of plate elements in a structural framing system. This procedure with its unique capabilities to capture the influence of load migration, boundary conditions and different tributary areas is presented herein and illustrated through examples.

Speckle reduction in optical coherence tomography imaging by affine-motion image registration

Signal-degrading speckle is one factor that can reduce the quality of optical coherence tomography images. We demonstrate the use of a hierarchical model-based motion estimation processing scheme based on an affine-motion model to reduce speckle in optical coherence tomography imaging, by image registration and the averaging of multiple B-scans. The proposed technique is evaluated against other methods available in the literature. The results from a set of retinal images show the benefit of the proposed technique, which provides an improvement in signal-to-noise ratio of the square root of the number of averaged images, leading to clearer visual information in the averaged image. The benefits of the proposed technique are also explored in the case of ocular anterior segment imaging.

Footwear modifies coronal plane forefoot and sagittal plane hallux kinematics during stance phase of walking gait

Footwear is designed to reduce injury, and enhance performance. However, the effect footwear has on foot and ankle kinematics currently remains unknown. Acknowledging the need for improved understanding, multi-segment models of the foot-shoe complex need to be established to both describe and quantify the effect footwear has on the foot and ankle during stance phase of gait. The purpose of this study was to quantify how footwear alters the kinematics of the foot inside the shoe during stance phase of walking gait.

Hessian-based affine adaptation of salient local image features

Affine covariant local image features are a powerful tool for many applications, including matching and calibrating wide baseline images. Local feature extractors that use a saliency map to locate features require adaptation processes in order to extract affine covariant features. The most effective extractors make use of the second moment matrix (SMM) to iteratively estimate the affine shape of local image regions. This paper shows that the Hessian matrix can be used to estimate local affine shape in a similar fashion to the SMM. The Hessian matrix requires significantly less computation effort than the SMM, allowing more efficient affine adaptation. Experimental results indicate that using the Hessian matrix in conjunction with a feature extractor that selects features in regions with high second order gradients delivers equivalent quality correspondences in less than 17% of the processing time, compared to the same extractor using the SMM.

An exploration of affine group laws for elliptic curves

Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.