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where <math>T</math> is the time (period) of a single rotation(revolution) and <math>f</math> is the frequen If a wheel turns by an angle <math>\theta</math> in a time <math>t</math> then the angular frequency at any moment is given by, ...

...' is the wave function, ''ħ'' is the reduced [[Planck constant]], ''t'' is time, ''x'' is position in space, ''Ĥ'' is a mathematical object known as the '' ...

...example in [[modular arithmetic]]. The algorithm has been known for a long time. It is already written down in a book called ''Chandah-sûtra''. That book ...

...andomized and works in <math>\tilde{O}(mn^{0.9}\log W)</math> total update time under the assumption of oblivious non-adaptive adversary. ...rithm with <math>\tilde{O}((mn^{1/2} + m^{7/5})\log W)</math> total update time, which improves over both previous results when <math>m = O(n^{1.42})</math ...

...andomized and works in <math>\tilde{O}(mn^{0.9}\log W)</math> total update time under the assumption of oblivious non-adaptive adversary. ...rithm with <math>\tilde{O}((mn^{1/2} + m^{7/5})\log W)</math> total update time, which improves over both previous results when <math>m = O(n^{1.42})</math ...

...possible that more than one packets want to use the same edge at the same time. We assume that a queue is associated to each edge, such that the packets t This is pretty bad, because we expect that the routing time is comparable to the diameter of the network, which is only <math>d=\log N< ...

...lem, and then give an FPTAS for the problem based on the pseudo-polynomial time algorithm. ...orithm through conditional expectation and give a deterministic polynomial time algorithm with approximation ratio <math>3/4</math>. ...

Algorithms can be written in regular English, but it takes a long time to do so. Instead, algorithms are written in [[pseudocode]], [[Flow chart|f ...hen we write algorithms, we like our algorithm to take the least amount of time so that we can solve our problem as quickly as possible. ...

...n</math>, returns the number of perfect matchings in <math>G</math> within time <math>O(n^22^n)</math>. ...

* sample uniformly from <math>K</math> in time polynomial of <math>n</math>; * compute its volume <math>\mathrm{vol}(K)</math> precisely in time polynomial of <math>n</math>. ...

#<math>\mathcal{M}_c</math> has mixing time <math>O(n\ln n)</math> whenever <math>q\ge\Delta+2</math>. # Random sampling of proper graph colorings can be done in polynomial time whenever <math>q\ge\Delta+1</math>. ...

...[[shape]] in space that is like the [[surface]] of a [[ball]]. Most of the time, the terms ball and sphere are used as the same. But in [[mathematics]], th ...

...riation distance to the stationary distribution monotonically decreases as time passes. Although this is rather intuitive at the first glance, the proof is ...pper bound its mixing time. The coupling technique for bounding the mixing time can be sumerized as follows: ...

...f. Philosophically, this can be stated as "nothing depends on time per se (time itself)". Therefore, energy does not vary with time. ...

..., Einstein (1905) drew the conclusion that the concepts of [[space]] and [[time]] needed a fundamental revision. The result was special relativity theory. ...rence that describes time and space homogeneously, isotropically, and in a time-independent manner. Shorthand: space the same everywhere at all times. ...

Last time we talked about algorithms. Today's topic is '''complexity'''. In this lecture, we are focused on the '''time complexity''', although there are other complexity measures in various comp ...

...ative (mathematics)|derivative]], or the rate of change of acceleration by time. Jerk is also called '''jolt''' (in British English), '''surge''', or '''lu ...

The time complexity of this sorting algorithm is measured by the '''number of compar ..., sorting which will cost us <math>\Omega(n^2)</math> comparisons, ''every time''! ...

#include<time.h> gsl_rng_set(r,int(time(NULL))); //设置随机数seed ...

Very often such problems were unresolved for centuries. With time, mathematicians came to understand their depth (in some cases), rather tha ...