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Using and Euclidean

Using the Euclidean algorithm: 455839 = 4300 · 106 + 39, then 106 = 2 · 39 + 28, then 39 = 28 + 11, then 28 = 2 · 11 + 6, then 11 = 6 + 5, then 6 = 5 + 1.

Using Euclidean division, 9 divided by 4 is 2 with remainder 1.

Using ideas from Whitney's embedding theorem, A can be embedded in k-dimensional Euclidean space with

Using and algorithm

Using to denote the size of the original grammar, the size blow-up in the worst case may range from to, depending on the transformation algorithm used.

Using the following observation, one can create a recursive algorithm that computes x n for an integer n using squaring and multiplication:

Using a similarity matrix, the algorithm delivered matches between meanings including a confidence factor.

Using this map, each router then independently determines the least-cost path from itself to every other node using a standard shortest paths algorithm such as Dijkstra's algorithm.

Using the material properties and the effect of the lights in the scene, this algorithm can determine the shading of this object.

Using different algorithms on a single data set can sometimes yield different " best " cladograms, because each algorithm may have a unique definition of what is " best ".

Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of ( decimal ) digits of b. He also proved a special case of Fermat's last theorem.

Using big-O notation, the performance of the interpolation algorithm on a data set of size N is O ( N ); however under the assumption of a uniform distribution of the data on the linear scale used for interpolation, the performance can be shown to be O ( log log N ).

Note: Using a stack instead of a queue would turn this algorithm into a depth-first search.

Using this information the AN / UYK-1 ran the least squares algorithm and provided a location reading in about fifteen minutes.

Using the XOR swap algorithm to exchange nibble s between variables without the use of temporary storage

Using the XOR swap algorithm, however, no temporary storage is needed.

Using this method, he showed how to solve the Hamiltonian cycle problem in arbitrary n-vertex graphs by a Monte Carlo algorithm in time O ( 1. 657 n ); for bipartite graphs this algorithm can be further improved to time O ( 1. 414 n ).

* Algorithm design – Using ideas from algorithm theory to creatively design solutions to real tasks.

Using modular exponentiation by repeated squaring, the running time of this algorithm is O ( k log 3 n ), where k is the number of different values of a we test ; thus this is an efficient, polynomial-time algorithm.

Using Fibonacci heaps for priority queues improves the asymptotic running time of important algorithms, such as Dijkstra's algorithm for computing the shortest path between two nodes in a graph.

Using PEG's, another representation of grammars, packrat parsers provide an elegant and powerful parsing algorithm.

Using the material properties and the effect of the lights in the scene, this algorithm can determine the shading of this object.

Using the same ideas used in minimum / maximum algorithms, we can construct a simple, but inefficient general algorithm for finding the kth smallest or kth largest item in a list, requiring O ( kn ) time, which is effective when k is small.

Using this programming method, a process scheduling algorithm will increase the priority of a process to the maximum priority of any process waiting for any resource on which the process has a resource lock.

Using and is

Using Edgerton's method, the fast-closing action is obtained from the blackening of a window by exploding a series of parallel lead wires.

Using the F-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution.

Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.

Using a byte-oriented approach, it is possible to combine the < tt > SubBytes </ tt >, < tt > ShiftRows </ tt >, and < tt > MixColumns </ tt > steps into a single round operation.

Using two anchors set approximately 45 ° apart, or wider angles up to 90 °, from the bow is a strong mooring for facing into strong winds.

Using the same techniques they calculated the length of the Nile as, which is longer than previous estimates but still shorter than the Amazon.

Using the biblical Book of Revelation as a point of departure, Caesar Antichrist presents a parallel world of extreme formal symbolism in which Christ is resurrected not as an agent of spirituality but as an agent of the Roman Empire that seeks to dominate spirituality.

Using archery to take game animals is known as bow hunting.

Using a bow and arrow to take fish is known as bow fishing.

Using this criterion of falsifiability, astrology is a pseudoscience.

Using the formula, the overall speed boost is 1 / 0. 4575

Using this binding mechanism, an antibody can tag a microbe or an infected cell for attack by other parts of the immune system, or can neutralize its target directly ( for example, by blocking a part of a microbe that is essential for its invasion and survival ).

* Using a suitable catalyst ( e. g. Wilkinson's catalyst ), it is possible to reduce just one of the double bonds of an allene.

Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S n → ℝ n that does not equalize on any antipodes then we can construct a map g: S n → S n-1 by the formula

Using an existing language to bootstrap a new language is one way to solve the " chicken or the egg " causality dilemma.

Using ballpoint pens to create artwork is not without limitations.

Using the familiar cartesian basis, a vector A is written ;

Using programs or proofs of bounded lengths, it is possible to construct an analogue of the Berry expression in a formal mathematical language, as has been done by Gregory Chaitin.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

Using numeric references that refer to permanently undefined characters and control characters is forbidden, with the exception of the linefeed, tab, and carriage return characters.

Using a three-digit Julian day number saves one byte of computer storage over a two-digit month plus two-digit day, for example, " January 17 " is 017 in Julian versus 0117 in month-day format.

Using color this way, the darkness and intensity ( or value ) of the color is evaluated by the eye as a measure of intensity or concentration.

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