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 a counting argument one can show that there exist transcendental numbers which have bounded partial quotients and hence are not Liouville numbers.

Using backwards analysis, we can show that the expected number of trapezoids created for each insertion is bounded by a constant.

Using, where possible, the functional organs of the diseased surplus body may partially alleviate this concern.

Using the limited store of raw materials available in the planet, in ten years the Precursor factory built a ( barely ) functional ship, which could be piloted only by the now grown genius child, who alone could interact with the Precursor central computer.

Using the functional calculus for larger classes of functions, we can for example define rigorously the " square root " of the ( negative ) Laplacian operator − Δ or the exponential

Using these orthology mappings ( between C. elegans and B. malayi ) and by incorporating the extensive genomic and functional genomic data, including genome-wide RNAi screens, that already exist for C. elegans, we identify potentially essential genes in B. malayi.

" Using neuropsychological, structural, and functional brain imaging measures, we found that superior memory is not driven by exceptional intellectual ability or structural brain differences.

Using these techniques, researchers attempt to discover the structural and functional differences in the anatomy of the brain in individuals who suffer from flashbacks compared to those who do not.

Using these functional oogonia may help to create patient-specific stem cells lines using this method.

Using functional neuroimaging, it can be seen that sensory-specific cortices are activated by different inputs.

Using a branch of mathematics known as tuple calculus, he demonstrated that such a system could support all the operations of normal databases ( inserting, updating etc.

Using these two examples, we can make some useful observations that motivate the major ideas in lambda calculus.

Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:

Using differential calculus, we can determine the limit, or the value that Δy / Δx approaches as Δy and Δx get closer to zero ; it follows that this limit is the exact slope of the tangent.

Using the probability calculus of Bayes Theorem, Salmon concludes that it is very improbable that the universe was created by the type of intelligent being theists argue for.

Using geometry and calculus, some simple combinations of sources are easily solved ; others are not.

Using a method called " calculus of statement ," Lentz helps the team to mitigate the pressure harming the plant operators.

Using the fundamental theorem of calculus often requires finding an antiderivative.

Using this in the sum, one can evaluate the remaining integral using the calculus of residues and arrive at the desired generating function.

Using the limit notation of calculus, the volume may be expressed as:

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

Using differential calculus we can obtain conditions on x under which this holds.

Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion with the one-parameter group indexed by rapidity.

* Using process calculus to model biological systems ( stochastic-calculus, BioAmbients, Beta Binders, BioPEPA, Brane calculus ).

Using calculus, Gershun could compute the irradiance falling on points () on a surface.

Using typed lambda calculus to implement formal systems on a machine.

Using modern predicate calculus, we quickly discover that the statement is ambiguous.

Using a cheap brush, coat one side of the bottom with the resin and then apply the cloth.

Using kinship terms in political speeches increased audience agreement with the speaker in one study.

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 the Fibonacci sequence would keep the number of grains within any one field at minimum.

Using what became one of van Vogt's recurring themes, it told the story of a 9-year-old superman living in a world in which his kind are slain by Homo sapiens.

Using a core from the original, the Lemba priests constructed a new one.

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

Using these tools, one can write a more complex text editor, and a simple compiler for a higher-level language and so on, until one can have a graphical IDE and an extremely high-level programming language.

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

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 one-point compactification, one can also easily construct compact spaces which are not Hausdorff, by starting with a non-Hausdorff space.

Using more than one codec or encoding scheme successively can also degrade quality significantly.

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

Using himself as the sole subject in his experiment, he memorized lists of three letter nonsense syllable words — two consonants and one vowel in the middle.

Using RPN, one could get the result of the mathematical expression this way:

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 a modified Doom engine, Heretic was one of the first first-person games to feature inventory manipulation and the ability to look up and down.

Using the questions or processes of one domain on the subject matter of another domain will logically produce puzzles, paradoxes, and inconsistencies.

Using a defense in depth strategy, should one defensive measure fail there are other defensive measures in place that continue to provide protection.

Using the thoroughbred racing convention of one length equaling one-fifth of a second to calculate Sham ’ s time, he also finished in under two minutes.

Using a telescope, Rømer observed the motions of Jupiter and one of its moons, Io.

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 quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge --- that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.