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For example, balanced two-phase power can be obtained from a three-phase network by using two specially constructed transformers, with taps at 50% and 86.6% of the primary voltage. This Scott T connection produces a true two-phase system with 90° time difference between the phases.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A difference equation is an equation where the unknown is a function f that occurs in the equation through f(x), f(x−1), ..., f(x−k), for some whole integer k called the order of the equation. If x is restricted to be an integer, a difference equation is the same as a recurrence relation
Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.
A transcendental equation need not be an equation between elementary functions, although most published examples are. In some cases, a transcendental equation can be solved by transforming it into an equivalent algebraic equation. Some such transformations are sketched below; computer algebra systems may provide more elaborated transformations. [a]
With denoting the static equation of motion of a system with a single degree of freedom the following calculations can be performed: Diagram of a ball placed in an unstable equilibrium. Second derivative < 0 The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state.
However, this assumption is sometimes modified to include a saturable response that follows Michaelis–Menten kinetics or a related model called a Hill equation. When the material in question is present at a concentration near the K M, it often behaves with pseudo first-order kinetics (see Rate equation) and the plateau principle applies ...
[3] [4] In contrast, linear algebra deals mostly with finite-dimensional spaces, and does not use topology. An important part of functional analysis is the extension of the theories of measure , integration , and probability to infinite-dimensional spaces, also known as infinite dimensional analysis .