Kramers’ modification

Early applications of WKB approximations to the Coulomb problem in Schrodinger theory demonstrated the necessity and expediency of the Kramers modification ) ... 

An approximate solution of Eq. (4.46) can be obtained for a general potential energy V (r) by means of the WKB method and expressions derived for a number of quantities. Using Kramers modification A = (i/ + ) in the differential equation (4.46), one defines the local wave number as... 

Once the function g(s) is known, one can make the following modification to the molecular-dynamics-Kramers-Grote-Hynes scheme we outlined at the end of the Introduction. 

Although the term amylose dates to 1895, it was not until the 1940s that it became associated with the mainly linear chains of starch (see Chapter 3). Before this, little was known about the structure or identity of starch polymers. In 1946, R.L. Whistler, a carbohydrate chemist, and H.H. Kramer, a geneticist, set out to produce a com modification that would be the opposite of waxy corn, i.e. one in which the starch would be... 

In this complex state of affairs it seemed of interest to examine some reactions at pressures so low that some differentiation between the proposed mechanisms would be possible, or at least some experimental data in a simplified form would be available. It is evident that, at sufficiently low pressures, a profound modification of the velocity constant should take place whether the mechanism be that of Christiansen and Kramers, Lindemann, Perrin or Rodebush. The relation between collision frequency and observed reaction rate at this point would also be of considerable significance.11... 

However, the degree of modification we can exert on the properties of optical phenomena by introducing a complex medium appears to be limited. These limits, called conservation or sum rules, seem to have fundamental physical reasons. For instance, the Eamett-Loudon sum rule [1] places a restriction on the modification of spontaneous emission rate regardless of the means used and is derived from the general causality-related laws such as the Kramers-Kronig relation. 

Chessin M, Kramer ER, Scott CC. Modification of the pharmacolc of reserpine and serotonin by iproniazid J Pharmacol Exp Ther( 957) 119,453-60. 

Kramer G, Buchhammer HM, Lunkwitz K (1997) Surface modification by polyelectrol)4e complexes influence of different polyelectrolyte components and substrates. Coll Surf A 122 1-12... 

Modification of SDG After SDG is built, the reduced digraph is obtained by removal of unmeasured nodes from the SDG (Kramer, 1987). The reduced digraph of CSTR process is shown in figure 1. And, physically feasible faults for each piece of equipment are defined and added on the root node in order to handle only physically meaningful faults (Lee et al., 1999). 

The microstructure observed for thick films shows fibrils, about 4-10 nm in diameter for polystyrene, in agreement with SAXS measurements on the crazes in the bulk polymer. Very thin films of polystyrene (100 nm) show modification in the craze structure as there is no plastic restraint normal to the film [397]. Deformation zones have also been studied in polycarbonate, polystyrene-acrylonitrile and other polymers [398]. Crazes in thermosets can be studied in thin films spun onto NaCl substrates which can be washed away when the film has been cured. Mass thickness measurements are difficult to make in radiation sensitive materials that is why most TEM work has been done on polystyrene and least on PMMA. After developing the techniques described above for TEM Donald and Kramer [398] applied similar methods in optical microscopy to study radiation sensitive materials and the kinetics and growth of deformation zones. Thin films were strained on grids in situ in a reflecting OM. Change of interference color, which depends on the film thickness, was a very sensitive method for observing film deformation. 

Klemm D, Schumann D, Kramer F, Hesler N, Koth D, Sultanova B (2009) Nanocellulose materials—different cellulose, different functionality. Macromol Symp 280 60-71 Lande S, Hoibo OA, Larnoy E (2010) Variation in treatability of Scots pine (Pinussylvestris) by the chemical modification agent furfuryl alcohol dissolved in water. Wood Sci Technol 44 105-118... 

---