Some mathematical explanations of science concepts



Robotics in mathematical explanation

A feedback controlled mechanical device. Robotics is the study of the design, applications, and control and sensory systems of robots; for example, the design of robot arms that can approach an object from any orientation and grip it.

A robot’s control system may be simple and consist of only a sequencing device so that the device moves in a repetitive pattern, or more sophisticated so that the robot’s movements are generated by computer from data about the environment. The robot’s sensory out of procedure, such as the rule of three, or transformation rules.

Theory of games in mathematical explanation

The mathematical study of the probabilities of each outcome in games. Although there is an element of chance in who wins, there are often general rules for maximizing the chances of one particular outcome. These are calculated from the rules of the game and the number of players, using techniques of probability.

Thomson lamp

A paradoxical machine devised as a thought – experiment by British philosopher James Thomson in 1970 to highlight the difficulty in zeno’s paradoxes of deciding whether a super task, an infinite number of tasks in finite time, has been completed.

The lamp is switched on, and after a minute switches off; after a further half minute it comes on again, goes off after another quarter minute, and so on, changing its state after each term of a convergent series of time intervals.

Since this series of intervals has a sum of two minutes, the process must have terminated after that time, so the lamp must be either on or off; yet it cannot be either on or off, since each time it entered either state is immediately switched again. This does not show, however, as Thomson argued, that zeno’s paradoxes are unresolved by taking limits, since paradoxes concern convergent rather than oscillating series of tasks.

Topology

A branch of modern mathematics rather of geometry, concerned with the general properties of shapes and space. In topology we study the properties that are not altered by continuous distortions such as stretching or twisting.

For example, a sphere and an ellipsoid are though different figures in geometry but are equivalent figure in topology since one can be transformed into the other by a continuous deformation.

Weak topology

The topology imposed on the underlying vector space by taking as sub-base all open half spaces-containing zero. This gives the weakest topology in which ass the norm continuous linear functional are continuous. A space is reflexive if the unit ball is weakly compact or equivalently, by the eberlein-Smulian theorem, if it is weakly sequentially compact.

Some mathematical explanations of science concepts Some mathematical explanations of science concepts Reviewed by knowledge people creators on February 02, 2020 Rating: 5
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