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Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.
To investigate the possible state/input/output sequences in an automaton using formal language theory, a machine can be assigned a starting state and a set of accepting states. Then, depending on whether a run starting from the starting state ends in an accepting state, the automaton can be said to accept or reject an input sequence.
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
^, the a posteriori state estimate mean at time k given observations up to and including at time k; P k ∣ k {\displaystyle \mathbf {P} _{k\mid k}} , the a posteriori estimate covariance matrix (a measure of the estimated accuracy of the state estimate).
The state machine recognizes two commands: "command_open" and "command_close", which trigger state changes. The entry action (E:) in state "Opening" starts a motor opening the door, the entry action in state "Closing" starts a motor in the other direction closing the door. States "Opened" and "Closed" stop the motor when fully opened or closed.
The state S 1 represents that there has been an even number of 0s in the input so far, while S 2 signifies an odd number. A 1 in the input does not change the state of the automaton. When the input ends, the state will show whether the input contained an even number of 0s or not.
The original, and best-known, example of an apportionment problem involves distributing seats in a legislature between different federal states or political parties. [1] However, apportionment methods can be applied to other situations as well, including bankruptcy problems , [ 2 ] inheritance law (e.g. dividing animals ), [ 3 ] [ 4 ] manpower ...
The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.