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A Petri net, also known as a place/transition net (PT net), is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements: places and transitions. Place elements are depicted as white circles ...
Nielsen realization problem (geometric topology) Nielsen–Schreier theorem (free groups) Niven's theorem (number theory) No-broadcasting theorem (quantum information theory) No-cloning theorem (quantum computation) No-communication theorem (quantum information theory) No-deleting theorem (quantum information theory)
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. [1] [2]: 10 It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix.
In algebra, the theorem of transition is said to hold between commutative rings if [1] [2] B {\displaystyle B} dominates A {\displaystyle A} ; i.e., for each proper ideal I of A , I B {\displaystyle IB} is proper and for each maximal ideal n {\displaystyle {\mathfrak {n}}} of B , n ∩ A {\displaystyle {\mathfrak {n}}\cap A} is maximal
The exponential of a Metzler (or quasipositive) matrix is a nonnegative matrix because of the corresponding property for the exponential of a nonnegative matrix. This is natural, once one observes that the generator matrices of continuous-time Markov chains are always Metzler matrices, and that probability distributions are always non-negative.
Pick a vector in the above span that is not in the kernel of A − 4I; for example, y = (1,0,0,0) T. Now, (A − 4I)y = x and (A − 4I)x = 0, so {y, x} is a chain of length two corresponding to the eigenvalue 4. The transition matrix P such that P −1 AP = J is formed by putting these vectors next to each other as follows
In the mathematics of probability, a transition kernel or kernel is a function in mathematics that has different applications. Kernels can for example be used to define random measures or stochastic processes. The most important example of kernels are the Markov kernels.
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.
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