Price smoothing

Ashley and Orr [8] disallow negative inventories or backlogging, but still find that production smoothing can bring about price smoothing. Under the assumption of deterministic demand and concavity of revenue, they find that price stickiness is realized when demand is foreseen to decrease but not when demand is predicted to increase. 

K. S. Lai. Price smoothing under capacity constraints. Southern Economic Journal, 57(1) 150-159, 1990. 

As PV module selling price has decreased, new markets have progressively emerged. This combination of market growth and price decrease has provided a smooth evolutionary path for the commercial industry of the 1990s. 

The price of using implicit methods is that one now has a system of equations to solve at each time step, and the solution methods are more complicated (particularly for nonlinear problems) than the straightforward explicit methods. Phenomena that happen quickly can also be obliterated or smoothed over by using a large time step, so implicit methods are not suitable in all cases. The engineer must decide if he or she wants to track those fast phenomena, and choose an appropriate method that handles the time scales that are important in the problem. 

Dr Price also examined relations between (A) and deton velocity (D). They are presented in Fig 3 for group 1 and in Fig 4 for group 2 Fig 3 shows a representative of group 1, an unconfined cylindrical charge of HBX-1 (RDX/TNT/A1/Wax - 40/38/17/5). Its voidless density is 1.76 g/cc. The curves are for charge diameters d, d, d d which are 6.4, 12.7, 25.4 50.8 mm, respectively. Solid lines are smoothed values from the experimental data which have been extrapolated to A=0.6. The limit line for failure was estimated, as shown on p 694 of Ref 17. A pattern of the same type was previously obtd by Stesik Akimova (Ref 3) for TNT... 

All hypotheses of evolution force us to accept transitional forms of some kind of living, feeding, and reproducing eggs that would survive 3 billion years to metamorphose into a living reproducing animal. Smoothness of phenotype transitions is not observed and all other explanation comes at a price. 

Linkages between periods have some desirable features in principle by allowing for longer-term smoothing of demand and supply shocks, but the solutions to price instability lie elsewhere. 

The above analyses were relatively straightforward the departures from the plane surface were quite simplistic. However, in turns out that any arbitrary surface, provided it is smooth and differs little from the plane, can be treated in essentially the same manner as above since any such surface may be represented either by Fourier series (if periodic) or by Fourier integral (if aperiodic) [91]. In fact, as Goldstein et al. [94] state, for the above approach to be applicable to all orders in the perturbation, a necessary condition is that the general surface shape function (here taken to be a cos(ky)) be infinitely differentiable. The price to pay for allowing more general but smooth surface structure is simply in the amount of tedious labor that must be expended, rather than any demand for new theoretical considerations. 

What has been said about chlorination applies generally for bromination, except that bromine is usually added in the liquid form to the reaction mixture. In isolated cases, however, better results are obtained if the bromine is introduced in the gaseous form. With sensitive substances, bromination often takes place more smoothly than chlorination and yields a purer, more easily crystallized product. Under these circumstances, the higher price of bromine is more than offset by the better yields. If concentrated sulfuric acid is used as the solvent in brominations, the hydrogen bromide formed in the reaction is more or less completely oxidized back to bromine by the sulfuric acid. In such cases, less than the calculated amount of bromine is used, sometimes only one-half or a little more. 

Crude soap curds contain glyccrtil and excess alkali as well as soap but can be purified Iry boiling with water and adding NaCl or KCl to precipitate the pure carboxylate salts. The smooth soap that precipitates is dried, perfumed, and pressed into bars for household use. Dyes are added to make colored soaps, antiseptics are added for medicated soaps, pumice is added for scourirg soaps, and air is blown in for soaps lhat float. Regardless of these extra treatments and regardless of price, though, all soaps are basically the same. 

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