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Catastrophe theory studies dynamical systems that describe the evolution [5] of a state variable over time : ˙ = = (,) In the above equation, is referred to as the potential function, and is often a vector or a scalar which parameterise the potential function.
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
Inverted U may refer to: Calmfors–Driffill hypothesis , an economic theory describing the relationship between collective bargaining and employment Kuznets curve , an economic theory describing the relationship between income per capita and wealth inequity
The Multi-dimensional Theory of Anxiety [7] is based on the distinction between somatic and cognitive anxiety. The theory predicts that a negative, linear relationship between somatic and cognitive anxiety, an Inverted-U relationship between somatic anxiety and performance, and that somatic anxiety declines once performance begins although cognitive anxiety may remain high, if confidence is low.
Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra).
A decade later, with AI more prevalent than ever, Professor Bostrom has decided to explore what will happen if things go right; if AI is beneficial and succeeds in improving our lives without ...
In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol ∅ {\displaystyle \emptyset } for the set that has no member.