Ordinary discontinuity

The methods presented include linear algebra methods (linearization, stability analysis of the linear system, constrained linear systems, computation of nominal interaction forces), nonlinear methods (Newton and continuation methods for the computation of equilibrium states), simulation methods (solution of discontinuous ordinary differential and differential algebraic equations) and solution methods for... 

The flow field in front of an expanding piston is characterized by a leading gas-dynamic discontinuity, namely, a shock followed by a monotonic increase in gas-dynamic variables toward the piston. If both shock and piston are regarded as boundary conditions, the intermediate flow field may be treated as isentropic. Therefore, the gas dynamics can be described by only two dependent variables. Moreover, the assumption of similarity reduces the number of independent variables to one, which makes it possible to recast the conservation equations for mass and momentum into a set of two simultaneous ordinary differential equations ... 

Optimal flow method, 261 Optimization non-constrained, 286 of functionals, 305 Ordinary value, 338 Orthogonalization, Schmidt," 65 Osaki, S., 664 Oscillation hysteresis, 342 Oscillations autoperiodic, 372 discontinuous theory, 385 heteroperiodic, 372 piecewise linear, 390 relaxation asymptotic theory, 388 relaxation, 383 Oscillatory circuit, 380 "Out field, 648 existence of, 723... 

Boyle believed there were many elements. He defined them as primitive and simple, or perfectly unmingled bodies, which are the ingredients of all mixtures and compounds. Boyle thought these elements accounted for all the different properties of chemicals. From Boyle s pioneering work it became clear that elements cannot be changed into one another by ordinary methods. Therefore, the attempts to convert base (nonprecious) metals into gold were discontinued. 

In principle the manufacture of cordite RDB was similar to that of ordinary cordite with the difference that instead of drying the damp nitrocellulose it was dehydrated with alcohol and the required amount of ether and additional alcohol were introduced in the kneader. The manufacture of cordite RDB was discontinued after the w3r since its ballistic properties were inferior to those of common cordite. 

The united ethereal solutions, which are brown in colour, are shaken for 5 minutes with potassium carbonate, then poured off, and dried for 12 hours over anhydrous sodium sulphate. When the greater part of the ether has been evaporated at ordinary pressure on a water bath, the distillation is continued under a pressure 10—12 mms. At ordinary temperature, ether first passes over. The distilling vessel is now warmed in warm water, when a first fraction is obtained, which still contains alcohol and ether, and also some glycocoll ester and alanine ester. When the temperature of the bath has risen to 55°, the main part of the alanine ester begins to boil. The operation is discontinued when, at a bath temperature of 80°, nothing more distils over. In this way 110—125 gms. distillate are obtained, consisting for the most part of alanine ester. 

Cocoa powder was more sensitive to friction than ordinary black powder. Samples were reported to have inflamed from shaking in a canvas bag. Cocoa powder was used in the Spanish-American war, 1898. When its use was discontinued, existing stocks were destroyed, and single grains of the powder are now generally to be seen only in museums/. ... 

Our ordinary waking consciousness... is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different, we may go through life without suspecting their existence but apply the requisite stimulus, and at a touch they are all there in all their completeness, definite types of mentality which probably somewhere have their field of application and adaptation. No account of the universe in its totality can be final which leaves these other forms of consciousness quite disregarded. How to regard them is the question-for they are so discontinuous with ordinary consciousness. 

A major discontinuity in the behavior of water occurs at about 2100 bars, where the equilibrium ice phase changes from ordinary ice Ih, which is less... 

By far the most important of the local nonuniform flow phenomena is that which occurs when supercritical flow has its velocity reduced to subcritical. We have seen in these example scenarios that there is no ordinary means of changing from lower- to upper-stage flow with a smooth transition, because the theory calls for a vertical slope of the water surface. The result, then, is a marked discontinuity in the surface, characterized by a steep upward slope of the profile, broken throughout with violent turbulence, and known universally as the hydraulic jump. 

Discontinuation effects also mean that in ordinary clinical practice people who take long-term medication and stop or reduce it for any... 

But now a problem is handed over to the philosophers. This discontinuous existence in space, thus assigned to electrons, is very unlike the continuous existence of material entities which we habitually assume as obvious. The electron seems to be borrowing the character which some people have assigned to the Mahatmas of Tibet. These electrons, with the correlative protons, are now conceived as being the fundamental entities out of which the material bodies of ordinary experience are composed. Accordingly, if this explanation is allowed, we have to revise all our notions of the ultimate character of material existence. For when we penetrate to these final entities, this startling discontinuity of spatial existence discloses itself (Whitehead 1967, pp. 34—35)... 

The use of sulfur dioxide in addition to lime makes a better clarification. In this method (sulfitation process), lime is added as usual, but then sulfur dioxide from a sulfur burner is bubbled through the juice. The precipitate is settled as in the ordinary clarification process. The bleaching effect of sulfur makes a lighter-colored sugar. The extra cost of sulfitation, increased sealing in heaters and evaporators, and higher ash in raw sugars are reasons for the discontinuance of this process. 

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