Glancing intersection

Glancing intersection Case in which two potential energy surfaces intersect such that their separation decreases to zero quadratically in the relevant nuclear coordinates. 

In case an activation energy is noticed the heat of desorption is higher than the heat of adsorption. A glance at Fig. 10 shows that the speed of the desorption reaction will be governed by the difference in height between level E and intersection point S, which is the sum of the heat of adsorption (A to E) and the activation energy (A to S). 

Although both diagrams appear similar at first glance, there are some important differences. In particular, in the reactive system all solid lines intersect at the origin. The dotted lines are parallel and change their orientation at the bisection line. Furthermore, the pathgrid of the reactive system is symmetric with respect to the bisection line due to the fact that both enantiomers behave the same. This topology has important implications for the construction of wave solutions as discussed in detail in Ref. [13]. 

Now we can visualize evolutionary optimization as a hill-climbing process on a landscape that is given by an extremely simple potential [Eqn. (11.15)]. This potential, an ( — 1 )-dimensional hyperplane in n-dimensional space, seems to be a trivial function at first glance. It is linear and hence has no maxima, minima, or saddle points. However, as with every chemical reaction, evolutionary optimization is confined to the cone of nonnegative concentration restricts the physically accessible domain of relative concentrations to the unit simplex (xj > 0, X2 > 0,..., x > 0 Z x = 1). The unit simplex intersects the (n — 1 )-dimensional hyperplane of the potential on a simplex (a three-dimensional example is shown in Figure 4). Selection in the error-free scenario approaches a corner of this simplex, and the stationary state corresponds to a corner equilibrium, as such an optimum on the intersection of a restricted domain with a potential surface is commonly called in theoretical economics. 

At a first glance we also identify in Gu cydes, i.e. Wrr which was originally present, and which is newly f[Pg.50]

The implication of an abstract minimal Radon partition to minimal Radon partition is still true as long as the abstract minimal Radon partition consists of exactly five atoms. For abstract minimal Radon partitions with fewer than five atoms, a quadruple of atoms with assigned zero-orientation may not lie exactly in a plane. However, as the convex hulls nearly intersect , we can interprete this as some kind of tolerance for Radon partitions. For more details and a proof of Remark 4.16 refer to [105]. However, the relevance of the statement given there is not obvious at a first glance, so we note the following ... 

At first glance it seems that Mendeleevs classification was more or less commonly known in 1880s Portuguese higher education, and by its more visible leaders. Some rational intersection between the periodic behavior of elements and the atomic theory appears to have been stated together with some astronomical... 

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