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The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. [1] [2] The Leslie matrix (also called the Leslie model) is one of the most well-known ways to describe the growth of populations (and their projected age distribution), in which a population is closed to migration, growing in an unlimited ...
In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures. The exponential formula is a power series version of a special case of Faà di Bruno's ...
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group.
In a relatively good approximation a diode is modelled by the single-exponential Shockley diode law. This nonlinearity still complicates calculations in circuits involving diodes so even simpler models are often used. This article discusses the modelling of p-n junction diodes, but the techniques may be generalized to other solid state diodes.
Just as the class P is defined in terms of polynomial running time, the class EXPTIME is the set of all decision problems that have exponential running time. In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O (2 p ( n ) ) time, where p ( n ) is a polynomial function of n .
Complex replacement is used for solving differential equations when the non-homogeneous term is expressed in terms of a sinusoidal function or an exponential function, which can be converted into a complex exponential function differentiation and integration. Such complex exponential function is easier to manipulate than the original function.
The sum of exponentials is a useful model in pharmacokinetics (chemical kinetics in general) for describing the concentration of a substance over time. The exponential terms correspond to first-order reactions, which in pharmacology corresponds to the number of modelled diffusion compartments. [2] [3]
A more general framework where the term 'exponential polynomial' may be found is that of exponential functions on abelian groups. Similarly to how exponential functions on exponential fields are defined, given a topological abelian group G a homomorphism from G to the additive group of the complex numbers is called an additive function, and a homomorphism to the multiplicative group of nonzero ...