On solution structure of the radial heat problem with singular data

Initial value problem solutions to radial heat problem with Laplace operator and singular dat

The radial heat equation and Laplace transforms

Integral representations involving Laplace transforms developed for use in solutions of radial heat equatio

Dual Functions and Heat Expansions

Radial heat polynomial transformations in series expansions of heat equatio

Imaging natural materials with a quasi-microscope

A Viking lander camera with auxilliary optics mounted inside the dust post was evaluated to determine its capability for imaging the inorganic properties of granular materials. During mission operations, prepared samples would be delivered to a plate positioned within the camera's field of view and depth of focus. The auxiliary optics would then allow soil samples to be imaged with an 11 pm pixel size in the broad band (high resolution, black and white) mode, and a 33 pm pixel size in the multispectral mode. The equipment will be used to characterize: (1) the size distribution of grains produced by igneous (intrusive and extrusive) processes or by shock metamorphism, (2) the size distribution resulting from crushing, chemical alteration, or by hydraulic or aerodynamic sorting; (3) the shape and degree of grain roundness and surface texture induced by mechanical and chemical alteration; and (4) the mineralogy and chemistry of grains

A mathematical model of a large open fire

A mathematical model capable of predicting the detailed characteristics of large, liquid fuel, axisymmetric, pool fires is described. The predicted characteristics include spatial distributions of flame gas velocity, soot concentration and chemical specie concentrations including carbon monoxide, carbon dioxide, water, unreacted oxygen, unreacted fuel and nitrogen. Comparisons of the predictions with experimental values are also given

THE LATERAL REACTION STEP IN TENNIS FOOTWORK

Anecdotal evidence suggests that the key to quickness in tennis is the "reaction step", or the first step in response to the ball. There are three possible lateral reaction steps towards a wide and difficult shot: 1) step first with the outside foot towards the ball (jab step); 2) pivot on the outside foot while turning the hips towards the ball (pivot step); 3) bring the outside foot towards the body away from the ball, allowing gravity to assist the motion (drop step or gravity step). A controlled study of 10 participants showed that when a player used the gravity step to reach a lateral shot requiring a quick response, the player was 52% more likely to reach the ball (p < 0.05) and 100% more likely to control the return shot (p < 0.05) when compared to the jab step. A simple experiment utilizing a 9-marker motion analysis system provided further evidence to support these findings