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with and () being a piecewise continuous periodic function with period and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem , due to Gaston Floquet ( 1883 ), gives a canonical form for each fundamental matrix solution of this common linear system .
Notation: If Y is a set then the power set of Y, which is the set of all subsets of Y, is denoted by 2 Y or 𝒫(Y). Definition : If X and Y are sets, a set-valued function in Y on X (also called a Y -valued multifunction on X ) is a function F : X → 2 Y with domain X that is valued in 2 Y .
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to ...
Numerous queueing models use continuous-time Markov chains. For example, an M/M/1 queue is a CTMC on the non-negative integers where upward transitions from i to i + 1 occur at rate λ according to a Poisson process and describe job arrivals, while transitions from i to i – 1 (for i > 1) occur at rate μ (job service times are exponentially ...
Ritz–Galerkin method (after Walther Ritz) typically assumes symmetric and positive definite bilinear form in the weak formulation, where the differential equation for a physical system can be formulated via minimization of a quadratic function representing the system energy and the approximate solution is a linear combination of the given set ...
A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
In terms of being considered as a random set, a sequence of random points is a random closed set if the sequence has no accumulation points with probability one [6] A point process is often denoted by a single letter, [1] [7] [8] for example , and if the point process is considered as a random set, then the corresponding notation: [1]
The α-algorithm or α-miner is an algorithm used in process mining, aimed at reconstructing causality from a set of sequences of events. It was first put forward by van der Aalst, Weijters and Măruşter. [1] The goal of Alpha miner is to convert the event log into a workflow-net based on the relations between various activities in the event log.