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MacSphere is McMaster University's Institutional Repository (IR). The purpose of an IR is to bring together all of a University's research under one umbrella, with an aim to preserve and provide access to that research. The research and scholarly output included in MacSphere has been selected and deposited by the individual university departments and centres on campus.

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TRABECULAR BONE TEXTURE IN RADIOGRAPHS OF THE KNEE
(2005) Patrick Emond
Tibio-femoral osteoarthritis (OA) accelerates the degeneration of cartilage which alters the biomechanical environment surrounding the joint. As stresses applied to the proximal tibia increase, subchondral cancellous bone remodels itself in response to biomechanical changes. In order to detect the changes in subchondral trabecular bone, radiographic texture in regions of interest (ROI) in the medial and lateral compartment of the proximal tibia were examined. Dominant knees of 151 subjects were radiographed using the fixed flexion technique. Two radiologists independently graded each radiograph accord ing to Kellgren-Lawrence (KL) scoring. Two ROIs were selected to contain a representative sample of the trabecular pattern in the tibia. Run-length and trabecular strut analysis were applied to measure several indices of ra diographic texture. Aggregate reproducibility of the indices were assessed by analysing duplicate radiographs of 12 patients acquired 1-week apart. In general the reproducibility of the run-length indices were < 5% compared to those derives from strut analysis (< 10%). There was strong evidence of structural change in trabecular bone pattern in groups of subjects with differing Kellgren-Lawrence (KL) scores. For example, the difference in bone surface (p<0.05), bone volume (p<0.0001), trabecular spacing (p<0.005) and connectivity index (p<0.05) were statistically significant between subjects with KL scores of 4 and <1. In subjects with moderate osteoarthritis (KL=2,3), there was a non-significant trend to have greater apparent bone surface and bone volume, reduced trabecular spacing and greater connectivity as identified by strut analysis. It was found that structural change in trabecular bone can be identified by computer-aided analysis of radiographs of osteoarthritic knees. However, this change could not be identified in non-severe OA without greater statistical power.
FLOW AND HEAT TRANSFER PHENOMENA IN A 90° BEND
(1964-11) William Schneider
This paper deals with the overall performance of a two-dimensional, 90°, potential flow bend having a contract ion ratio of 2:1 and using air as the working fluid. It deals as well with the effect on the boundary layer and the heat transfer rate at the inner bend surface due to the cooling and curvature of the inner wall. The overall characteristics of the bend are reported for four inlet velocities from 60 to 175 ft./sec. Static pressure distributions for the inner and outer walls of the bend and velocity and turbulence profiles at the bend inlet, mid-bend, and bond outlet are given. Both the pressure dis tributions and the velocity profiles are compared to those predicted by ideal potential flow and neglecting the velocity decay at the walls due to the boundary layer, agreement is very good. The characteristics of the boundary layer formed at the inner surface of the bend arc reported for the four in- let velocities. Velocity profiles are plotted for isother mal flow conditions in dimensional form, universal velocity profile form, and logarithmic form. The effects on the velocity profiles due to varying inlet velocities and temp erature differences between the wall and the flow’ of up to 60°F are shown to be small. The temperature profiles for all the variations of speed and temperature difference are shown and as the temp erature difference increases the temperature boundary layer thickens slightly. The convective heat transfer coefficient is reported for a point on the inner surface at raid-bend. Evaluations by the accepted heat transfer correlation and from shear stress results agree but actual measurements using a heat flow transducer show that the heat transfer rate is substan tially reduced due to the effect of curvature. These re ductions in heat transfer occur in a region where the accel eration which the flow experiences due to turning is from 730 to 3,3'30 times the acceleration duo to gravity.
THE DETERMINATION OF PORE SIZE DISTRIBUTION AND SURFACE AREA FROM ADSORPTION ISOTHERMS
(1954-10) Eva Voigt
Theoretical isotherms have been developed which when com pared to experimental isotherms showing hysteresis, allow the calculation of pore size, pore size distribution and surface area of the sorbent. Interpretation of some experimental iso therms obtained with porous vycor glass shows that this system can best be represented by the ’’ink bottle” pore model with a Gaussian distribution of pore sizes. The mean pore radius of the porous glass is about two thirds of the Kelvin radius, and the surface area about twice that obtained from the B.E.T. theory. The Kelvin radius is interpreted as a weighted aver age, but the B.E.T. surface area appears more fundamentally different. As a consequence of the present theory multilayer adsorption, as opposed to capillary condensation^seems highly improbable on porous glass
Lagrance Multiplier Tests of Autoregressive Models
(1995) Saha, Tarit Kami
The Lagrange multiplier test procedure is applied to hypotheses concerning autoregressive time series models. One reasonable method of testing the specification of a statistical model is by overfitting: the null hypothesis that the model is correct is tested against a suitable alternative hypothesis of which the null hypothesis is a special case. Considering that the white noise process is distributed as t with v degrees of freedom and an extreme-value (Weibull) distribution with shape parameter, c, Lagrange Multiplier test statistics have been derived under the null hypothesis. The estimates of the parameters under the null hypothesis have been calculated by solving the system of nonlinear equations with the help of IMSL, NAG and FORTRAN 77 programming. Simulation results are presented to assess the performance of the tests. Consider the modelling of time series data with a lower limit of detection L, i.e. all the observations below L are censored, the score test statistics have been derived under the null hypothesis to test the autodependence in the data. Some simulation experiments are performed to assess the closeness and validity of the test under the null hypothesis. To illustrate the methodology in a real situation, data from the Niagara River containing on Total Lead Concentration (mg∕L) for the period 1986-1992 have been used for illustration.
Partially Ordered, Primitive Regular Semigroups
(1973-02) Rompke, Jurgen
The theory of partially ordered, primitive regular semigroups is developed under the hypothesis that the partial order admits enough integral idempotents. This is done in analogy to the theory of partially ordered groups. In particular, results are given which - in a purely algebraic way - determine the existence of partial orders and characterize the semigroup of integral elements of a directed, primitive regular semigroup

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