Search results
Results from the WOW.Com Content Network
The transitive reduction of a finite directed graph G is a graph with the fewest possible edges that has the same reachability relation as the original graph. That is, if there is a path from a vertex x to a vertex y in graph G, there must also be a path from x to y in the transitive reduction of G, and vice versa.
The transitive closure of a DAG is the graph with the most edges that has the same reachability relation as the DAG. It has an edge u → v for every pair of vertices ( u , v ) in the reachability relation ≤ of the DAG, and may therefore be thought of as a direct translation of the reachability relation ≤ into graph-theoretic terms.
Specifically, taking a strict partial order relation (, <), a directed acyclic graph (DAG) may be constructed by taking each element of to be a node and each element of < to be an edge. The transitive reduction of this DAG [b] is then the Hasse diagram. Similarly this process can be reversed to construct strict partial orders from certain DAGs.
In organic chemistry, neighbouring group participation (NGP, also known as anchimeric assistance) has been defined by the International Union of Pure and Applied Chemistry (IUPAC) as the interaction of a reaction centre with a lone pair of electrons in an atom or the electrons present in a sigma or pi bond contained within the parent molecule but not conjugated with the reaction centre.
Reductive elimination is an elementary step in organometallic chemistry in which the oxidation state of the metal center decreases while forming a new covalent bond between two ligands. It is the microscopic reverse of oxidative addition, and is often the product-forming step in many catalytic processes. Since oxidative addition and reductive ...
Given a set of objects and a transitive relation with (,) modeling a dependency "a depends on b" ("a needs b evaluated first"), the dependency graph is a graph = (,) with the transitive reduction of R. For example, assume a simple calculator.
The concept of a transition state has been important in many theories of the rates at which chemical reactions occur. This started with the transition state theory (also referred to as the activated complex theory), developed independently in 1935 by Eyring, Evans and Polanyi, and introduced basic concepts in chemical kinetics that are still used today.
The Staudinger reduction is conducted in two steps. First phosphine imine-forming reaction is conducted involving treatment of the azide with the phosphine. The intermediate, e.g. triphenylphosphine phenylimide, is then subjected to hydrolysis to produce a phosphine oxide and an amine: R 3 P=NR' + H 2 O → R 3 P=O + R'NH 2