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 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 the extension of the code, the encoded string 0011001011 can be grouped into codewords as 0 – 011 – 0 – 01 – 011, and these in turn can be decoded to the sequence of source symbols acabc.

Using this sequence, he constructs nested intervals whose intersection contains a real number not in the sequence.

Using a mathematical formulation, let ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub >) be the input sequence of n distinct values over the finite field F ; then the codebook C created from the tuplets of values obtained by evaluating every polynomial ( over F ) of degree less than k at each x < sub > i </ sub > is

Using the concept of the impossibility of a gambling system, von Mises defined an infinite sequence of zeros and ones as random if it is not biased by having the frequency stability property i. e. the frequency of zeros goes to 1 / 2 and every sub-sequence we can select from it by a " proper " method of selection is also not biased.

Using a parsimony criterion is only one of several methods to infer a phylogeny from molecular data ; maximum likelihood and Bayesian inference, which incorporate explicit models of sequence evolution, are non-Hennigian ways to evaluate sequence data.

Using Marcin Ciura's gap sequence, with an inner insertion sort.

Using command objects makes it easier to construct general components that need to delegate, sequence or execute method calls at a time of their choosing without the need to know the owner of the method or the method parameters.

Using a heuristic method, BLAST finds similar sequences, not by comparing either sequence in its entirety, but rather by locating short matches between the two sequences.

Using this grammar, the sequence of symbols

Using the following sample signal that is composed of a set of four sinusoidal waveforms joined together in sequence.

Using the Tor functor's long exact sequences, one can then easily prove facts about a short exact sequence

Using the axiom of choice, they select and memorize a representative sequence from each equivalence class.

Using digitized sound and 256-color VGA graphics, it consists of a sequence of several levels, each of them in different action style, and the story is carried between levels with comic book-style strips and spoken dialogue.

Using cryptographic hashes inside the port knock sequence can mean that even sniffing the network traffic in and out of the source and target machines is ineffective against discovering the port knock sequence or using traffic replay attacks to repeat prior port knock sequences.

Using this weighted-union heuristic, a sequence of m MakeSet, Union, and Find operations on n elements requires O ( m + nlog n ) time.

Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves.

Using Kyte-Doolittle analysis, the amino acid sequence of CD36 predicts a hydrophobic region near each end of the protein large enough to span cellular membranes.

Using the long exact sequence of pairs and the excision theorem, one can show that H < sub > n </ sub >( X, A ) is the same as the n-th reduced homology groups of the quotient space X / A.

Using recombinant DNA technology and synthetic DNA, literally any DNA sequence may be created and introduced into any of a very wide range of living organisms.

Using this, a complex operation can be accomplished in a single command line using a sequence of commands connected together in a pipeline.

Using a 375 residue query sequence a speed of 106 billion cell updates per second ( GCUPS ) was achieved on a dual Intel Xeon X5650 six-core processor system, which is over six times more rapid than software based on Farrar's ' striped ' approach.

Using the techniques of modern biotechnology, one or two genes ( Smartstax from Monsanto in collaboration with Dow AgroSciences will use 8, starting in 2010 ) may be transferred to a highly developed crop variety to impart a new character that would increase its yield.

Using the number 2 would give the symbol for singular " You "; adding the plural indicator ( a small cross at the top ) would produce the pronouns " We " and plural " You ".

Using this population density as a base for calculation, and allotting 10 % of food towards surplus for trade and assuming that city dwellers do no farming, he calculates that " in order to maintain a city with a population of 1, 000, and without taking the cost of transportation into account, an area of 100, 000 square kilometers would have been required.

Using the relative yardstick favoured in many European countries, 27 % of Chileans would be poor, according to Juan Carlos Feres of the ECLAC.

Using this essay as his guideline, Howard began plotting " The Tower of the Elephant ", a new Conan story that would be the first to truly integrate his new conception of the Hyborian world.

Using cathode ray tubes, Fred Williams would invent the Williams tube, which would be the first random access computer memory.

Using uniformitarianism, which states that one cannot make an appeal to any force or phenomenon which cannot presently be observed ( see catastrophism ), Darwin theorized that the evolutionary process must occur gradually, not in saltations, since saltations are not presently observed, and extreme deviations from the usual phenotypic variation would be more likely to be selected against.

Using just the basic notes on the instrument would mean playing in a specific mode for each position.

Using their E-REV ( Extended-Range Electric Vehicle ) powertrain technology, the Hummer plug-in hybrid would run up to 40 miles per day on its battery alone, then a small 4-cylinder internal combustion engine would start to generate more electricity.

Using gestures and objects, not asking questions in a language that the person might know, Pike would begin to analyze the language before the audience.

Using developments in behavioral science and technology, an interactive system ( Technology Assisted Reading Acquisition, TARA ) would enable young pre-literate children to accurately perceive and learn properties of written language by simply exposure to the written form.

Using a large silver bowl for an ashtray, he would chainsmoke during the show and blow smoke in his guests ' faces.

Using a system of destruction they would later employ in hunting predatory animals, the Chewa hunted down and butchered the Akafula.

Using vernacular language that would be understandable to the majority of China's populace, he put forward his socialist political views, calling for revolution against the government ; in one notable article, he proclaimed the need for a " Great Union of the Popular Masses ", but failed to put forward an expressly Marxist analysis of how that revolution should proceed.

Using first-hand remarks ( which would later be published in Philosophical Investigations, Culture and Value, and other works ), philosophers such as Peter Winch and Norman Malcolm developed what has come to be known as contemplative philosophy, a Wittgensteinian school of thought rooted in the " Swansea tradition " and which includes Wittgensteinians such as Rush Rhees, Peter Winch and D. Z. Phillips, among others.

Using the stadia of Diodorus Siculus, one obtains 42. 5 days for the time that would be spent in circumnavigating Britain.

* Using the finish flat one would most likely use a 1 / 2 " nap roller

* Using the finish eggshell one would most likely use a 3 / 8 " nap roller

* Using the finish satin or pearl one would most likely use a 3 / 8 " nap roller

* Using the finish semi-gloss or gloss one would most likely use a 3 / 16 " nap roller

Using significant with the layperson meaning " of practical significance " in such contexts would qualify as punning, such as the webcomic xkcd's double pun " statistically significant other ".