New PDF release: An extended doubly-adaptive quadrature method based on the

By Hasegawa T., Hibino S., Hosoda Y.

Summary An development is made to an automated quadrature as a result of Ninomiya (J. Inf. technique. 3:162–170, 1980) of adaptive style in keeping with the Newton–Cotes rule by means of incorporating a doubly-adaptive set of rules because of Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We evaluate the current approach in functionality with a few others by utilizing a number of try out difficulties together with Kahaner’s ones (Computation of numerical quadrature formulation. In: Rice, J.R. (ed.) Mathematical software program, 229–259. educational, Orlando, FL, 1971).Keywords computerized quadrature · Adaptive set of rules · Numerical comparability

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Illustration: FIG. ] The following report (taken from the Faversham News, 22nd Oct. 1887) of experiments conducted in the presence of several scientific and mining men will show its value:--"A large wrought-iron tank, of 45 cubic feet capacity, had been sunk level with the ground in the middle of the yard; to this tank the gas had been laid CHAPTER III. 42 on, for a purpose that will be explained later on. '" Operations were commenced by the top of the tank being covered over and plastered down in order to make it air-tight; then a sufficient quantity of coal gas was placed in it to make it highly inflammable and explosive, the quantity being ascertained by a meter which had been fixed specially for the purpose.

At some works the cotton is dried upon shelves in a drying house through which hot air circulates, the shelves being of canvas or of brass wire netting. The hot air CHAPTER III. 31 must pass under the shelves and through the cotton, or the process will be a very slow one. ~--The dry cotton has now to be nitrated. This is done by dipping it into a mixture of nitric and sulphuric acids. 52, and should contain as little nitric oxide as possible. , and contain about 97 per cent. of the mono-hydrate (H_{2}SO_{4}).

Two per cent. of carbonate of soda is sometimes added, but it is not really necessary if the cotton has been properly washed. ~--The gun-cotton, in the state in which it is removed from the poacher, contains from 28 to 30 per cent. of water. In order to remove this, the cotton has to be compressed by hydraulic power. The dry compressed gun-cotton is packed in boxes containing 2,500 lbs. of dry material. In order to ascertain how much of the wet cotton must be put into the press, it is necessary to determine the percentage of water.

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An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes by Hasegawa T., Hibino S., Hosoda Y.


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