Regular group action

The Pectolyase Y-23 catalytic activity was studied on several solutions of pectin at pH 3.0 and 6.0 and of polygalacturonic acid at pH 4.1. During pectin depolymerisation, the PL activity is about 20 times lower than the one of the PG and reaches its saturation value after about 30 min whereas the PG activity increases regularly with time. This dual behaviour is probably connected to the competitive hydrolytic action of PE that quickly transforms the pectin into the polygalacturonic acid. Accordingly, the reducing group formation is mainly due to the PG action and the pectin depolymerisation derives from the sequential action of PE and PG. 

Any person who has or may possibly have information relating to an incident should be considered a potential witness. This concept extends heyond the traditionally identified people who were direct participants or eyewitnesses to the occurrence. Indirect witnesses, such as regularly assigned service personnel who are not operations personnel, often contribute valuable information. Examples of this group include workers from maintenance, contract maintenance, laboratory, janitorial, and shipping. Occasionally regular delivery personnel who routinely visit the process unit are familiar with some aspects of what was normal routine and may have noticed some unusual condition, remark, or actions. These people should not he ignored, because they have the potential to contribute valuable information that can help resolve mysteries that would otherwise remain unresolved. 

A third project which the team helped start was FRODA (Friends and Relatives of Drug Abusers), a self-help group which meets on a regular basis to help its members to cope with their burden and occasionally generate action from statutory services. 

If G is the symmetry group of system (5), then, under some additional assumption of regularity of the action of the group G, we can find all its G-invariant solutions by solving the reduced system of differential equations S/G. Note that by construction the system S/G has fewer independent variables that is, the dimension of the initial system is reduced (hence this procedure is called the symmetry reduction method). 

In what follows, we will suppose that the action of the group G in M and its projective actions in ft are regular and the orbits of these actions have the same dimension 5. This dimension is called the rank of the group G (or, alternatively, the rank of the Lie algebra g). Note that the condition rank G —. v is equivalent to the requirement that the relation... 

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