Robin problem

Kapila, A. K., Matkowsky, B. J., and Vega, J. (1980). Reactive-diffusive systems with Arrhenius kinetics the Robin problem. SIAM J. Appl. Math., 38, 391-401. 

There are three kinds of boundary conditions for elliptic equations. If the values of the unknown function are prescribed on the boundary, then the problem is called the Dirichlet problem. If the derivatives of the unknown function are prescribed on the boundary, then it is called the Neumann problem. If a linear combination of the function values and the derivatives is specified, then it is called the Robin problem. 

As a first step in the direction outlined here some manufacturers and BAM last year discussed the problems and the possible procedures of such a system of quality assurance. As a result of this meeting round robin tests for the harmonization of the measurements of film system parameters and a possible procedure of surveillance of the quality of film systems were proposed. Closely related to these the BAM offers to perform the classification of film systems. But as during the production of films variations of the properties of the different batches cannot be avoided, the results of measurements of films of a single batch will be restricted to this charge, while only the measurements and mean of several batches of a film type will give representative values of its properties. This fact is taken into account already in section 4 of the standard EN 584-1 which can be interpreted as a kind of continuous surveillance. In accordance with this standard a film system caimot be certified on the base of measurements of a single emulsion only. 

O-isopropylidene derivative (57) must exist in pyridine solution in a conformation which favors anhydro-ring formation rather than elimination. Considerable degradation occurred when the 5-iodo derivative (63) was treated with silver fluoride in pyridine (36). The products, which were isolated in small yield, were identified as thymine and l-[2-(5-methylfuryl)]-thymine (65). This same compound (65) was formed in high yield when the 5 -mesylate 64 was treated with potassium tert-hx Xy -ate in dimethyl sulfoxide (16). The formation of 65 from 63 or 64 clearly involves the rearrangement of an intermediate 2, 4 -diene. In a different approach to the problem of introducing terminal unsaturation into pento-furanoid nucleosides, Robins and co-workers (32,37) have employed mild base catalyzed E2 elimination reactions. Thus, treatment of the 5 -tosylate (59) with potassium tert-butylate in tert-butyl alcohol afforded a high yield of the 4 -ene (60) (37). This reaction may proceed via the 2,5 ... 

Most of the mixed-valence systems mentioned by Robin and Day and by Hush were in the solid state. The problem of creating discrete chemical systems for which experiments could be carried out either in solution or in the solid state was first attacked experimentally by Creutz and Taube (6). Their approach was to link together the two metal sites through a ligand bridge, which led to dimers and oligomers. 

Pictorially, the problem can be described as looking at a robin pulling a worm out of a hole. Does the robin get the entire worm or some fraction of the worm The factors are similar and deal with the length of the worm and how far into the hole it is. If it is largely within the hole then it can grasp the dirt, roots, etc. around it to hold on for dear life. If not, the worm is a meal for the early bird. ... 

The overall mercury recovery in the process is 67 15%. The precision of the method is about 20%, and the detection limit is about 0.01 ppm mercury for a 1-g sample of coal. Reliability of the method was determined by the accurate analysis of two coal samples used in the Bureau of Mines study of the problems involved in determining mercury in coal (9) and then by the agreement within experimental error of the results from the 11 Bureau of Mines round-robin coal samples and their probable mercury contents (4). 

Although calcium arsenates may readily precipitate in acid mine drainage and form in flue gas treatment systems, Robins and Tozawa (1982) warn that the compounds may not have long-term stability, which could lead to disposal and environmental problems. Besides dissolving under acidic conditions, the presence of carbonate, bicarbonate, or CO2 may decompose calcium arsenates. When calcium arsenates react with CO2, calcium carbonate forms and the arsenic could be released into the environment (Ghimire et al., 2003, 4946 Jing, Korfiatis and Meng, 2003, 5055-5056). 

Figure 6. Organic chemicals causing problems in the round-robin and proficiency tests...

By contrast, quite different results have been obtained with dilute polymer solutions. Here the extensional viscosity may be as much as thousand times the shear viscosity. Measurement of extensional viscosity of such mobile liquids is far more difficult than shear viscosity, or even impossible. According to Barnes et al. (General references, 1993) "The most that one can hope for is to generate flow which is dominated by extension and then to address the problem of how best to interpret the data in terms of material functions that are Theologically meaningful". An example of the difficulties that arise with the measurement of extensional viscosity is shown In Fig. 16.21 for a Round Robin test... 

Both untransformed (Hashimofo and Yamada, 1994) and transformed root cultures of Datura, Hyoscyamus, Atropa and Duboisia species (Robins and Walton, 1993) accumulate high levels of fhe fropane alkaloids, hyoscyamine and scopolamine (Fig. 2.3). These medically imporfanf fropane alkaloids present not only an interesting biochemical problem but also a realistic... 

At boundary nodes where the variable values are given by Dirichlet conditions, no model equations are solved. When the boundary condition involve derivatives as defined by Neumann conditions, the boundary condition must be discretized to provide the required equation. The governing equation is thus solved on internal points only, not on the boundaries. Mixed or Robin conditions can also be used. These conditions consist of linear combinations of the variable value and its gradient at the boundary. A common problem does arise when higher order approximations of the derivatives are used at... 

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