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The use of digital elevation models, which represent the surface of the earth by a matrix of heights, has proved an ideal introductory topic for developing both the matrix-handling and computational skills of undergraduate mathematicians. This article looks at the solving of an easily understandable, but not necessarily simple problem: given a particular date, time and terrain, and within the software skills available to first-year students via a computer algebra system, produce a map which can show those parts of the terrain which lie in shadow. (Contains 7 figures.)

This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward, notation. Programs are presented that can produce these equations in various coordinate systems, as is the algebra system used to obtain solutions for specific examples in parallel and rotational flow.

The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in the field of computer mapping and thus addressed by geographical information systems. The problems include simple identification of local maximum points, visualization by cross-sectional profiles, contour maps and three-dimensional views, consideration of the visual impact of the placement of large buildings and issues arising from reservoir creation. Motion through a virtual landscape can be simulated by an animation facility. This approach has been successful with first year students: the 'real world' problems considered are more accessible than many alternatives, and the attraction of using large matrices is retained.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can be successfully demonstrated using a popular computer algebra system to formulate and solve the equations, and display an animation of the motion.

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the angles through which they move, and for as many as a hundred pendulums if the angles remain sufficiently small. An attractive and informative graphical display of the motion in animated form can be obtained from the solution, and the effect of varying the initial conditions can be investigated visually. (Contains 8 figures.)

Presents a study which utilized transmission electron microscopy and x-ray photoelectron microscopy to examine the surface heat treated gratings. Experimental procedures; Results and discussion; Conclusion.

Background: This study was undertaken to determine the true incidence of renal impairment after aortic surgery and its association with intraoperative fluctuations in renal artery blood flow and cardiac output., Methods: Direct measurements of renal artery blood flow were undertaken with electromagnetic flowmetry in 19 patients undergoing elective infrarenal aortic surgery. Renal function was assessed before and after operation by measurement of creatinine clearance., Results: Twelve patients (63%) had renal impairment as defined by a 40% or greater reduction in creatinine clearance after operation. This group of patients had significantly lower renal artery blood flow during the period of aortic cross-clamping than had those who preserved their renal function (p < 0.001)., Conclusions: Renal impairment is common after infrarenal aortic surgery and may be a result of intraoperative ischemia secondary to reduced renal artery blood flow.

Purpose: In an investigation of the effects of isovolemic hemodilution, 39 consecutive patients undergoing elective infrarenal aortic operation had detailed measurements of renal function, renal artery blood flow, and cardiac hemodynamics., Methods: The patients were randomly allocated to receive acute preoperative isovolemic hemodilution to a hematocrit of 28%, with 20 patients receiving hemodilution and 19 being control subjects., Results: Twelve (63%) of the control group had renal impairment, compared with only four (20% in the group receiving hemodilution (p < 0.01). Hemodilution also prevented the fall in cardiac output induced by cross-clamping (p < 0.01) and significantly reduced the need for transfusion of donor blood (p < 0.01)., Conclusions: Acute isovolemic hemodilution is clearly a useful adjunct in the management of patients undergoing elective aortic operation.

Spores of the thermophilic, acidophilic, Bacillus acidocaldarius were covered by a thick outer coat and a laminated inner coat (5.5 nm periodicity). Small membranous vesicles were present in the spore core and they disappeared as germination proceeded. After depolymerization of the cortex, and a 30% increase in spore diameter a localized gap appeared in the laminated inner coat only. This inner coat gap was narrow and could be the whole length of the spore. The germ cell appeared to grow, or to be pushed towards the inner coat gap, at which stage the outer coat disappeared in the same localized area. As the vegetative cell grew out the spore coat fell away, with loose cortical material still attached to it. The young germ cell developed a large spherical electron dense inclusion body in the cytoplasm, at the same time as the ribosomal and nuclear areas became distinct.